Overview

This monograph is devoted to adaptive control for nonlinear mechanical systems. The mathematical analysis of the problem of synthesizing mechanical systems is accompanied by the derivation of special control algorithms, which have many immediate, practical applications. The aim of this book is to give detailed deductions and qualitative descriptions of hindrance-resistant adaptive control algorithms for the functioning of regulated devices with tuning parameters for the realization of a given property motion. Particular emphasis is placed upon the construction of stabilized, optimal, and suboptimal adaptive controls (strategics) in the form of inverse relations, without measuring the highest derivatives. Methods are investigated to obtain an indirect adaptive control of nonlinear mechanical systems in various problems on stabilization and optimization of motion in circumstances where the exterior bounded perturbations are lacking or acting, provided that the control system parameters execute an unknown smooth drift in time.

Full Product Details

Author:   V.Y. Tertychny-Dauri
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   2002 ed.
Volume:   538
Dimensions:   Width: 15.50cm , Height: 3.00cm , Length: 23.50cm
Weight:   1.093kg
ISBN:  

9781402003981

ISBN 10:   1402003986
Pages:   507
Publication Date:   28 February 2002
Audience:   College/higher education ,  Professional and scholarly ,  Undergraduate ,  Postgraduate, Research & Scholarly
Format:   Hardback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

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.

Reviews

Author Information

Tab Content 6

Author Website:  

Customer Reviews

Recent Reviews

No review item found!

Add your own review!

Countries Available

All regions