Estimation and Control of Nonlinear Discrete-time Systems

Abstract

Real world systems with unknown dynamics, uncertainties and disturbances pose a great challenge in developing control schemes. As a consequence, conventional controllers cannot be used for such nonlinear systems acted upon uncertainties. Hence, more advanced techniques such as robust control to mitigate disturbances and uncertainties, adaptive control using neural networks to learn unknown dynamics, and robust adaptive control to mitigate unknown dynamics and uncertainties have been introduced in the past decade. As a first step, the unknown system dynamics have to be constructed using online approximates such as neural networks and then controllers have to be designed. In this chapter, estimation or system identification and control using neural networks is thoroughly investigated. To begin with, some basic concepts on the neural networks are introduced, and then some stability properties are proposed for a general class of nonlinear discretetime systems. Later, the development of nonlinear estimation techniques for a class of nonlinear discrete-time systems is introduced. Finally, neural networks control strategies are presented for controlling a class of nonlinear discrete-time system. Rigorous mathematical results for asymptotic stability on the estimation and control scheme are demonstrated. Additionally, some simulation examples are used to illustrate the performance of the estimation and control schemes, respectively.