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Stochastic Averaging and Stochastic Extremum Seeking 2012 ed. [Kõva köide]

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  • Formaat: Hardback, 224 pages, kõrgus x laius: 235x155 mm, kaal: 524 g, XII, 224 p., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 17-Jun-2012
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1447140869
  • ISBN-13: 9781447140863
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Stochastic Averaging and Stochastic Extremum Seeking 2012 ed.Suurem pilt
  • Formaat: Hardback, 224 pages, kõrgus x laius: 235x155 mm, kaal: 524 g, XII, 224 p., 1 Hardback
  • Sari: Communications and Control Engineering
  • Ilmumisaeg: 17-Jun-2012
  • Kirjastus: Springer London Ltd
  • ISBN-10: 1447140869
  • ISBN-13: 9781447140863
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9781447140863.html
Märksõnad:
Stochastic Averaging and Extremum Seeking treats methods inspired by attempts to understand the seemingly non-mathematical question of bacterial chemotaxis and their application in other environments. The text presents significant generalizations on existing stochastic averaging theory developed from scratch and necessitated by the need to avoid violation of previous theoretical assumptions by algorithms which are otherwise effective in treating these systems. Coverage is given to four main topics. Stochastic averaging theorems are developed for the analysis of continuous-time nonlinear systems with random forcing, removing prior restrictions on nonlinearity growth and on the finiteness of the time interval. The new stochastic averaging theorems are usable not only as approximation tools but also for providing stability guarantees. Stochastic extremum-seeking algorithms are introduced for optimization of systems without available models. Both gradient- and Newton-based algorithms are presented, offering the user the choice between the simplicity of implementation (gradient) and the ability to achieve a known, arbitrary convergence rate (Newton). The design of algorithms for non-cooperative/adversarial games is described. The analysis of their convergence to Nash equilibria is provided. The algorithms are illustrated on models of economic competition and on problems of the deployment of teams of robotic vehicles. Bacterial locomotion, such as chemotaxis in E. coli, is explored with the aim of identifying two simple feedback laws for climbing nutrient gradients. Stochastic extremum seeking is shown to be a biologically-plausible interpretation for chemotaxis. For the same chemotaxis-inspired stochastic feedback laws, the book also provides a detailed analysis of convergence for models of nonholonomic robotic vehicles operating in GPS-denied environments. The book contains block diagrams and several simulation examples, including examples arising from bacterial locomotion, multi-agent robotic systems, and economic market models. Stochastic Averaging and Extremum Seeking will be informative for control engineers from backgrounds in electrical, mechanical, chemical and aerospace engineering and to applied mathematicians. Economics researchers, biologists, biophysicists and roboticists will find the applications examples instructive.

This book develops stochastic averaging theorems and stochastic extremum-seeking algrithms, illustrating their use in a variety of models. Includes simulation examples based in bacterial locomotion, multi-agent robotic systems, and economic market models.

Arvustused

From the book reviews:

This research monograph presents and consolidates new results on the well-known topic of stochastic averaging and in the emerging area of stochastic extremum seeking. The monograph develops averaging from scratch for ordinary differential equations in deterministic and stochastic settings. This book will be of interest to researchers interested in stochastic search techniques applied to a large variety of engineering systems. (IEEE Control Systems Magazine, October, 2013)

