@conference {
	title = {Reachability Analysis for Linear Hybrid Set-Dynamics Driven by Random Convex Compact Sets},
	author = {Matei, Ion., Baras, John S.},
	year = {2017},
	month = {05/2017},
	abstract = {This paper studies linear set-dynamics driven by random convex compact sets (RCCSs), where the parameter matrix evolves according to an underlying Markovian random process taking values in a finite set. We derive dynamics of the expectations of the associated reach sets. We establish that such expectations evolve according to coupled deterministic set{\textendash}dynamics. We provide sufficient conditions for the convergence of the reach sets expectations. We also give conditions under which the reach sets remain asymptotically bounded with probability one. As an illustrative example, we apply our results to evaluate the expectations of the reach sets associated to the position of a quadrotor},
	address = {Seattle, WA},
	booktitle = {2017 American Control Conference},
	pages = {pp.  1765-1770},
	organization = {Sheraton Seattle Hotel}
}
@conference {
	title = {Distributed Nonlinear Programming Methods for Optimization Problems with Inequality Constraints},
	author = {Matei, Ion., Baras, John S.},
	year = {2015},
	month = {12/2015},
	abstract = {In this paper, we consider a distributed optimization problem, where a set of agents interacting and cooperating locally have as common goal the minimization of a function expressed as a sum of (possibly non-convex) differentiable functions. Each function in the sum is associated with an agent and each agent has assigned an inequality constraint, therefore generating an optimization problem with inequality constraints. In this paper, we present a distributed algorithm for solving such a problem~and give local convergence results. Our approach is based on solving (in a centralized manner) an equivalent augmented optimization problem with mixed constraints. The structure of this augmented problem ensures that the resulting algorithm is distributed. The main challenge in proving the convergence results comes from the fact that the local minimizers are no longer regular due to the distributed formulation. We present also an extension of this algorithm that solves a constrained optimization problem, where each agent has both equality and inequality constraints.},
	address = {Osaka, Japan},
	booktitle = {54th Conference on Control (CDC 2015)},
	pages = {pp. 2649-2654}
}
@conference {
	title = {An Extension of the Method of Multipliers for Distributed Nonlinear Programming},
	author = {Matei, Ion., Baras, John S., Nabi, Marzieh., Kurtoglu, Tolga.},
	year = {2014},
	month = {12/2014},
	abstract = {In this paper we consider a distributed optimization problem, where a set of agents interacting through a communication graph have as common goal the minimization of a function expressed as a sum of (possibly non-convex) differentiable functions. Each function in the sum corresponds to an agent and each agent has associated an equality constraint. In this paper we investigate how the standard method of multipliers can be used to solve an optimization problem with equality constraints in a distributed manner. The method of multipliers is applied to a lifted optimization problem whose solution embeds the solution of the original problem. We modify the standard convergence results to deal with the fact the (local) minimizers of the lifted optimization problem are not regular, as a results of the distributed formulation},
	booktitle = {53rd IEEE Conference on Decision and Control},
	pages = {pp. 6951-6956},
	organization = {Los Angeles, California, USA.}
}
@conference {
	title = {Distributed Algorithms for Optimization Problems with Equality Constraints},
	author = {Matei, Ion., Baras, John S.},
	year = {2013},
	month = {12/2013},
	abstract = {In this paper we introduce two discrete-time, distributed optimization algorithms executed by a set of agents whose interactions are subject to a communication graph. The algorithms can be applied to optimization problems where the cost function is expressed as a sum of functions, and where each function is associated to an agent. In addition, the agents can have equality constraints as well. The algorithms are not consensus-based and can be applied to non-convex optimization problems with equality constraints. We demonstrate that the first distributed algorithm results naturally from applying a first order method to solve the first order necessary conditions for a lifted optimization problem with equality constraints; the solution of our original problem is embedded in the solution of this lifted optimization problem. Using an augmented Lagrangian idea, we derive a second distributed algorithm that requires weaker conditions for local convergence compared to the first algorithm. For both algorithms we address the local convergence properties.},
	address = {Florence, Italy},
	booktitle = {52nd IEEE Conference on Decision and Control},
	pages = {pp. 2352-2357}
}
@conference {
	title = {Reachability Analysis for Linear Discrete Time Set{\textendash}Dynamics Driven by Random Convex Compact Sets},
	author = {Rakovic, Sasa V., Matei, Ion., Baras, John S.},
	year = {2012},
	month = {12/2012},
	abstract = {This paper studies linear set{\textendash}dynamics driven by random convex compact sets (RCCSs), and derives the set{\textendash}dynamics of the expectations of the associated reach sets as well as the dynamics of the corresponding covariance functions. It is established that the expectations of the reach sets evolve according to deterministic linear set{\textendash}dynamics while the associated dynamics of covariance functions evolves on the Banach space of continuous functions on the dual unit ball. The general framework is specialized to the case of Gaussian RCCSs, and it is shown that the Gaussian structure of random sets is preserved under linear set{\textendash}dynamics of random sets.},
