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Dynamic Programming for Impulse Feedback and Fast Controls: The Linear Systems Case 2020 ed. [Kõva köide]

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  • Formaat: Hardback, 275 pages, kõrgus x laius: 235x155 mm, kaal: 606 g, 1 Illustrations, color; 25 Illustrations, black and white; XIII, 275 p. 26 illus., 1 illus. in color., 1 Hardback
  • Sari: Lecture Notes in Control and Information Sciences 468
  • Ilmumisaeg: 30-Mar-2019
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1447174364
  • ISBN-13: 9781447174363
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Dynamic Programming for Impulse Feedback and Fast Controls: The Linear Systems Case 2020 ed.Suurem pilt
  • Formaat: Hardback, 275 pages, kõrgus x laius: 235x155 mm, kaal: 606 g, 1 Illustrations, color; 25 Illustrations, black and white; XIII, 275 p. 26 illus., 1 illus. in color., 1 Hardback
  • Sari: Lecture Notes in Control and Information Sciences 468
  • Ilmumisaeg: 30-Mar-2019
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1447174364
  • ISBN-13: 9781447174363
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781447174363.html
Märksõnad:
Dynamic Programming for Impulse Feedback and Fast Controls offers a description of feedback control in the class of impulsive inputs. This book deals with the problem of closed-loop impulse control based on generalization of dynamic programming techniques in the form of variational inequalities of the HamiltonJacobiBellman type. It provides exercises and examples in relation to software, such as techniques for regularization of ill-posed problems. It also gives an introduction to applications such as hybrid dynamics, control in arbitrary small time, and discontinuous trajectories.This book walks the readers through:









the design and description of feedback solutions for impulse controls;

the explanation of impulses of higher order that are derivatives of delta functions;

the description of their physically realizable approximations - the fast controls and their approximations;

the treatment of uncertaintyin impulse control and the applications of impulse feedback.















Of interest to both academics and graduate students in the field of control theory and applications, the book also protects users from common errors , such as inappropriate solution attempts, by indicating Hamiltonian techniques for hybrid systems with resets.

Arvustused

This is an advanced monograph on impulse control and optimal impulse control theory of linear systems, with a special emphasis on feedback control in the class of impulsive inputs. The book is intended for both academics and graduate students in the field of control theory and applications. (Monica Motta, Mathematical Reviews, October, 2019) I would like to recommend it to students and researchers interested in impulsive models. (Jin Liang, zbMATH 1425.93004, 2019)

