Author | Tertychny-Dauri, Vladimir Yu. author |
---|---|
Title | Adaptive Mechanics [electronic resource] / by Vladimir Yu. Tertychny-Dauri |
Imprint | Dordrecht : Springer Netherlands : Imprint: Springer, 2002 |
Connect to | http://dx.doi.org/10.1007/978-94-007-0787-0 |
Descript | XXV, 507 p. online resource |
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 MooreโPenrose 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