	address = {Maui, Hawaii},
	booktitle = {51st IEEE Conference on Decision and Control},
	pages = {pp. 4751-4756}
}
@conference {
	title = {A Randomized Gossip Consensus Algorithm on Convex Metric Spaces},
	author = {Matei, Ion., Somarakis, Christoforos., Baras, John S.},
	year = {2012},
	month = {12/2012},
	abstract = {A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces. We study the convergence properties of the algorithm using stochastic differential equations theory. We show that the dynamics of the distances between the states of the agents can be upper bounded by the dynamics of a stochastic differential equation driven by Poisson counters. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces.},
	address = {Maui, Hawaii},
	booktitle = {51st IEEE Conference on Decision and Control,},
	pages = {pp. 7425-7430}
}
@conference {
	title = {A comparison between upper bounds on performance of two consensus-based distributed optimization algorithms},
	author = {Matei, Ion., Baras, John S.},
	year = {2012},
	month = {09/2012},
	abstract = {In this paper we address the problem of multi-agent optimization for convex functions expressible as sums of convex functions. Each agent has access to only one function in the sum and can use only local information to update its current estimate of the optimal solution. We consider two consensus-based iterative algorithms, based on a combination between a consensus step and a subgradient decent update. The main difference between the two algorithms is the order in which the consensus-step and the subgradient descent update are performed. We obtain upper bounds on performance metrics of the two algorithms. We show that updating first the current estimate in the direction of a subgradient and then executing the consensus step ensures a tighter upper bound compared with the case where the steps are executed in reversed order. In support of our analytical results, we give some numerical simulations of the algorithms as well.},
	address = {Santa Barbara, CA},
	booktitle = {3rd IFAC Workshop on Distributed Estimation and Control in Networked Systems(NecSys 2012), pp. 168-173, Santa Barbara, California},
	pages = {pp. 168-173}
}
@conference {
	title = {Flow Control in Time-Varying, Random Supply Chain Networks},
	author = {Matei, Ion., Gueye, Assane., Baras, John S.},
	year = {2012},
	month = {07/2012},
	abstract = {Todays supply chains are more and more complex. They depend on a network of independent, yet interconnected moving parts. They rely on critical infrastructures and experience a lot of time variability and randomness.Designing strategies that deal with such constantly changing supply chains is necessary in this increasingly globalized economy where supply chain disruptions have impacts that propagate not only locally but also globally.In this paper we propose a randomized flow control algorithm for a time varying, random supply chain network. We formulate a constrained stochastic optimization problem that maximizes the profit function in terms of the long-run,time-average rates of the flows in the supply chain. We show that our algorithm, which is based on queueing theory and stochastic analysis concepts, can get arbitrarily close to the solution of the aforementioned optimization problem.},
	address = {Melbourne, Australia},
	booktitle = {20th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2012)},
	pages = {pp. 1-4}
}
@conference {
	title = {Trust-Based Multi-Agent Filtering for Increased Smart Grid Security},
	author = {Matei, Ion., Baras, John S., Srinivasan, Vijay.},
	year = {2012},
	month = {07/2012},
	abstract = {We address the problem of state estimation of the power system for the Smart Grid. We assume that the monitoring of the electrical grid is done by a network of agents with both computing and communication capabilities. We propose a security mechanism aimed at protecting the state estimation process against false data injections originating from faulty equipment or cyber-attacks. Our approach is based on a multi-agent filtering scheme, where in addition to taking measurements, the agents are also computing local estimates based on their own measurements and on the estimates of the neighboring agents. We combine the multi-agent filtering scheme with a trust-based mechanism under which each agent associates a trust metric to each of its neighbors. These trust metrics are taken into account in the filtering scheme so that information transmitted from agents with low trust is disregarded. In addition, a mechanism for the trust metric update is also introduced, which ensures that agents that diverge considerably from their expected behavior have their trust values lowered.},
	address = {Barcelona, Spain},
	booktitle = {Proceedings of the 2012 Mediterranean Control Conference},
	pages = {pp. 716-721}
}
@conference {
	title = {Power Allocation Policy for Distributed Estimation in Wireless Networks},
	author = {Matei, Ion., Baras, John S.},
	year = {2011},
	month = {12/2011},
	abstract = {We consider a sensor network monitoring a stochastic process. The sensors exchange information over wireless communication channels affected by noise. The goal of the sensors is to compute accurate estimates of the state of the stochastic process under limited energy available for communications. We introduce a distributed algorithm which computes a power allocation scheme aimed at ensuring accurate state estimates and at saving communication energy. The distributed algorithm arise from solving an approximate convex optimization problem with constraints. We present how the power allocation scheme can be used for performing distributed estimation in the case where measurements are shared between sensors.},
	address = {Orlando, FL},
	booktitle = {50th IEEE Conference on Decision and Control Conference (CDC-ECC 2011)},
	pages = {pp. 7275-7280}
}
@conference {
