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Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems: A Practical Guide for Engineers [Pehme köide]

(Vadim Azhmyakov
Department of Mathematical Sciences,
Universidad EAFIT,
Medellin, Republic of Colombia)
  • Formaat: Paperback / softback, 434 pages, kõrgus x laius: 235x191 mm, kaal: 930 g
  • Ilmumisaeg: 20-Feb-2019
  • Kirjastus: Butterworth-Heinemann Inc
  • ISBN-10: 0128147881
  • ISBN-13: 9780128147887
Teised raamatud teemal:
Relaxation-Based Approach to Optimal Control of Hybrid and Switched Systems: A Practical Guide for EngineersSuurem pilt
  • Formaat: Paperback / softback, 434 pages, kõrgus x laius: 235x191 mm, kaal: 930 g
  • Ilmumisaeg: 20-Feb-2019
  • Kirjastus: Butterworth-Heinemann Inc
  • ISBN-10: 0128147881
  • ISBN-13: 9780128147887
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9780128147887.html
Märksõnad:

A Relaxation Based Approach to Optimal Control of Hybrid and Switched Systems: A Practical Guide for Engineers proposes a unified approach to effective and numerically tractable relaxation schemes for optimal control problems of hybrid and switched systems. The book gives an overview of the existing (conventional and newly developed) relaxation techniques associated with the conventional systems described by ordinary differential equations. Next, it constructs a self-contained relaxation theory for optimal control processes governed by various types (sub-classes) of general hybrid and switched systems. It contains all mathematical tools necessary for an adequate understanding and using of the sophisticated relaxation techniques.

In addition, readers will find many practically oriented optimal control problems related to the new class of dynamic systems. All in all, the book follows engineering and numerical concepts. However, it can also be considered as a mathematical compendium that contains the necessary formal results and important algorithms related to the modern relaxation theory.

