Adaptive Mechanics
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Bibliographic Information
Adaptive Mechanics
（Mathematics and its applications, v. 538）
Kluwer Academic, c2002
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Includes bibliographical references and index
Description and Table of Contents
Description
Over the last thirty years an abundance of papers have been writ ten on adaptive dynamic control systems. Nevertheless, now it may be predicted with confidence that the adaptive mechanics, a new division, new line of inquiry in one of the violently developing fields of cybernetic mechanics, is emerging. The birth process falls far short of being com pleted. There appear new problems and methods of their solution in the framework of adaptive nonlinear dynamics. Therefore, the present work cannot be treated as a certain polished, brought-to-perfection school textbook. More likely, this is an attempt to show a number of well known scientific results in the parametric synthesis of nonlinear systems (this, strictly speaking, accounts for the availability of many reviews), as well as to bring to notice author's developments on this question undoubtedly modern and topical. The nonlinear, and practically La grangian, systems cover a wide class of classical objects in theoretical mechanics, and primarily solid-body (robotic, gyroscopic, rocket-cosmic, and other) systems. And what is rather important, they have a direct trend to practical application. To indicate this discussion, I should like to notice that it does not touch upon the questions concerned with the linear and stochastic con trolobjects. Investigated are only nonlinear deterministic systems being in the conditions when some system parameters are either unknown or beyond the reach of measurement, or they execute an unknown limited and fairly smooth drift in time.
Table of Contents
- Preface. Acknowledgments. Introduction
- V.Yu. Tertychny-Dauri. Part I: Problems and Methods of Adaptive Mechanical-System Control. 1. Adaptive Stabilization of Mechanical Systems by the Method of Recurrent Objective Inequalities. 2. Searchless Self-Adjustable Adaptation and Control Systems. 3. Rate Gradient Algorithms in the Problems of Adaptive Control of Mechanical Systems. 4. Overview of Some Methods and Results of Nonlinear Parametric Synthesis. Part II: Integral Transformation Method in the Theory of Adaptive Systems. 5. Synthesis of Dissipative and Stabilizing Systems of Adaptive Control. 6. Adaptive Stabilization of Controlled Mechanical Systems in the Conditions of Unknown Parametric Drift. 7. Optimum Stabilization of Holonomic and Nonholonomic Mechanical Systems. 8. Parametric Universal Integral Tests in the Problem of Optimal Stabilization of Mechanical Systems. Part III: Adaptive Mechanics and Solution of Special Optimization Problems. 9. Adaptive Optimization Synthesis: Equivalence, Suboptimality, and Robustness. 10. Optimal Synthesis of Adaptive Mechanical Systems Imposed by General Constraints. 11. Synthesis of Adaptive Controllable Information Systems Based on the Canonic Hamilton-Jacobi Transformation Method. 12. Optimization of Adaptive Controllable Distributed Parameter Systems. Part IV: Elements of Theory and all other Attendant Reference Sources. Appendices. A: Lyapunov Function Method in the Theory of Controllable Dynamic Systems. B: Introduction to Theory of Singularly Perturbed Differential Equations. C: Pseudo-Inversion and Rectangular Matrices. D: Approximate Methods of Solving Volterra Integral and Integro-Differential Equations. References. Index.
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