	title = {Convergence results for the agreement problem on Markovian random topologies},
	author = {Matei, Ion., Baras, John S.},
	year = {2011},
	month = {08/2011},
	abstract = {We study the linear distributed asymptotic agreement(consensus) problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state, Markov process, each topology corresponding to a state of the process. We address both the cases where the dynamics of the agents is expressed in continuous and discrete time. We show that, if the consensus matrices are doubly stochastic, convergence to average consensus is achieved in the mean square and almost sure sense, if and only if the graph resulted from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems.},
	address = {Milano, Italy},
	booktitle = {2011 IFAC World Conference},
	pages = {pp. 8860-8865}
}
@conference {
	title = {The Geometry of a Probabilistic Consensus of Opinion Algorithm},
	author = {Matei, Ion., Baras, John S.},
	year = {2011},
	month = {06/2011},
	abstract = {We consider the problem of a group of agents whose objective is to asymptotically reach agreement of opinion. The agents exchange information subject to a communication topology modeled by a time-varying graph. The agents use a probabilistic algorithm under which at each time instant an agent updates its state by probabilistically choosing from its current state/opinion and the ones of its neighbors. We show that under some minimal assumptions on the communication topology (infinitely often connectivity and bounded intercommunication time between agents), the agents reach agreement with probability one. We show that this algorithm has the same geometric properties as the linear consensus algorithm in Rn. More specifically, we show that the probabilistic update scheme of an agent is equivalent to choosing a point from the (generalized) convex hull of its current state and the states of its neighbors; convex hull defined on a particular convex metric space where the states of the agents live and for which a detailed description is given.},
	address = {San Francisco, CA},
	booktitle = {2011 American Control Conference},
	pages = {pp.  2198-2205}
}
@conference {
	title = {Consensus-Based Linear Distributed Filtering},
	author = {Matei, Ion., Baras, John S.},
	year = {2010},
	month = {12/2010},
	abstract = {We address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) is asymptotically stable. Next, we provide a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations. We continue with presenting a connection between the consensus based distributed linear filter and the optimal linear filter of a Markovian jump linear system, appropriately defined. More specifically, we show that if the Markovian jump linear system is (mean square) detectable, then the stochastic process is detectable under the consensus-based distributed linear filtering scheme. We also show that the optimal gains of a linear filter for estimating the state of a Markovian jump linear system appropriately defined can be used to approximate the optimal gains of the consensus-based linear filter.},
	address = {Atlanta, Georgia},
	booktitle = {49th IEEE Conference on Decision and Control (CDC 2010)},
	pages = {pp.  7009- 7014}
}
@conference {
	title = {The asymptotic consensus problem on convex metric spaces},
	author = {Matei, Ion., Baras, John S.},
	year = {2010},
	month = {09/2010},
	abstract = {We consider the consensus problem of a group of dynamic agents whose communication network is modeled by a directed time-varying graph. In this paper we generalize the asymptotic consensus problem to convex metric spaces. A convex metric space is a metric space endowed with a convex structure. Using this convex structure we define convex sets and in particular the convex hull of a (finite) set. Under minimal connectivity assumptions, we show that if at each iteration an agent updates its state by choosing a point from a particular subset of the convex hull generated by the agent{\textquoteright}s current state and the states of its neighbors, then asymptotic agreement is achieved. In addition, we give bounds on the distance between the consensus point and the initial values of the agents.},
	address = {Annecy, France},
	booktitle = {2nd IFAC Workshop on Distributed Estimation and Control in Networked Systems (NecSys{\textquoteright}10)},
	pages = {pp. 287- 292}
}
@conference {
	title = {Performance Evaluation of Multi-Agent Distributed Collaborative Optimizationunder Random Communication Topologies},
	author = {Matei, Ion., Baras, John S.},
	year = {2010},
	month = {07/2010},
	abstract = {We investigate collaborative optimization in a multi-agent setting, when the agents execute in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, independent of other time instances. Specifically, we study the performance of the consensus-based multi-agent subgradient method, for the case of a constant stepsize, as measured by two metrics: rate of convergence and guaranteed region of convergence, evaluated via their expected values. Under a strong convexity type of assumption, we provide upper bounds on the performance metrics, which explicitly depend on the probability distribution of the random graph and on the agents{\textquoteright} estimates of the optimal solution. This provides a guide for tuning the parameters of the communication protocol such that good performance of the multi-agent subgradient method is ensured.},
	address = {Budapest, Hungary},
	booktitle = {Proceedings of the19th International Symposium on Mathematical Theory of Networks and Systems (MTNS 2010)},
	pages = {pp.1-8}
}
@conference {
	title = {A Trust Based Distributed Kalman Filtering Approach for Mode Estimation in Power Systems},
	author = {Jiang, Tao., Matei, Ion., Baras, John S.},
	year = {2010},
	month = {04/2010},