1 Introduction: Why Impulses? 1(14)
1.1 The Motivations
1(1)
1.2 Why Impulse Controls?
2(3)
1.2.1 The Mathematical Nature
2(3)
1.3 Physical Nature
5(4)
1.3.1 The Physical Nature
5(4)
1.4 Notations and Preliminaries
9(6)
References
10(5)
Part I Ordinary Impulses
2 Open-Loop Impulse Control
15(28)
2.1 Linear Systems: Open-Loop Control Under Ordinary Impulses
15(2)
2.2 The Impulse Control Problem
17(1)
2.3 Reachability Under Impulse Controls: Direct Solutions
18(6)
2.4 Solution of the Problem
24(8)
2.4.1 In the Absence of Controllability
30(1)
2.4.2 Controlling a Subset of Coordinates
30(1)
2.4.3 The Problem with Set-Valued Boundary Conditions
31(1)
2.5 Time-Optimal Impulse Control
32(4)
2.5.1 Scheme A
33(1)
2.5.2 Scheme B
34(2)
2.6 The Mayer-Bolza Problem with Controls as Measures
36(2)
2.7 Examples
38(3)
References
41(2)
3 Closed-Loop Impulse Control
43(34)
3.1 Feedback Solutions and the HJB Equation
43(15)
3.1.1 The Problem and the Value Function
43(5)
3.1.2 The Hamilton-Jacobi-Bellman Equation
48(4)
3.1.3 The Control Law
52(4)
3.1.4 Reachability and Solvability Through Dynamic Programming
56(2)
3.2 The Problem of Feedback Control Under Impulses
58(6)
3.2.1 The Problem
58(4)
3.2.2 Constructive Motions
62(1)
3.2.3 Space-Time Transformation
63(1)
3.3 Examples
64(5)
3.4 Solvability (Backward Reachability) and the Construction of Invariant Sets
69(5)
3.4.1 The RIB Equation
70(3)
3.4.2 Equations of the Backward Reach Set
73(1)
3.5 Stabilization by Impulses
74(1)
References
75(2)
4 Impulse Control Under Uncertainty
77(26)
4.1 The Problem of Impulse Control Under Uncertainty
77(2)
4.2 The HJBI Equation
79(11)
4.2.1 The Principle of Optimality Under Uncertainty
80(4)
4.2.2 The Hamilton-Jacobi-Bellman-Isaacs Equation
84(6)
4.3 Calculating Value Functions Under Uncertainty
90(6)
4.3.1 Min max and Max min Value Functions
91(3)
4.3.2 Value Function with Corrections
94(1)
4.3.3 The Closed-Loop Value Function
95(1)
4.4 A 1D Impulse Control Problem
96(5)
4.4.1 An Open-Loop Min max Value Function in 1D
96(2)
4.4.2 A Value Function with Corrections in 1D
98(1)
4.4.3 The Closed-Loop Value Function in 1D
99(1)
4.4.4 An Example in 1D
100(1)
References
101(2)
5 State-Constrained Impulse Control
103(34)
5.1 The Main Problem
103(1)
5.2 Open-Loop Impulse Control Under State Constraints
104(6)
5.3 The HJB Equation Under State Constraints
110(3)
5.4 Reachability Under State Constraints
113(4)
5.5 Backward Reachability and the Problem of Control Synthesis
117(4)
5.6 State-Constrained Control Under Uncertainty
121(15)
5.6.1 The Feedback Control Problem
122(1)
5.6.2 The Principle of Optimality and the HJBI Equation
123(3)
5.6.3 Open-Loop Min max and Max min Value Functions
126(4)
5.6.4 Backward Reachability Under Uncertainty and State Constraints
130(3)
5.6.5 Feedback Control Strategies Under Uncertainty and State Constraints
133(3)
References
136(1)
6 State Estimation Under Ordinary Impulsive Inputs
137(26)
6.1 The Problem of Observation (Guaranteed Estimation)
137(8)
6.1.1 The Solution Scheme
137(3)
6.1.2 Duality of Observation and Control Under Ordinary Impulsive Inputs
140(2)
6.1.3 On-Line State Estimation. The Information Set
142(3)
6.2 Optimal Estimation Through Discrete Measurements
145(8)
6.2.1 Open-Loop Assignment of Measurement Times
145(3)
6.2.2 Closed-Loop Calculation of Information Sets
148(2)
6.2.3 Closed-Loop Estimation Under Given Observation Times
150(2)
6.2.4 Calculating the Information Set. Ellipsoidal Method
152(1)
6.3 Closed-Loop Control Under Incomplete Measurements
153(7)
6.3.1 The System and the Information Set
153(2)
6.3.2 The Problem of Output Feedback Control
155(3)
6.3.3 The Dynamic Programming Approach
158(2)
References
160(3)
Part II Impulses of Higher Order. Realizability and Fast Control
7 The Open-Loop and Closed-Loop Impulse Controls
163(16)
7.1 Linear Systems Under Higher Order Controls: The Problems
163(2)
7.2 Solutions. Controllability in Zero Time. Ultrafast Controls
165(2)
7.2.1 The Open-Loop Solution
165(2)
7.2.2 The Types of Open-Loop Control
167(1)
7.3 Reduction to First-Order Systems Under Vector Measures
167(2)
7.4 HJB Theory and High-Order Impulsive Feedback
169(2)
7.5 Reduction to the "Ordinary" Impulse Control Problem
171(1)
7.6 Reachability Under High-Order Impulse Controls
172(4)
References
176(3)
8 State-Constrained Control Under Higher Impulses
