Structural Analysis and Optimization of Nonlinear Control Systems Using Singular Value Decomposition

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 for linear systems, but it has not been applied to 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 using the mode shapes. Optimizing control effort and performance is achieved by truncating some mode shapes in the linear mode shape combinations. The proposed method is applied to the temperature control of a thermal system, and design guidelines are provided to overcome input-constraint-violating solutions.