	abstract = {We consider distributed mode estimation in power systems. The measurements are observed by PMUs (Power Management Units). We introduce a novel model of trust, using weights on the graph links and nodes that represent the networked PMUs. We describe two algorithms that intergarte distributed Kalman filtering with these trust weights. We consider two interpretations of these trust weights as information accuracy and reliability. We show that by appropriate use of these weights from the distributed estimation algorithm avoids using information from untrusted PMUs. Simulation experiments further demonstrate the behavior of these algorithms.},
	address = {Stockholm, Sweden},
	booktitle = {First Workshop on Secure Control Systems (SCS) as part of CPSWeek 2010},
	pages = {pp. 1-6}
}
@conference {
	title = {A Composite Trust Model and its Application to Collaborative Distributed Information Fusion},
	author = {Matei, Ion., Baras, John S., Jiang, Tao.},
	year = {2009},
	month = {07/2009},
	abstract = {We consider distributed state estimation of~linear dynamic systems, observed by various sensors, as a problem in information fusion. We introduce a novel model of trust, using weights on the graph links and nodes that represent the sensor network. These weights can represent several interpretations of trustworthiness in sensor networks. We describe three algorithms that integrate distributed Kalman filtering with these trust weights. We consider two interpretations of these trust weights as information accuracy and reliability. We show that by appropriate use of these weights the distributed estimation algorithm avoids using information from untrusted sensors. Simulation experiments further demonstrate the behavior of these algorithms.},
	address = {Seattle, WA},
	booktitle = {12th International Conference on Information Fusion (Fusion 2009)},
	pages = {pp. 1950-1957}
}
@conference {
	title = {Consensus Problems with Directed Markovian Communication Patterns},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2009},
	month = {06/2009},
	abstract = {This paper is a continuation of our previous work and discusses the consensus problem for a network of dynamic agents with directed information flows and random switching topologies. The switching is determined by a Markov chain, each topology corresponding to a state of the Markov chain. We show that in order to achieve consensus almost surely and from any initial state, each union of graphs from the sets of graphs corresponding to the closed positive recurrent sets of states of the Markov chain must have a spanning tree. The analysis relies on tools from matrix theory, Markovian jump linear systems theory and random process theory. The distinctive feature of this work is addressing the consensus problem with {\textquotedblleft}Markovian switching{\textquotedblright} topologies.},
	address = {St. Louis, Missouri},
	booktitle = {2009 American Automatic Control Conference},
	pages = {pp.1298-1303}
}
@conference {
	title = {Almost Sure Convergence to Consensus in Markovian Random Graphs},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {12/2008},
	abstract = {In this paper, we discuss the consensus problem for a network of dynamic agents with undirected information flow and random switching topologies. The switching is determined by a Markov chain, each topology corresponding to a state of the Markov chain. We show that in order to achieve consensus almost surely and from any initial state the sets of graphs corresponding to the closed positive recurrent sets of the Markov chain must be jointly connected. The analysis relies on tools from matrix theory, Markovian jump linear systems theory and random processes theory. The distinctive feature of this work is addressing the consensus problem with {\textquotedblleft}Markovian switching{\textquotedblright} topologies.},
	address = {Cancun, Mexico},
	booktitle = {47th IEEE Conference on Decision and Control},
	pages = {pp. 3535-3540}
}
@conference {
	title = {Optimal Linear Quadratic Regulator for Markovian Jump Linear Systems, in the Presence of One Stop-Time Step Delayed Mode Observations},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {07/2008},
	abstract = {In this paper, we provide the solution to the optimal Linear Quadratic Regulator (LQR) paradigm for Markovian Jump linear Systems, when the continuous state is available at the controller instantaneously, but the mode is available only after a delay of one-time step. This paper is the first to investigate the LQR paradigm in the presence of such mismatch between the delay in observing the mode and the continuous state at the controller. We show that the optimal LQR policy is a time-varying matrix gain multiplied by the continuous component of the state, where the gain is indexed in time by the one-step delayed mode. The solution to the LQR is expressed as a collection of coupled Riccati iterations and equations, for the finite and the infinite horizon cases respectively. In the infinite horizon case, the solution of the coupled Riccati equations or a certificate of infeasibility is obtained by solving a set of linear matrix inequalities. We also explain the difficulties of solving the LQR problem when the mode is observed by the controller with a delay of more than one step. We show that, with delays of more than one time-step, the optimal control will be a time-varying nonlinear function of the continuous state and of the control input, without presenting an exact solution.},
	address = {Seoul, Korea},
	booktitle = {17th IFAC World Congress},
	pages = {pp. 8056-8061}
}
@conference {
	title = {Optimal State Estimation for Discrete-Time Markovian Jump Linear Systems, in the Presence of Delayed Mode Observations},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {06/2008},
