In this paper, a new system equivalence relation, using the framework of differential geometry of jets and prolongations of infinite order, is studied. In this setting, two systems are said to be equivalent if any variable of one system may be expressed as a function of the variables of the other system and of a finite number of their time derivatives. This is a Lie–Bäcklund isomorphism. This q...

A new algorithm is proposed for computing locally the linearizing output of single-input and multi-input nonlinear affine system. The algorithm modifies the extended Goursat normal form to iteratively obtain the successive integrations of one dimensional distributions of control system. The algorithm takes ideas from both vector field approach of feedback linearization and exterior differential...

The inverse of a non-minimum-phase system being unstable, standard input-output feedback linearization is not effective to control such systems. In this chapter is a presentation of a new tracking control method for the nonlinear non-minimum-phase system. Indeed, the main idea here is to dismiss a part of system dynamics in order to make the approximate system input-state feedback linearizable....

This paper considers the problem of adaptive output feedback tracking control for a class of nonstrict-feedback nonlinear systems with unknown time-varying delays and unknown backlash-like hysteresis. Fuzzy logic systems are used to estimate the unknown nonlinear functions. Based on the Lyapunov–Krasovskii method, the control scheme is constructed by using the backstepping and adaptive techniqu...

Stimulated by the growing demand for improving system performance and reliability, fault-tolerant system design has been receiving significant attention. This paper proposes a new fault-tolerant control methodology using adaptive estimation and control approaches based on the learning capabilities of neural networks or fuzzy systems. On-line approximation-based stable adaptive neural/fuzzy cont...

Many discrete-time dynamic models of current interest are based on functions that, while generally continuous, are nonsmooth; examples include speci c multimodels, hinging hyperplane models, and hybrid systems. We consider two models for which we can vary the smoothness and examine its in uence on qualitative behavior. In the smooth regime, both models exhibit asymptotic stability for suÆcientl...

Nonlinear control theory has received considerable attention m the last decades. As a result, there exists nowadays a sophisticated framework using (differential) geometric methods for dealmg with a large number of controller design problems. The book under review, Nonlinear Control Design, Geometric, Adaptiue and Robust presents according to the back cover of the book “A self-contained introdu...