H∞ Codesign for Uncertain Nonlinear Control Systems Based on Policy Iteration Method
研究如何同时求解不确定非线性控制系统的可调参数和H∞控制器，通过引入有界函数和特殊代价函数将问题转化为带约束优化，并基于平方和技术提出新的策略迭代算法，仿真验证了有效性。
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.