  • Illustrates the use of the relaxation approaches in engineering optimization
  • Presents application of the relaxation methods in computational schemes for a numerical treatment of the sophisticated hybrid/switched optimal control problems
  • Offers a rigorous and self-contained mathematical tool for an adequate understanding and practical use of the relaxation techniques
  • Presents an extension of the relaxation methodology to the new class of applied dynamic systems, namely, to hybrid and switched control systems
Preface xi
Chapter 1 Introduction and Motivation
7(8)
1.1 Optimal Control of Hybrid and Switched Dynamic Systems
1(8)
1.2 Questions Relaxation Theory Can Answer
9(2)
1.3 A Short Historical Remark
11(1)
1.4 Outline of the Book
12(2)
1.5 Notes
14(1)
Chapter 2 Mathematical Background
15(1)
2.1 Necessary Results and Facts From Topology and Functional Analysis
15(13)
2.2 Elements of Convex Analysis and Approximation Theory
28(19)
2.3 Notes
47(2)
Chapter 3 Convex Programming
49(1)
3.1 Problem Formulation
49(4)
3.2 Existence Theorems
53(6)
3.3 Optimality Conditions
59(2)
3.4 Duality
61(3)
3.5 Well-Posedness and Regularization
64(13)
3.6 Numerical Methods in Convex Programming
77(8)
3.7 Notes
85(2)
Chapter 4 Short Course in Continuous Time Dynamic Systems and Control
87(1)
4.1 Caratheodory Differential Equations
87(6)
4.2 Absolute Continuity
93(2)
4.3 Sobolev Spaces
95(4)
4.4 Impulsive Control Systems
99(4)
4.5 Set-Valued Functions and Differential Inclusions
103(4)
4.6 Lipschitz Set-Valued Functions
107(2)
4.7 Measurable Selections
109(3)
4.8 The Filippov-Himmelberg Implicit Functions Theorem
112(2)
4.9 Continuous Selections of the Differential Inclusions and the Michael Theorem
114(3)
4.10 Trajectories of Differential Inclusions
117(3)
4.11 Differential Inclusions in Control Theory
120(3)
4.12 Constructive Approximations of Differential Inclusions
123(3)
4.13 Notes
126(1)
Chapter 5 Relaxation Schemes in Conventional Optimal Control and Optimization Theory
127(1)
5.1 Young Measures
127(2)
5.2 The Gamkrelidze-Tikhomirov Generalization
129(6)
5.3 Chattering Lemma and Relaxed Trajectories
135(1)
5.4 The Fattorini Approach
136(2)
5.5 Some Further Generalizations of the Young Measures
138(1)
5.6 On the Rubio Relaxation Theory
139(2)
5.7 Convex Compactifications in Lebesgue Spaces
141(1)
5.8 The Buttazzo Relaxation Scheme
142(2)
5.9 Approximation of Generalized Solutions
144(21)
5.10 The β-Relaxations
165(7)
5.11 Generalized Solutions in Calculus of Variation
172(5)
5.12 The McCormic Envelopes
177(2)
5.13 Notes
179(2)
Chapter 6 Optimal Control of Hybrid and Switched Systems
181(90)
6.1 Main Definitions and Concepts
181(5)
6.1.1 The Abstract Optimal Control Problem
181(3)
6.1.2 Optimal Solution Concepts, Lagrangians
184(2)
6.2 Some Classes of Hybrid and Switched Control Systems
186(13)
6.3 Optimal Control Theory for Hybrid and Switched Systems
199(18)
6.3.1 Linear Quadratic Hybrid and Switched Optimal Control Problems
199(10)
6.3.2 Optimization of Impulsive Hybrid Systems
209(2)
6.3.3 On the Convex Switched Optimal Control Problems
211(2)
6.3.4 Pontryagin-Type Maximum Principle for Hybrid and Switched Optimal Control Problems
213(4)
6.4 Numerical Approaches to Optimal Control Problems of Hybrid and Switched Systems
217(18)
6.4.1 The Mayer-Type Hybrid Optimal Control Problem
217(5)
6.4.2 Numerics of Optimal Control
222(10)
6.4.3 Some Examples
232(3)
6.5 Approximations Based on the Optimal Control Methodology
235(34)
6.5.1 Approximations of the Zeno Behavior in ASSs
235(12)
6.5.2 Sliding Mode Control Approximations
247(22)
6.6 Notes
269(2)
Chapter 7 Numerically Tractable Relaxation Schemes for Optimal Control of Hybrid and Switched Systems
271(66)
7.1 The Gamkrelidze-Tikhomirov Generalization for HOCPs
271(12)
7.1.1 Relaxation of the General HOCPs
271(5)
7.1.2 Full Relaxation of the HOCPs Associated With the Switched Mode Dynamics
276(7)
7.2 The Bengea-DeCarlo Approach
283(1)
7.3 The β-Relaxations Applied to Hybrid and Switched OCPs
284(11)
7.4 Weak Approximation Techniques for Hybrid Systems
295(6)
7.5 A Remark on the Rubio Generalization
301(3)
7.6 Special Topics
304(28)
7.6.1 A Constrained LQ-Type Optimal Control
304(9)
7.6.2 A Simple Switched System and the Corresponding SOCP
313(9)
7.6.3 On the Hybrid Systems in Mechanics and the Corresponding HOCPs
322(10)
7.7 Weak Relaxation of the Singular HOCPs
332(3)
7.8 Notes
335(2)
Chapter 8 Applications of the Relaxation-Based Approach
337(48)
8.1 On the Existence of Optimal Solutions to OCPs Involving Hybrid and Switched Systems
337(3)
8.2 Necessary Optimality Conditions and Relaxed Controls
340(16)
8.2.1 Application of the Pontryagin Maximum Principle to Some Classes of Relaxed Hybrid and Switched OCPs
341(4)
8.2.2 On the Constraint Qualifications
345(11)
8.3 Well-Posedness and Regularization of the Relaxed HOCPs
356(4)
8.4 Numerical Treatment of the HOCPs
360(5)
8.5 Examples
365(7)
8.6 A Remark About the Practical Stabilization of a Class of Control-Affine Dynamic Systems
372(11)
8.7 Notes
383(2)
Chapter 9 Conclusion and Perspectives
385(10)
Bibliography 395(16)
Index 411
Vadim Azhmyakov graduated in 1989 from the Department of Applied Mathematics of the Technical University of Moscow. He gained a Ph.D. in Applied Mathematics in 1994, and a Postdoc in Mathematics in 2006 of the EMA University of Greifswald, Greifswald, Germany. He has experience in Applied Mathematics: optimal control, optimization, numerical methods nonlinear analysis, convex analysis, differential equations and differential inclusions, engineering mathematics; and Control Engineering: hybrid and switched dynamic systems, systems optimization, robust control, control over networks, multiagent systems, robot control, Lagrange mechanics, stochastic dynamics, smart grids, energy management systems.