基于SOS技术的多项式非线性系统鲁棒控制综合

针对一类具有多项式向量场的仿射不确定非线性系统,借助多项式平方和(Sum of Squares, SOS)技术,研究其状态反馈鲁棒控制综合问题。给出了该类系统鲁棒镇定控制、以及带有保性能和H性能目标的优化控制问题的充分可解性条件。所给出的条件均被描述为由状态依赖线性矩阵不等式(LMI)组成的SOS规划,可由SOS技术直接求解。此外,通过引入附加变量给出了描述多项式矩阵的逆以及有理式矩阵的方法。最后,通过数值仿真验证了方法的有效性

Robust Control Synthesis of Polynomial Nonlinear Systems Using Sum of Squares Technique

In this paper, sum of squares (SOS) technique is used to analyze the robust state feedback synthesis problem for a class of uncertain affine nonlinear systems with polynomial vector fields. Sufficient conditions are given to obtain the solutions to the above control problem either without or with guaranteed cost or H_∞ performance objectives. Moreover, such solvable conditions can be formulated as SOS programming problems in terms of state dependent linear matrix inequalities (LMIs) which can be dealt with by the SOS technique directly. Besides, an idea is provided to describe the inverse of polynomial or even rational matrices by introducing some extra polynomials. A numerical example is presented to illustrate the effectiveness of the approach.