Optimization of sampling intervals for tracking control of nonlinear systems: A game theoretic approach

Abstract

This paper presents a near optimal adaptive event-based sampling scheme for tracking control of an affine nonlinear continuous-time system. A zero-sum game approach is proposed by introducing a novel performance index. The optimal value function, i.e., the solution to the associatedHamilton–Jacobi–Issac (HJI) equation is approximated using a functional link neural network (FLNN) with event-based aperiodic state feedback information as inputs. The saddle point approximated optimal solution is employed to design the near optimal event-based control policy and the sampling condition. An impulsive weight update scheme is designed to guarantee local ultimate boundedness of the closed-loop parameters, which is analyzed via extension of Lyapunov stability theory for the impulsive hybrid dynamical systems. Zeno-freeness of the event-sampling scheme is enforced and its effect on stability is analyzed. Finally, numerical simulation results are included to corroborate the analytical design, which shows a 48.82% reduction of feedback communication and computational load.