Analysis and Control of Nonlinear Systems

This paper describes my work on nonlinear analysis and control over the last twenty years. The first part of the paper concerns the development of nonlinear analysis tools for predicting stability and forced response characteristics of high speed ground vehicles. The principal motivation was to develop an alternative to “brute force” time domain simulation. The developed tools were extensions of “describing function” or “equivalent linearization” methods for both periodic and stochastic excitation. The “statistical linearization” analysis tools were then extended and applied to design control laws for nonlinear stochastic regulators. The second part of the paper was motivated by control system design for highly nonlinear, multivariable systems, such as automotive powertrain control and aircraft flight control. For these classes of systems, statistical linearization procedures are computationally cumbersome and also provide no stability or robustness guarantees. A method which has proven extremely powerful, both theoretically and experimentally, is “sliding control.” This technique is a form of input/output linearization that directly incorporates model error information with stability and performance measures. My students and I found several difficulties in the direct application of this method to automotive and aircraft control. This paper describes our solutions to the problems of repeated model differentiation, differentiation of model error, undesirable “internal dynamics” and systems with saturating control inputs.