Data-Driven $H_{\infty }$ Control of Networked Nonlinear Systems With External Disturbances and Random Communication Packet Losses

This paper investigates 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> control problem for partially unknown discrete-time nonlinear systems with external disturbances and Bernoulli model-based random packet losses in different communication channels. Based on the game theory, the computed control input and external disturbances are respectively considered as the minimizing and maximizing players for satisfying an <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> control performance index of the concerned networked nonlinear system. Then, a Bernoulli model-based stochastic zero-sum game is formulated and a Bernoulli model-based Hamilton-Jacobi-Isaacs equation is established. It is proven that the solutions to the developed equation results in a globally stochastically asymptotically stable closed-loop system when external disturbances are not taken into account and, if accounted, 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> control performance index is satisfied for all kinds of deterministic square-summable external disturbances. An adaptive/approximate dynamic programming and reinforcement leaning based data-driven value iteration algorithm is developed to approximately solve the associated equation and learn the ideal feedback policy for 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> control problem with guaranteed convergence. Finally, a simulation study on the proposed data-driven value iteration algorithm is provided to demonstrate its effectiveness.