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2022 | Book

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Neural Network-Based Adaptive Control of Uncertain Nonlinear Systems

Authors: Kasra Esfandiari, Farzaneh Abdollahi, Ph.D. Heidar A. Talebi

Publisher: Springer International Publishing

Part of: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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About this book

The focus of this book is the application of artificial neural networks in uncertain dynamical systems. It explains how to use neural networks in concert with adaptive techniques for system identification, state estimation, and control problems. The authors begin with a brief historical overview of adaptive control, followed by a review of mathematical preliminaries. In the subsequent chapters, they present several neural network-based control schemes. Each chapter starts with a concise introduction to the problem under study, and a neural network-based control strategy is designed for the simplest case scenario. After these designs are discussed, different practical limitations (i.e., saturation constraints and unavailability of all system states) are gradually added, and other control schemes are developed based on the primary scenario. Through these exercises, the authors present structures that not only provide mathematical tools for navigating control problems, but also supply solutions that are pertinent to real-life systems.

Table of Contents

Frontmatter
Chapter 1. Introduction
Abstract
In this chapter, we introduce the subject of the monograph. The main purpose of the chapter is to provide the reader with an overview on adaptive systems, the motivation for using such systems, and some challenging problems in the field of adaptive systems. The outline of the monograph is also presented here.
Kasra Esfandiari, Farzaneh Abdollahi, Heidar A. Talebi
Chapter 2. Mathematical Preliminaries
Abstract
This chapter is devoted to presenting some basic concepts that are widely used in the monograph. In this regard, we first review some properties of signals and functions. Then, nonlinear systems theory is briefly discussed and the concepts of Lie derivative, relative degree, diffeomorphism mapping, normal form, zero dynamics, and uniformly ultimately boundedness are introduced. Finally, we present some fundamental concepts about the structure of multi-layer neural networks, their function approximation capabilities and the general structure of neural networks-based identification and control strategies.
Kasra Esfandiari, Farzaneh Abdollahi, Heidar A. Talebi
Chapter 3. NN-Based Adaptive Control of Affine Nonlinear Systems
Abstract
Design of adaptive controllers for affine uncertain nonlinear systems is investigated in this chapter. In the first part of the chapter, it is assumed that all system states are available for measurement and a state feedback control strategy is designed. In order to address the fact that the systems actuators are not able to apply any demanded control signal, an NN-based control methodology that is capable of handling such a limitation, i.e., saturation constraint, is proposed. In the final part of this chapter, the unrealistic assumption of accessibility of all system states is also relaxed, and an observer-based controller is presented for affine nonlinear systems subject to saturation constraint. In all presented control strategies, weights of both NN layers are adjusted simultaneously and stability analysis of the overall system is guaranteed using Lyapunov’s direct method.
Kasra Esfandiari, Farzaneh Abdollahi, Heidar A. Talebi
Chapter 4. NN-Based Adaptive Control of Nonaffine Canonical Nonlinear Systems
Abstract
This chapter presents three direct adaptive control schemes for uncertain nonlinear systems given in canonical forms. Unlike the control schemes developed in the previous chapter, the control strategies presented here are applicable to nonaffine nonlinear systems. Towards this end, Mean Value and Implicit Function Theorems are first employed to transform the original system dynamics into an equivalent affine system. Then, two full state feedback controllers are presented for systems without and with saturation constraint. Finally, high-gain observer estimation capabilities are utilized to design an output feedback controller based on the structure of the previously developed state feedback control schemes. All these control strategies use nonlinear in parameter neural networks approximation capabilities. The suggested adaption laws for weights of NNs layers have two parts: the first part is based on the gradient descent optimization algorithm and the second part acts as a damping term introduced to guarantee closed-loop system stability.
Kasra Esfandiari, Farzaneh Abdollahi, Heidar A. Talebi
Chapter 5. NN-Based Adaptive Control of Nonaffine Noncanonical Nonlinear Systems
Abstract
This chapter deals with the design of indirect adaptive control schemes for a general class of uncertain nonaffine systems. To achieve this goal, an NN-based series-parallel identification scheme is first presented to identify the dynamics of a class of nonlinear systems in canonical form. The suggested identifier has a multi-layer perceptron NN with dynamic back propagation updating rules and it does not require any prior information about system nonlinearities and control direction. Then, an NN-based state feedback controller is designed by using the information obtained from the identifier. Finally, a more general control architecture is presented by extending the previously presented ideas for the state feedback case to the output feedback control problem of nonlinear systems in non-canonical form. The stability of the overall system is ensured via Lyapunov’s direct method for both state feedback and output feedback cases and it is shown that the tracking errors converge to adjustable neighborhoods of the origin.
Kasra Esfandiari, Farzaneh Abdollahi, Heidar A. Talebi
Chapter 6. NN-Based Adaptive Control of MIMO Nonaffine Noncanonical Nonlinear Systems
Abstract
This chapter is concerned with the tracking problem of Multi Input Multi Output (MIMO) nonaffine nonlinear systems having saturated actuators and internal dynamics. In order to give a more realistic scheme, it is assumed that not all system states are available for measurement. Therefore, an adaptive observer, which benefits from the advantages of neural networks as well as high-gain observers, is designed to reconstruct the system states. Then, the estimated states are fed into an NN-based controller to generate the control signal. The stability of the augmented system is proven by decomposing the system into some subsystems and using Lyapunov’s direct method. The NNs, used in the structures of controller and observer, are nonlinear in parameter type, and the corresponding adaption laws are derived such that the square of tracking and observation errors are minimized. Hence, full capabilities of NNs are used to approximate unknown terms. Finally, the performance of the proposed structure is evaluated by using computer simulations and carrying out experiments on a robotic manipulator.
Kasra Esfandiari, Farzaneh Abdollahi, Heidar A. Talebi
Backmatter
Metadata
Title
Neural Network-Based Adaptive Control of Uncertain Nonlinear Systems
Authors
Kasra Esfandiari
Farzaneh Abdollahi
Ph.D. Heidar A. Talebi
Copyright Year
2022
Electronic ISBN
978-3-030-73136-6
Print ISBN
978-3-030-73135-9
DOI
https://doi.org/10.1007/978-3-030-73136-6

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