Model-free event-triggered control algorithm for continuous-time linear systems with optimal performance

This paper proposes a new model-free event-triggered optimal control algorithm for continuous-time linear systems. The problem is formulated as an infinite-horizon optimal adaptive learning problem, and we are able to simultaneously address the issue of designing a control and a triggering mechanism with guaranteed optimal performance by design. In order to provide a model-free solution, we adopt a Q-learning framework with a critic network to approximate the optimal cost and a zero-order hold actor network to approximate the optimal control. Since we have dynamics that evolve in continuous and discrete-time, we write the closed-loop system as an impulsive model and prove asymptotic stability of its equilibrium. Numerical simulation of an unknown unstable system is presented to show the efficacy of the proposed approach.