	abstract = {In this paper, we investigate an optimal state estimation problem for Markovian Jump Linear Systems. We consider that the state has two components: the first component of the state is finite-valued and is denoted as mode, while the second (continuous) component is in a finite dimensional Euclidean space. The continuous state is driven by a deterministic control input and a zero mean, white and Gaussian process noise. The observable output has two components: the first is the mode delayed by a fixed amount and the second is a linear combination of the continuous state observed in zero mean white Gaussian noise. Our paradigm is to design optimal estimators for the current state, given the current output observation. We provide a solution to this paradigm by giving a recursive estimator of the continuous state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditional on the observed output. We show that the optimal estimator is nonlinear on the observed output and on the control input. In addition, we show that the computation complexity of our recursive schemes is an exponential function of the mode observation delay.},
	address = {Seattle, Washington},
	booktitle = {2008 Automatic Control Conference},
	pages = {pp.  3560-3565}
}
@conference {
	title = {Optimal State Estimation for Discrete-Time Markovian Jump Linear Systems, in the Presence of Delayed Output Observations},
	author = {Matei, Ion., Martins, Nuno C., Baras, John S.},
	year = {2008},
	month = {05/2008},
	abstract = {In this paper, we investigate the design of optimal state estimators for Markovian Jump Linear Systems. We consider that the state has two components: the first component is finite-valued and is denoted as mode, while the second (continuous) component is in a finite dimensional Euclidean space. The continuous state is driven by a zero mean, white and Gaussian process noise. The observation output has two components: the first is the mode and the second is a linear combination of the continuous state observed and zero mean white Gaussian noise. Both output components are affected by delays, not necessarily equal. Our paradigm is to design optimal estimators for the current state, given the current output observation. We provide a solution to this paradigm by giving a recursive estimator for the continuous state, in the minimum mean square sense, and a finitely parameterized recursive scheme for computing the probability mass function of the current mode conditioned on the observed output. We show that when the mode is observed with a greater delay than the continuous output component, the optimal estimator nonlinear in the observed outputs.},
	address = {Porto, Portugal},
	booktitle = {IEEE Information Theory Workshop (ITW 2008)},
	pages = {pp. 237-242}
}
@article {
	title = {A Generalized Gossip Algorithm on Convex Metric Spaces},
	author = {Matei, Ion., Somarakis, Christoforos., Baras, John S.},
	year = {2015},
	month = {05/2015},
	abstract = {A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper, we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces, where the communication between agents is based on a set of Poisson counters. We study the convergence properties of the algorithm using stochastic differential equations theory. In particular, we show that the distances between the states of the agents converge to zero with probability one and in the rth mean sense. In the special case of complete connectivity and uniform Poisson counters, we give upper bounds on the dynamics of the first and second moments of the distances between the states of the agents. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations. th~mean sense. In the special case of complete connectivity and uniform Poisson counters, we give upper bounds on the dynamics of the first and second moments of the distances between the states of the agents. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations.},
	pages = {pp. 1175 - 1187},
	volume = {Vol. 60},
	number = {No. 5},
	journal = {IEEE Transactions on Automatic Control.}
}
@article {
	title = {The Asymptotic Consensus Problem on Convex Metric Spaces},
	author = {Matei, Ion., Baras, John S.},
	year = {2015},
	month = {04/2015},
	abstract = {A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. The agents exchange information according to a communication network modeled as a directed time-varying graph and evolve in a convex metric space; a metric space endowed with a convex structure. In this paper, we generalize the asymptotic consensus problem to convex metric spaces. Under weak connectivity assumptions, we show that if at each iteration an agent updates its state by choosing a point from a particular subset of the generalized convex hull generated by the agent{\textquoteright}s current state and the states of its neighbors, then agreement is achieved asymptotically. In addition, we present several examples of convex metric spaces and their corresponding agreement algorithms.},
	pages = {pp. 907-921},
	volume = {Vol. 60},
	number = {No. 4},
	journal = {IEEE Transactions on Automatic Control.}
}
@article {
	title = {Flow Control in Time-Varying, Random Supply Chains},
	author = {Matei, Ion., Gueye, Assane., Baras, John S.},
	year = {2015},
	month = {01/2015},
	abstract = {This paper focuses on the logistics aspect of supply chain management. It proposes a randomized flow management algorithm for a time-varying, random, supply chain network. A constrained stochastic optimization problem that maximizes the profit function in terms of the long-run, time-average of the flows in the supply chain is formulated. The algorithm is distributed and based on queueing theory and stochastic Lyapunov analysis concepts. The long-run, time averages of the flows generated by the algorithm can get arbitrarily close to the solution of the aforementioned optimization problem. In support of the theoretical results, numerical simulations are also presented.},
	pages = {pp. 311-330},
	volume = {Vol. 77},
	journal = {Transportation Research Part E: Logistics and Transportation Review}
}
@techreport {
	title = {Nonlinear Programming Methods for Distributed Optimization},
	author = {Matei, Ion., Baras, John S.},
