Optimal Event Triggered Control of Nondeterministic Linear Systems

We consider an event-triggered controller synthesis problem to replace the continuous feedback policy with an intermittent feedback one for a non-deterministic linear system. An event-triggered framework communicates the measurement to the controller only at certain discrete time instances which are generated by an event-generator. The objective of this work is to synthesize an optimal event generator and controller such that the trajectory of the states of the event-triggered system mimics the trajectory of the state of the feedback system with arbitrary precision. The optimality is in the sense that the least number of state measurements are sent to the controller in order to compute the control signal. The results of this paper show that such an optimal event-triggered controller retains the linear structure when the continuous feedback controller is linear; and the optimal event-generator follows a threshold based policy, where the eventgenerator decides to send the state measurement to the controller every time a certain signal exceeds that threshold. Finally, the similar framework was extended for a controller synthesis of infinite horizon. The structural properties of the optimal eventtriggered controller and event-generator remain unchanged when extended to an infinite horizon.