Approximate Dynamic Programming for Event-Driven H∞ Constrained Control

Abstract

We study the dynamic event-driven <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> constrained control problem through approximate dynamic programming (ADP). Differing from the existing literature considering systems with either symmetric constraints or asymmetric constraints, we consider the two different constraints simultaneously. Initially, by constructing a generalized nonquadratic value function, we transform the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty}$</tex-math> </inline-formula> constrained control problem into an unconstrained two-player zero-sum game. Then, we present an event-driven Hamilton–Jacobi–Isaacs equation (ED-HJIE) corresponding to the zero-sum game for lowering down the computational load. To solve the ED-HJIE, we propose a dynamic triggering mechanism together with a sole critic neural network (CNN) being built under the ADP framework. The CNN’s weights are tuned via the gradient descent approach. After that, we prove uniform ultimate boundedness of the closed-loop system and the CNN’s weight estimation error via Lyapunov’s method. Finally, we separately use an F16 aircraft plant and an inverted pendulum system to validate the present theoretical claims.