<i>H<sub>∞</sub> </i> Codesign for Uncertain Nonlinear Control Systems Based on Policy Iteration Method
Quan‐Yong Fan, Dongsheng Wang, Bin Xu
Abstract
In this article, the problem of <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> codesign for nonlinear control systems with unmatched uncertainties and adjustable parameters is investigated. The main purpose is to solve the adjustable parameters and <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> controller simultaneously so that better robust control performance can be achieved. By introducing a bounded function and defining a special cost function, the problem of solving the Hamilton–Jacobi–Isaacs equation is transformed into an optimization problem with nonlinear inequality constraints. Based on the sum of squares technique, a novel policy iteration algorithm is proposed to solve the problem of 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> codesign. Moreover, one modified algorithm for optimizing the robust performance index is given. The convergence and the performance improvement of new iteration policy algorithms are proved. Simulation results are presented to demonstrate the effectiveness of the proposed algorithms.