Event-Based Distributed Finite-Horizon $H_\infty$ Consensus Control for Constrained Nonlinear Multiagent Systems

Abstract

This article presents an event-triggered adaptive dynamic programming (ETADP) algorithm to address the distributed finite-horizon <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> consensus problem of nonlinear homogeneous multiagent systems subject to asymmetric input constraints and exogenous disturbances. By considering the exogenous disturbances as control inputs, the original control problem can be equivalently transformed into a multiplayer zero-sum differentiable game. Then, in contrast with the traditional dual networks framework to implement ETADP algorithm, a single critic network is introduced to attain approximate solutions of the time-varying event-triggered Hamilton–Jacobi–Isaacs equation, which circumvents the potential approximation error resulted from actor network. Note that the critic weight vector is tuned by using experience replay technique and normalized gradient descent method together, and in this situation, the persistence of excitation condition is removed. It is strictly proven that the local consensus error and the critic weight error are uniformly ultimately bounded, and the minimal intersample time is verified to be lower bounded. Simulation results verify the validity of the developed ETADP algorithm.