A Methodology for Designing Robust Multivariable Nonlinear Feedback Control Systems

This paper presents an outline of a methodology for the design of nonlinear dynamic compensators for nonlinear multivariable systems with guarantees of closed-loop stability, robustness, and performance. The method is an extension of the Linear-Quadratic-Gaussian with Loop-Transfer-Recovery (LQG/LTR) methodology for linear systems, thus hinging upon the idea of constructing an approximate nonlinear inverse operator for the plant. A major feature of the method is a unification of both the state-space and Input-Output formulations. The major results of the paper are: i) Properties of the solution of certain optimal control problems; ii) New results on nonlinear estimation, including a new nonlinear observer with certain guaranteed properties; iii) The Loop Operator Recovery (LOR) procedure, and iv) Inclusion of command-following and disturbance rejection with a goal of a closed-loop stable, robust system.