Model-reference adaptive control. A primer
This book considers various adaptive control problems in the presence of uncertainty. Adaptive control is a promising technology that can improve the performance of control systems in the presence of uncertainty due to a variety of factors such as degradation and modeling uncertainty, as well as unforeseen internal changes in system dynamics or external disturbances. Various types of uncertainty are defined. Many of new adaptive control methods have added new capabilities in terms of improved performance and robustness and can be applied in aerospace flight control and other settings. It is shown that the adaptive approach is applied to construction of various nonlinear control methods that deal with systems with uncertainty. A brief overview of nonlinear systems is presented in this book. Nonlinear systems possess many complex behaviors that are not observed in linear systems. At the same time linearization can provide information on the local stability of a region about an equilibrium point. The existence and uniqueness of a solution of a nonlinear differential equation are stated in the book by the Cauchy theorem and the Lipschitz condition. Stability of nonlinear systems is discussed also. In particular, various stability concepts for autonomous and non-autonomous systems, such as local stability, asymptotic stability, exponential stability, uniform stability, and uniform boundedness are investigated. Applications of Lyapunov's direct method and LaSalle's invariant set theorem for analyzing stability of nonlinear systems; as well as uniform continuity concept and Barbalat's lemma for analyzing stability of non-autonomous systems are considered. This book presents the fundamental theories of least-squares function approximation and least-squares adaptive control of systems with unstructured uncertainty. The function approximation theory based on polynomials, in particular the Chebyshev orthogonal polynomials, and neural networks is presented. Both direct and indirect adaptive control methods are discussed. Least-squares direct adaptive control methods with polynomial approximation and neural network approximation are presented. It is shown that least-squares methods can also be used in adaptive control as indirect adaptive control methods to estimate unknown system parameters to provide the information for adjusting the control gains. In the book, the fundamental theory of model-reference adaptive control is presented. The composition of a model reference adaptive control system is presented. Limitations and weaknesses of model-reference adaptive control are discussed. It is mentioned that time-delay systems are another source of challenge for model-reference adaptive control, which is sensitive to the amplitude of the time delay. Several techniques for improved robustness of model-reference adaptive control is presented. This techniques, namely the optimal control modification, is developed from the optimal control theory. It is shown that the linear asymptotic property of the optimal control modification can be used to estimate the time-delay margin of a closed loop adaptive system. The book is intended for students beginning masters or doctoral courses, and control practitioners wishing to get up to speed in the subject expeditiously.
scientific article; zbMATH DE number 6813244