非线性解耦问题的解及其唯一性

一、引言控制系统的反馈解耦问题已有很多研究,对于非线性系统,最先开始的研究是文1]和2].它们推广了单对单解耦问题著名的 Falb-Wolovich 条件.具有开拓性的研究是文3]和4].在获奖文4]中,Isidori 等首次给出了非线性解耦问题的几何刻划.之后有更多、更进一步的研究.关于解耦问题的历史和发展,请读者参阅文献8]和9].近年来,解耦问题的研究兴趣还包括有动态反馈和奇异反馈设计.

ON THE SOLUTION AND ITS UNIQUENESS OF NONLINEAR DECOUPLING PROBLEMS

Through a newly proposed algorithm to compute the maximal controlled invariant distri-bution,this paper is devoted to a study of the solution and its uniqueness of the disturbancedecoupling and general input-output block decoupling problems of nonlinear systems.Forboth problems,simple algebraic criteria are derived,which are generalizations of the well-known Falb-Wolovich condition for the 1-1 decoupling problem.Necessary and sufficient con-ditions are also found for the uniqueness of the controllability distribution(s) that can arise assolutions to the nonlinear decoupling problems.