一类多项式非线性系统鲁棒H∞控制

摘要

By employing the sum of squares (SOS) technique, we investigate the robust H-infinity state-feedback controller design for a class of uncertain affine nonlinear systems with polynomial vector fields. The advantage of this approach lies in its avoidance of difficulties in solving the intricate Hamilton Jacobi inequality (HJI) and constructing Lyapunov functions. By using the SOS technique, both the robust stability analysis and the controller design problems are transformed into solving the matrix inequalities with parameters of the Lyapunov function as decision variables. Besides, the robust H-infinity controller which guarantees the local stability of the closed-loop system is presented by using the SOS programming and S-procedure simultaneously. Finally, the simulation results of the nonlinear mass-spring-damper system show the effectiveness of the proposed approach.%针对一类具有多项式向量场的仿射型不确定非线性系统,给出一种基于多项式平方和(sum of squares,SOS)技术的鲁棒H∞状态反馈控制器设计方法.该方法的优点在于控制器的设计避开了直接求解复杂的哈密尔顿-雅可比不等式(Hamilton Jacobi inequality,HJI)和构造Lyapunov函数带来的困难.将鲁棒稳定性分析和控制器设计问题转化为求解以Lyapunov函数为参数的矩阵不等式,该类不等式可利用SOS技术直接求解.此外,在前文基础上研究了基于SOS规划理论与S-procedure技术的局部稳定鲁棒H∞控制器设计方法.最后以非线性质量弹簧阻尼系统作为仿真算例验证该方法的有效性.