	year = {2015},
	month = {01/2015},
	abstract = {In this paper we investigate how standard nonlinear programming algorithms can be used to solve constrained optimization problems in a distributed manner. The optimization setup consists of a set of agents interacting through a communication graph that have as common goal the minimization of a function expressed as a sum of (possibly non-convex) differentiable functions. Each function in the sum corresponds to an agent and each agent has associated an equality constraint. By re-casting the distributed optimization problem into an equivalent, augmented centralized problem, we show that distributed algorithms result naturally from applying standard nonlinear programming techniques. Due to the distributed formulation, the standard assumptions and convergence results no longer hold. We emphasize what changes are necessary for convergence to still be achieved for three algorithms: two algorithms based on Lagrangian methods, and an algorithm based the method of multipliers. The changes in the convergence results are necessary mainly due to the fact that the (local) minimizers of the lifted optimization problem are not regular, as a results of the distributed formulation. Unlike the standard algorithm based on the method of multipliers, for the distributed version we cannot show that the theoretical superlinear convergence rate can be achieved.}
}
@techreport {
	title = {A non-consensus based distributed optimization algorithm},
	author = {Matei, Ion., Baras, John S.},
	year = {2014},
	month = {01/2014},
	abstract = {In this paper we introduce a discrete-time, distributed optimization algorithm executed by a set of agents whose interactions are subject to a communication graph. The algorithm can be applied to optimization costs that are expressed as sums of functions, where each function is associated to an agent. The algorithm can be applied to continuously differentiable cost functions, it is not consensus-based and is derived naturally by solving the first order necessary conditions of a lifted optimization problem with equality constraints. We show that, provided the agents{\textquoteright} initial values are sufficiently closed to a local minimizer and the step-size is sufficiently small, each agent converges to the local minimizer at a linear rate. In addition, we revisit two popular consensus-based distributed optimization algorithms and give sufficient conditions so that there use is extended to non-convex functions as well. We take a closer look at their rate of convergence and also show that unlike our algorithm, for a constant step-size, the consensus-based algorithms do not converge to a local minimizer even though the agents start close enough to the local minimizer}
}
@techreport {
	title = {A non-heuristic distributed algorithm for non-convex constrained optimization},
	author = {Matei, Ion., Baras, John S.},
	year = {2013},
	month = {12/2013},
	abstract = {In this paper we introduce a discrete-time, distributed optimization algorithm executed by a set of agents whose interactions are subject to a communication graph. The algorithm can be applied to optimization problems where the cost function is expressed as a sum of functions, and where each function is associated to an agent. In addition, the agents can have equality constraints as well. The algorithm can be applied to non-convex optimization problems with equality constraints, it is not consensus-based and it is not an heuristic. We demonstrate that the distributed algorithm results naturally from applying a first order method to solve the first order necessary conditions of an augmented optimization problem with equality constraints; optimization problem whose solution embeds the solution of our original problem. We show that, provided the agents{\textquoteright} initial values are sufficiently close to a local minimum, and the step-size is sufficiently small, under standard conditions on the cost and constraint functions, each agent converges to the local minimum at a linear rate.}
}
@techreport {
	title = {Distributed Algorithms for Optimization Problems with Equality Constraints},
	author = {Matei, Ion., Baras, John S.},
	year = {2013},
	month = {09/2013},
	abstract = {In this paper we introduce two discrete-time, distributed optimization algorithms executed by a set of agents whose interactions are subject to a communication graph. The algorithms can be applied to optimization problems where the cost function is expressed as a sum of functions, and where each function is associated to an agent. In addition, the agents can have equality constraints as well. The algorithms are not consensus-based and can be applied to non-convex optimization problems with equality constraints. We demonstrate that the first distributed algorithm results naturally from applying a first order method to solve the first order necessary conditions for a lifted optimization problem with equality constraints; the solution of our original problem is embedded in the solution of this lifted optimization problem. We show that, provided the agents{\textquoteright} initial values are sufficiently close to a local minimizer, and the step-size is sufficiently small, under standard conditions on the cost and constraint functions, each agent converges to the local minimizer at a linear rate. Next, we use an augmented Lagrangian idea to derive a second distributed algorithm whose local convergence requires weaker sufficient conditions than in the case of the first algorithm.}
}
@article {
	title = {Convergence Results for the Linear Consensus Problem under Markovian Random Graphs},
	author = {Matei, Ion., Baras, John S., Somarakis, Christoforos.},
	year = {2013},
	month = {01/2013},
