Finite-time Event-triggered Control for a Class of Nonlinear Systems

This paper considers an approximate solution of the event-triggered Hamilton-Jacobi-Bellman (ET-HJB) equation to derive a finite-time suboptimal event-triggered control law for a class of nonlinear systems. To reduce the communication and computation overhead, the control law is computed and actuated after violating a predefined state-dependent event triggering condition. To obtain the controller gain, the ET-HJB equation is approximated as a state-dependent differential Riccati equation (SDRE). After converting the ET-HJB into an SDRE, a frozen time concept is used to eliminate the issues related to state dependency in the system and input matrices between two consecutive events. This helps reframe the SDRE into a simple differential Riccati equation (DRE), where the state-dependent system and input matrices remain fixed until the next event occurs. Using the solution of a differential Lyapunov equation, the solution of the DRE is computed forward in time. The designed event-triggered control law is readily amenable to an online implementation, and also it ensures the input-to-state stability of closed-loop systems. Simulation results are reported to prove the efficacy of the proposed control approach.