Structural analysis of nonlinear control systems using singular value decomposition: Part I - Approach

Structural information of a system/controller allows a designer to diagnose performance characteristics in advance and to make better choices of solution methods. Singular value decomposition (SVD) is a powerful structural analysis tool that has been applied to linear systems and controller designs, but it has not been used for nonlinear systems. In this paper, SVD is used to structurally analyze and to optimally design nonlinear control systems using the linear algebraic equivalence of the nonlinear controller. Specifically, SVD is used to identify control input/output mode shapes, and the control input/output distribution patterns are analyzed with the mode shapes. Optimizing control effort and performance is achieved by truncating some mode shapes in the linear mode shape combinations.