	abstract = {This paper discusses the linear asymptotic consensus problem for a network of dynamic agents whose communication network is modeled by a randomly switching graph. The switching is determined by a finite state Markov process, each topology corresponding to a state of the process. We address the cases where the dynamics of the agents is expressed both in continuous time and in discrete time. We show that, if the consensus matrices are doubly stochastic, average consensus is achieved in the mean square sense and the almost sure sense if and only if the graph resulting from the union of graphs corresponding to the states of the Markov process is strongly connected. The aim of this paper is to show how techniques from the theory of Markovian jump linear systems, in conjunction with results inspired by matrix and graph theory, can be used to prove convergence results for stochastic consensus problems.},
	pages = {pp. 1574-1591},
	volume = {Vol.  51},
	number = {No. 2},
	journal = {SIAM Journal on Control and Optimization}
}
@article {
	title = {A Linear Distributed Filter Inspired by the Markovian Jump Linear System Filtering Problem},
	author = {Matei, Ion., Baras, John S.},
	year = {2012},
	month = {08/2012},
	abstract = {In this paper, we introduce a consensus-based distributed filter, executed by a sensor network, inspired by the Markovian jump linear system filtering theory. We show that the optimal filtering gains of the Markovian jump linear system can be used as an approximate solution of the optimal distributed filtering problem. This parallel allows us to interpret each filtering gain corresponding to a mode of operation of the Markovian jump linear system as a filtering gain corresponding to a sensor in the network. The approximate solution can be implemented distributively and guarantees a quantifiable level of performance.},
	pages = {Pages 1924-1928},
	volume = {Volume 48},
	number = {Issue 8},
	journal = {Automatica}
}
@article {
	title = {Consensus-Based Linear Distributed Filtering},
	author = {Matei, Ion., Baras, John S.},
	year = {2012},
	month = {08/2012},
	abstract = {We address the consensus-based distributed linear filtering problem, where a discrete time, linear stochastic process is observed by a network of sensors. We assume that the consensus weights are known and we first provide sufficient conditions under which the stochastic process is detectable, i.e. for a specific choice of consensus weights there exists a set of filtering gains such that the dynamics of the estimation errors (without noise) is asymptotically stable. Next, we develop a distributed, sub-optimal filtering scheme based on minimizing an upper bound on a quadratic filtering cost. In the stationary case, we provide sufficient conditions under which this scheme converges; conditions expressed in terms of the convergence properties of a set of coupled Riccati equations.},
	pages = {Pages 1776-1782},
	volume = {Volume 48},
	number = {Issue 8},
	journal = {Automatica}
}
@techreport {
	title = {Flow Control in Time-Varying, Random Supply Chains},
	author = {Matei, Ion., Baras, John S.},
	year = {2012},
	month = {05/2012},
	abstract = {Today{\textquoteright}s supply chains are more and more complex. They depend on a network of independent, yet~interconnected moving parts. They rely on critical infrastructures and experience a lot of time variability~and randomness. Designing strategies that deal with such constantly changing supply chains is necessary~in this increasingly globalized economy where supply chain disruptions have impacts that propagate not~only locally but also globally. In this paper we propose a randomized flow control algorithm for a time~varying, random supply chain network. We formulate a constrained stochastic optimization problem that~maximizes the profit function in terms of the long-run, time-average rates of the flows in the supply~chain. We show that our algorithm, which is based on queueing theory and stochastic analysis concepts,~can get arbitrarily close to the solution of the aforementioned optimization problem. In addition, we~describe how the flow control algorithm can be extended to a multiple firms supply chain setup and~present numerical simulations of our algorithm for different supply chain topologies.}
}
@techreport {
	title = {A performance comparison between two consensus-based distributed optimization algorithms},
	author = {Matei, Ion., Baras, John S.},
	year = {2012},
	month = {05/2012},
	abstract = {In this paper we address the problem of multi-agent optimization for convex functions expressible as sums of convex functions. Each agent has access to only one function in the sum and can use only local information to update its current estimate of the optimal solution. We consider two consensus-based iterative algorithms, based on a combination between a consensus step and a subgradient decent update. The main difference between the two algorithms is the order in which the consensus-step and the subgradient descent update are performed. We show that updating first the current estimate in the direction of a subgradient and then executing the consensus step ensures better performance than executing the steps in reversed order. In support of our analytical results, we give some numerical simulations of the algorithms as well.}
}
@techreport {
	title = {A randomized gossip consensus algorithm on convex metric spaces},
	author = {Matei, Ion., Somarakis, Christoforos., Baras, John S.},
	year = {2012},
	month = {02/2012},
	abstract = {A consensus problem consists of a group of dynamic agents who seek to agree upon certain quantities of interest. This problem can be generalized in the context of convex metric spaces that extend the standard notion of convexity. In this paper we introduce and analyze a randomized gossip algorithm for solving the generalized consensus problem on convex metric spaces. We study the convergence properties of the algorithm using stochastic differential equations theory. We show that the dynamics of the distances between the states of the agents can be upper bounded by the dynamics of a stochastic differential equation driven by Poisson counters. In addition, we introduce instances of the generalized consensus algorithm for several examples of convex metric spaces together with numerical simulations.}
