Mathematics and Its Applications

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.