179(14)
8.1 The Problem of State-Constrained Control
179(12)
8.1.1 Solvability of Problem 8.1
182(5)
8.1.2 Optimization of the Generalized Control. The Maximum Principle
187(3)
8.1.3 A Reciprocal Problem of Optimization
190(1)
References
191(2)
9 State Estimation and State Constrained Control
193(18)
9.1 Guaranteed State Estimation Under High-Order Inputs
193(4)
9.2 The Duality Principle-A Dual Interpretation
197(4)
9.2.1 State Estimation Under Higher Impulses
198(1)
9.2.2 Control by Impulses of Higher Order-The Duality Principle
199(2)
9.3 Estimation and Control Under Smooth Inputs
201(8)
9.3.1 The Problem of Observation
201(4)
9.3.2 The Problem of State-Constrained Smooth-Input Control
205(4)
References
209(2)
10 Generalized Duality Theory. The Increasing and Decreasing Lagrangian Scales
211(22)
10.1 Duality in the Mathematical Sense
211(1)
10.2 Duality Scale in Problems of State-Constrained Impulse Control
212(5)
10.3 Duality Scale in Problems of Guaranteed State Estimation
217(4)
10.4 Duality in the System Sense-Between Problems of Control and Estimation
221(10)
10.4.1 Problems Under Ordinary Impulses
221(3)
10.4.2 Problems Under Impulses of Higher Order
224(3)
10.4.3 Problems Under Smooth Inputs
227(4)
References
231(2)
11 Realistic Controls
233(12)
11.1 Dynamic Programming Under Double Constraints
233(5)
11.1.1 Control Under Double Constraints
233(2)
11.1.2 From Ideal Impulse Control to Realistic
235(3)
11.2 Convergence of Realistic Solutions to Ideal Impulsive Feedback
238(2)
11.3 Delta-Like Approximating Sequences
240(3)
11.3.1 Discontinuous Approximations
241(1)
11.3.2 The Growth Rate of Fast Controls
241(2)
References
243(2)
12 Closed-Loop Fast Controls
245(20)
12.1 HJB Equation Types for Fast Controls
245(2)
12.2 Fast Controls Under Uncertainty
247(1)
12.3 Disturbance Attenuation. Error Estimates
248(9)
12.3.1 The Problem
248(1)
12.3.2 Generalized Controls
249(2)
12.3.3 An Example
251(1)
12.3.4 Control Inputs for the Original System
252(5)
12.4 Other Examples
257(6)
References
263(2)
Appendix A: Uniqueness of Viscosity Solutions 265(8)
Index 273
Alexander B. Kurzhanski was born in 1939. He graduated with honours in electrical engineering at the Technical University of Ural, Sverdlovsk, USSR (1962). He did his graduate studies in mathematics and mechanics at classical University of Ural (19621965), having received his PhD-equivalent degree in 1965 and habilitation doctorate in 1971. He became full professor in 1974. In 19671984 he was at Institute of Mathematics and Mechanics, Ural Branch, Academy of Sciences of USSR as a Senior Researcher, Head of Department and finally Director. He was Chairman of Systems and Decision Sciences Program, Deputy Director at IIASA (the International Institute for Applied Systems Analysis), Laxenburg, Austria (19841992). He is Head of Department of Systems Analysis, Lomonosov Moscow State University (MSU), Faculty of Computational Mathematics and Cybernetics (1992present) and also a distinguished professor of MSU (1999). He was elected associate member of the Russian (former Soviet)Academy of Sciences in 1981 and Full Member in 1990. He is Chairman of Russian National Committee on Automatic Control (the IFAC NMO, 1998present). He also holds a visiting research position at UC-Berkeley, USA. His research interests and achievements are in the field of estimation and control under uncertainty and incomplete (realistic) information, feedback control of complex systems, inverse problems of mathematical physics, computational methods in dynamics and control and mathematical modeling for applied systems analysis.





 





Alexander N. Daryin was born in 1979. He graduated with honours from the Faculty of Computational Mathematics and Cybernetics at Lomonosov Moscow State University in 2001. He did his graduate studies in mathematics (pure and applied) at same faculty (20012004). He received PhD-equivalent degree in 2004. He worked as an associate professor at same faculty, Department of Systems Analysis (20042014). He currently works at Google Research in Zurich. He authored or coauthored more than 25 research journal and conference papers. His interests lie in the theory and applications of feedback control for complex systems, including control under uncertainty, impulse control and computational methods.