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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 policy for a nondeterministic 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 paper is to synthesize an optimal-event generator and controller pair such that the state trajectory of the event-triggered system mimics that 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 event generator 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 event-triggered controller and event generator remain unchanged when extended to an infinite horizon.