}
@article {
	title = {Optimal State Estimation for Discrete-Time Markovian Jump Linear Systems, in the Presence of Delayed Output Observations},
	author = {Matei, Ion., Baras, John S.},
	year = {2011},
	month = {09/2011},
	abstract = {We investigate the design of optimal state estimators for Markovian Jump Linear Systems. We consider that the output observations and the mode observations are affected by delays not necessarily identical. Our objective is to design optimal estimators for the current state, given the current observations.We provide a solution to this paradigm by giving an optimal recursive estimator for the state, the probability in the minimum mean square sense, and a finitely parameterized recursive scheme the probability computing mass function of the current mode conditioned on the observed output. We also show that ifthe output delay is less then the one in observing the mode, then the optimal state estimation becomes nonlinear in the output observations.},
	pages = {pp. 2235 - 2240},
	volume = {Volume 56.},
	number = {Issue 9},
	journal = {IEEE Transactions on Automatic Control.}
}
@article {
	title = {Performance Evaluation of the Consensus-based Distributed Subgradient Method Under Random Communication Topologies},
	author = {Matei, Ion., Baras, John S.},
	year = {2011},
	month = {08/2011},
	abstract = {We investigate the collaborative optimization of an objective function expressed as a sum of local convex functions, when the agents make decisions in a distributed manner using local information, while the communication topology used to exchange messages and information is modeled by a graph-valued random process, assumed independent and identically distributed. Specifically, we study the performance of the consensus-based multi-agent distributed subgradient method and show how it depends on the probability distribution of the random graph. For the case of a constant stepsize, we first give an upper bound on the difference between the objective function, evaluated at the agents{\textquoteright} estimates of the optimal decision vector, and the optimal value. Second, for a particular class of convex functions, we give an upper bound on the distances between the agents{\textquoteright} estimates of the optimal decision vector and the minimizer. In addition, we provide the rate of convergence to zero of the time varying component of the aforementioned upper bound. The addressed metrics are evaluated via their expected values. As an application, we show how the distributed optimization algorithm can be used to perform collaborative system identification and provide numerical experiments under the randomized and broadcast gossip protocols.},
	pages = {pp. 754-771},
	volume = {Volume 5.},
	number = {No. 4},
	journal = {IEEE Journal of Selected topics in Signal Processing}
}
@techreport {
	title = {The asymptotic consensus problem on convex metric spaces},
	author = {Matei, Ion., Baras, John S.},
	year = {2010},
	month = {04/2010},
	abstract = {We consider the consensus problem of a group of dynamic agents whose communication network is modeled by a directed time-varying graph. In this paper we generalize the asymptotic consensus problem to convex metric spaces. A convex metric space is a metric space on which we define a convex structure. Using this convex structure we define convex sets and in particular the convex hull of a (finite) set. Under minimal connectivity assumptions, we show that if at each iteration an agent updates its state by choosing a point from a particular subset of the convex hull generated by the agent{\textquoteright}s current state and the states of his/her neighbors, then the asymptotic agreement is achieved. In addition, we give bounds on the distance between the consensus point(s) and the initial values of the agents. As application example, we use this framework to introduce an iterative algorithm for reaching consensus of opinion. In this example, the agents take values in the space of discrete random variable on which we define an appropriate metric and convex structure. For this particular convex metric space we provide a more detail analysis of the convex hull generated by a finite set points. In addition we give some numerical simulations of the consensus of opinion algorithm.}
}
@techreport {
	title = {Distributed subgradient method under random communication topology - the effect of the probability distribution of the random graph on the performance metrics},
	author = {Matei, Ion., Baras, John S.},
	year = {2009},
	month = {09/2009},
	abstract = {In this note we study the performance metrics (rate of convergence and guaranteed region of convergence) of a multi-agent subgradient method for optimizing a sum of convex functions. We assume that the agents exchange information according to a communication topology modeled as a random graph, independent of other time instances. Under a strong convexity type of assumption, we express the performance metrics directly as functions of the estimates of the optimal decision vector. We emphasize how the probability distribution of the random graph affects the upper bounds on the performance metrics. This provide a guide for tuning the parameters of the communication protocol such that good performance of the multi-agent subgradient method is ensured. We perform the tuning of the protocol parameters for two communication scenarios. In the first scenario, we assume a randomized scheme for link activation with no-error transmissions while in the second scenario we use a pre-established order of transmissions but we consider the interference effect. Both these scenarios are applied on a small world type of topology.}
}
