Systems and Control
Broad in scope, this text shows the multidisciplinary role of dynamics and control, presents neural networks, fuzzy systems, and genetic algorithms, and provides a self-contained introduction to chaotic systems.
TABLE OF CONTENTS Systems and Control
Chapter 6: Sliding Modes
As philosopher of science Karl Popper has emphasized, a good theory is characterized by the fact that it makes a number of predictions that could in principle be disproved or falsified by observation. Each time new experiments are observed to agree with the predictions the theory survives, and our confidence in it is increased; but if ever a new observation is found to disagree, we have to abandon or modify the theory. At least that is what is supposed to happen, but you can always question the competence of the person who carried out the observation.
Stephen Hawking, A Brief History of Time [117]
6.1 Simple Variable Structure Systems
The purpose of this section is to informally introduce the reader to variable structure sliding mode control systems. A formal analysis is presented in the following sections.
A variable structure system is a dynamical system whose structure changes in accordance with the current value of its state. A variable structure system can be viewed as a system composed of independent structures together with a switching logic between each of the structures. With appropriate switching logic, a variable structure system can exploit the desirable properties of each of the structures the system is composed of. Even more, a variable structure system may have a property that is not a property of any of its structures. We illustrate the above ideas with two numerical examples.
Example 6.1
This example was adapted from Utkin [284]. We consider a dynamical system model
having...
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