Modeling and Control of Nonlinear Dynamic Systems

This chapter mainly introduces the fundamental concepts of the modeling and control for nonlinear dynamic systems. The Lyapunov stability is the theory basis for ensuring the stability of nonlinear dynamic systems. Lyapunov stability and asymptotic stability definitions of an equilibrium point of a nonlinear system are first described. The Lyapunov direct method including the concept of uniform stability is then introduced as an important mathematical tool for analyzing stability of nonlinear systems. As an essential tool for analyzing asymptotic stability of adaptive control systems, the Barbalat lemma together with the uniform continuity definition of a real-valued function is also presented. After that, the basic concepts of nonlinear dynamic system modeling and adaptive control techniques are described herein. These include direct and indirect adaptive control, model reference adaptive control, feedback linearization and adaptive Backstepping control techniques. These constitute the basis of subsequent researches of the book.