Mixed H2/H∞ control for nonlinear parameter-varying systems

DOI编号  10.7641/CTA.2020.90808
2020,37(10):2231-2241

 作者 单位 E-mail 朱平芳 厦门大学 yiyizpf@126.com 周燕茹 厦门理工学院 曾建平 厦门大学 jpzeng@xmu.edu.cn

本文研究了一类非线性变参数系统的混合 H2/H∞ 保性能控制问题. 基于Lyapunov稳定性理论, 建立了状态反馈混合 H2/H∞ 保性能控制的可解性条件. 该条件是依赖于状态和参数的线性矩阵不等式, 显式地体现了系统的时变和非线性特性, 通过多项式平方和方法, 可以转化为优化问题. 特别地, 本文构造一种新颖的控制器和Lyapounov范数. 在此基础上, 研究了基于多项式平方技术的不确定非线性变参数系统混合 H2/H∞ 保性能控制问题. 最后, 通过倾转旋翼飞行器实例和数值仿真均验证本文方法的可行性和有效性.

This paper investigates the mixed H2/H∞ guaranteed cost control problem for a class of nonlinear parameter-varying systems. Based on Lyapunov stability theory, the solvable conditions of the mixedH2/H∞ guaranteed cost control for state feedback are established, those conditions are given in terms of state-and-parameter-dependent linear matrix inequalities, without hiding the time-varying nature or ignoring the nonlinearities, the above conditions can be transformed into a convex problem based on the polynomial sum of squares method. Specifically, a novel structure of state feedback controller and a new Lyapunov function are employed in this paper. And on this basis, this paper also studies the mixed H2/H∞ guaranteed cost control problem for a class of uncertain nonlinear parameter-varying systems based on the polynomial sum of squares method. Finally, the simulation results of a tilt rotor aircraft control and numerical example demonstrate the feasibility and effectiveness of the proposed method.