Event-Based Near Optimal Sampling and Tracking Control of Nonlinear Systems

Abstract

This paper presents a near optimal event-based tracking control scheme for nonlinear continuous time systems. In order to simultaneously design the event-based sampling intervals and the control policy, the problem of designing the event-triggering mechanism and the feedback controller is posed as a min-max optimization problem. Using the resultant saddle point solution, the feedback control policy and the threshold for the event-based sampling condition is designed. The proposed control scheme is realized by approximating the solution to the associated Hamilton-Jacobi-Issac (HJI) equation using event-based neural networks (NN). The NN weights are updated using an impulsive update scheme. Extension of Lyapunov stability analysis for the impulsive hybrid dynamical system is utilized to prove the local ultimate boundedness of the tracking and NN weight estimation errors. Furthermore, Zeno free behavior of the event-triggering mechanism is guaranteed along with the numerical simulation to corroborate the analytical design.