1 Introduction to Averaging
1(10)
1.1 Averaging for Ordinary Differential Equations
1(6)
1.1.1 Averaging for Globally Lipschitz Systems
1(3)
1.1.2 Averaging for Locally Lipschitz Systems
4(3)
1.2 Stochastic Averaging
7(4)
1.2.1 Averaging for Stochastic Perturbation Process
7(1)
1.2.2 Averaging for Stochastic Differential Equations
8(3)
2 Introduction to Extremum Seeking
11(10)
2.1 Motivation and Recent Revival
11(1)
2.2 Why Stochastic Extremum Seeking?
12(1)
2.3 A Brief Introduction to Stochastic Extremum Seeking
13(8)
2.3.1 A Basic Deterministic ES Scheme
14(1)
2.3.2 A Basic Stochastic ES Scheme
15(1)
2.3.3 A Heuristic Analysis of a Simple Stochastic ES Algorithm
16(5)
3 Stochastic Averaging for Asymptotic Stability
21(36)
3.1 Problem Formulation
21(1)
3.2 Main Theorems
22(7)
3.2.1 Uniform Strong Ergodic Perturbation Process
22(4)
3.2.2 Ø-Mixing Perturbation Process
26(3)
3.3 Proofs of the Theorems
29(22)
3.3.1 Proofs for the Case of Uniform Strong Ergodic Perturbation Process
29(7)
3.3.2 Proofs for the Case of ø-Mixing Perturbation Process
36(15)
3.4 Examples
51(4)
3.4.1 Perturbation Process Is Asymptotically Periodic
51(1)
3.4.2 Perturbation Process Is Almost Surely Exponentially Stable
52(2)
3.4.3 Perturbation Process Is Brownian Motion on the Unit Circle
54(1)
3.5 Notes and References
55(2)
4 Stochastic Averaging for Practical Stability
57(22)
4.1 General Stochastic Averaging
57(7)
4.1.1 Problem Formulation
57(4)
4.1.2 Statements of General Results on Stochastic Averaging
61(3)
4.2 Proofs of the General Theorems on Stochastic Averaging
64(10)
4.2.1 Proof of Lemma 4.1
64(1)
4.2.2 Proof of Approximation Result (4.22) of Theorem 4.1
65(1)
4.2.3 Preliminary Lemmas for the Proof of Approximation Result (4.23) of Theorem 4.1
66(3)
4.2.4 Proof of Approximation Result (4.23) of Theorem 4.1
69(1)
4.2.5 Proof of Theorem 4.2
70(2)
4.2.6 Proof of (4.45)
72(2)
4.3 Discussions of the Existence of Solution
74(4)
4.4 Notes and References
78(1)
5 Single-parameter Stochastic Extremum Seeking
79(16)
5.1 Extremum Seeking for a Static Map
81(5)
5.2 Stochastic Extremum Seeking Feedback for General Nonlinear Dynamic Systems
86(7)
5.3 Notes and References
93(2)
6 Stochastic Source Seeking for Nonholonomic Vehicles
95(26)
6.1 Vehicle Model and Problem Statement
96(1)
6.2 Stochastic Source Seeking Controller
96(2)
6.3 Stability Analysis
98(5)
6.4 Convergence Speed
103(4)
6.5 Simulations and Dependence on Design Parameters
107(1)
6.5.1 Basic Simulations
107(1)
6.5.2 Dependence of Annulus Radius ρ on Parameters
108(1)
6.6 Dependence on Damping Term d0
108(4)
6.6.1 No Damping (d0 = 0)
108(2)
6.6.2 Effect of Damping (d0 > 0)
110(2)
6.7 Effect of Constraints of the Angular Velocity and Design Alternatives
112(4)
6.7.1 Effect of Constraints of the Angular Velocity
112(1)
6.7.2 Alternative Designs
112(4)
6.8 System Behavior for Elliptical Level Sets
116(1)
6.9 Notes and References
117(4)
7 Stochastic Source Seeking with Tuning of Forward Velocity
121(8)
7.1 The Model of Autonomous Vehicle
121(1)
7.2 Search Algorithm and Convergence Analysis
122(4)
7.3 Simulation
126(1)
7.4 Notes and References
127(2)
8 Multi-parameter Stochastic Extremum Seeking and Slope Seeking
129(18)
8.1 Multi-input Stochastic Averaging
129(3)
8.2 Multi-parameter Stochastic ES for Static Maps
132(6)
8.2.1 Algorithm for Multi-parameter Stochastic ES
132(2)
8.2.2 Convergence Analysis
134(4)
8.3 Stochastic Gradient Seeking
138(8)
8.3.1 Single-parameter Stochastic Slope Seeking
138(4)
8.3.2 Multi-parameter Stochastic Gradient Seeking
142(4)
8.4 Notes and References
146(1)
9 Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs
147(14)
9.1 Problem Formulation
148(1)
9.2 Stochastic Nash Equilibrium Seeking Algorithm
149(3)
9.3 Proof of the Algorithm Convergence
152(3)
9.4 Numerical Example
155(4)
9.5 Notes and References
159(2)
10 Nash Equilibrium Seeking for Quadratic Games and Applications to Oligopoly Markets and Vehicle Deployment
161(20)
10.1 N-Player Games with Quadratic Payoff Functions
161(6)
10.1.1 General Quadratic Games
161(5)
10.1.2 Symmetric Quadratic Games
166(1)
10.2 Oligopoly Price Games
167(2)
10.3 Multi-agent Deployment in the Plane
169(9)
10.3.1 Vehicle Model and Local Agent Cost
169(1)
10.3.2 Control Design
170(2)
10.3.3 Stability Analysis
172(6)
10.3.4 Simulation
178(1)
10.4 Notes and References
178(3)
11 Newton-Based Stochastic Extremum Seeking
181(20)
11.1 Single-parameter Newton Algorithm for Static Maps
181(4)
11.2 Multi-parameter Newton Algorithm for Static Maps
185(3)
11.2.1 Problem Formulation
185(1)
11.2.2 Algorithm Design and Stability Analysis
186(2)
11.3 Newton Algorithm for Dynamic Systems
188(9)
11.4 Simulation
197(2)
11.5 Notes and References
199(2)
Appendix A Some Properties of p-Limit and p-Infinitesimal Operator 201(2)
Appendix B Auxiliary Proofs for Section 3.2.2 203(12)
References 215(8)
Index 223
Miroslav Krstic is an author of several books on adaptive control, stochastic nonlinear control, extremum seeking, and control of PDEs. Several of these books have had a high impact in the control field and inspired many researchers to work on the topics that the books have covered and apply the tools from the books in their research and in practice. Shujun Liu is a young researcher in mathematics and control theory in China with strong connections with the leading research groups in control theory at the Chinese Academy of Sciences. Her doctoral work on stochastic stability and stabilization has had considerable influence on a number of research groups in China who have taken on this topic after her initial work with her doctoral advisor Professor Jifeng Zhang. Much of the material of this book was developed while the first author was a postdoctoral scholar with the second author at University of California, San Diego.