Adaptive Mechanics

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.- 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.- II Integral transformation method in the theory of adaptive systems.- 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.- Appendices.- A-Lyapunov function method in the theory of controllable dynamic systems.- A.1 Basic definitions and notions. Lyapunov functions.- A.2 Basic theorems on stability.- A.2.1 Lyapunov theorems.- A.2.2 Homogeneous stability.- A.2.3 Stability in large.- A.2.4 Exponential stability.- A.2.5 Stability with constant perturbations.- A.2.6 Dissipative systems.- A.3 Link between the Lyapunov function method and optimal control.- A.4 Special questions of stability theory.- A.4.1 Trajectory stability.- A.4.2 Stability of periodic motions and orbital stability.- A.4.3 Vector Lyapunov functions.- B-Introduction to theory of singularly perturbed differential equations.- B.1 Tikhonov theorem.- B.2 Asymptotic expansions and representation accuracy estimation.- B.2.1 Preliminary remarks.- B.2.2 Asymptotic expansion of a regularly perturbed initial problem.- B.2.3 Asymptotic expansion of the solution to a singularly perturbed input problem.- B.2.4 Estimation of remaining term.- B.3 On stability of singularly perturbed systems.- B.3.1 Linear systems.- B.3.2 Nonlinear systems.- B.4 Decomposition of singularly perturbed systems on integral manifolds.- C-Pseudo-inversion and rectangular matrices.- C.1 Finite-dimensional spaces and linear manifolds.- C.2 Moore—Penrose pseudo-inversion.- C.3 Pseudo-inversion operation and skeleton matrix arrangement.- C.4 Methods of pseudo-inverse matrice calculation.- C.4.1 Computational procedure by Gram-Schmidt orthogonalization method.- C.4.2 Computational procedure for the Jordan-Gauss elimination method.- D-Approximate methods of solving Volterra integral and integro-differential equations.- D.1 Approximated Volterra integral equations.- D.2 Approximate solution to the Cauchy problem for Volterra integro-differential equations.- D.2.1 Preliminary integral transformations.- D.2.2 Solution of IDE by successive iterations.- D.2.3 Solution of IDE by parametric method.- D.2.4 Solution of IDE by quadrature method.- D.2.5 Solution of IDE by Chaplygin method.- D.3 Approximate solution of boundary problems for the Volterra integro-differential equations.- D.3.1 Solution of polylocal boundary problem.- D.3.2 Solution of the integral boundary problem.- D.3.3 Solution of IDE by the method of averaging functional correction.- 467.- 503.