Title Stochastic averaging and stochastic extremum seeking / Shu-Jun Liu, Miroslav Krstic

Published London ; New York : Springer, ©2012

Click on the following:
Springer Engineering eBooks
Springer eBooks

Copies

Description 1 online resource Series Communications and control engineering, 0178-5354 Communications and control engineering. Contents 880-01 Introduction to Averaging -- Introduction to Extremum Seeking -- Stochastic Averaging for Asymptotic Stability -- Stochastic Averaging for Practical Stability -- Single-parameter Stochastic Extremum Seeking -- Stochastic Source Seeking for Nonholonomic Vehicles -- Stochastic Source Seeking with Tuning of Forward Velocity -- Multi-parameter Stochastic Extremum Seeking and Slope Seeking -- Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs -- Nash Equilibrium Seeking for Quadratic Games and Applications to Oligopoly Markets and Vehicle Deployment -- Newton-Based Stochastic Extremum Seeking 880-01/(S Machine generated contents note: 1. Introduction to Averaging -- 1.1. Averaging for Ordinary Differential Equations -- 1.1.1. Averaging for Globally Lipschitz Systems -- 1.1.2. Averaging for Locally Lipschitz Systems -- 1.2. Stochastic Averaging -- 1.2.1. Averaging for Stochastic Perturbation Process -- 1.2.2. Averaging for Stochastic Differential Equations -- 2. Introduction to Extremum Seeking -- 2.1. Motivation and Recent Revival -- 2.2. Why Stochastic Extremum Seeking-- 2.3. Brief Introduction to Stochastic Extremum Seeking -- 2.3.1. Basic Deterministic ES Scheme -- 2.3.2. Basic Stochastic ES Scheme -- 2.3.3. Heuristic Analysis of a Simple Stochastic ES Algorithm -- 3. Stochastic Averaging for Asymptotic Stability -- 3.1. Problem Formulation -- 3.2. Main Theorems -- 3.2.1. Uniform Strong Ergodic Perturbation Process -- 3.2.2. Ø-Mixing Perturbation Process -- 3.3. Proofs of the Theorems -- 3.3.1. Proofs for the Case of Uniform Strong Ergodic Perturbation Process -- 3.3.2. Proofs for the Case of ø-Mixing Perturbation Process -- 3.4. Examples -- 3.4.1. Perturbation Process Is Asymptotically Periodic -- 3.4.2. Perturbation Process Is Almost Surely Exponentially Stable -- 3.4.3. Perturbation Process Is Brownian Motion on the Unit Circle -- 3.5. Notes and References -- 4. Stochastic Averaging for Practical Stability -- 4.1. General Stochastic Averaging -- 4.1.1. Problem Formulation -- 4.1.2. Statements of General Results on Stochastic Averaging -- 4.2. Proofs of the General Theorems on Stochastic Averaging -- 4.2.1. Proof of Lemma 4.1 -- 4.2.2. Proof of Approximation Result (4.22) of Theorem 4.1 -- 4.2.3. Preliminary Lemmas for the Proof of Approximation Result (4.23) of Theorem 4.1 -- 4.2.4. Proof of Approximation Result (4.23) of Theorem 4.1 -- 4.2.5. Proof of Theorem 4.2 -- 4.2.6. Proof of (4.45) -- 4.3. Discussions of the Existence of Solution -- 4.4. Notes and References -- 5. Single-parameter Stochastic Extremum Seeking -- 5.1. Extremum Seeking for a Static Map -- 5.2. Stochastic Extremum Seeking Feedback for General Nonlinear Dynamic Systems -- 5.3. Notes and References -- 6. Stochastic Source Seeking for Nonholonomic Vehicles -- 6.1. Vehicle Model and Problem Statement -- 6.2. Stochastic Source Seeking Controller -- 6.3. Stability Analysis -- 6.4. Convergence Speed -- 6.5. Simulations and Dependence on Design Parameters -- 6.5.1. Basic Simulations -- 6.5.2. Dependence of Annulus Radius ρ on Parameters -- 6.6. Dependence on Damping Term d0 -- 6.6.1. No Damping (d0 = 0) -- 6.6.2. Effect of Damping (d0> 0) -- 6.7. Effect of Constraints of the Angular Velocity and Design Alternatives -- 6.7.1. Effect of Constraints of the Angular Velocity -- 6.7.2. Alternative Designs -- 6.8. System Behavior for Elliptical Level Sets -- 6.9. Notes and References -- 7. Stochastic Source Seeking with Tuning of Forward Velocity -- 7.1. Model of Autonomous Vehicle -- 7.2. Search Algorithm and Convergence Analysis -- 7.3. Simulation -- 7.4. Notes and References -- 8. Multi-parameter Stochastic Extremum Seeking and Slope Seeking -- 8.1. Multi-input Stochastic Averaging -- 8.2. Multi-parameter Stochastic ES for Static Maps -- 8.2.1. Algorithm for Multi-parameter Stochastic ES -- 8.2.2. Convergence Analysis -- 8.3. Stochastic Gradient Seeking -- 8.3.1. Single-parameter Stochastic Slope Seeking -- 8.3.2. Multi-parameter Stochastic Gradient Seeking -- 8.4. Notes and References -- 9. Stochastic Nash Equilibrium Seeking for Games with General Nonlinear Payoffs -- 9.1. Problem Formulation -- 9.2. Stochastic Nash Equilibrium Seeking Algorithm -- 9.3. Proof of the Algorithm Convergence -- 9.4. Numerical Example -- 9.5. Notes and References -- 10. Nash Equilibrium Seeking for Quadratic Games and Applications to Oligopoly Markets and Vehicle Deployment -- 10.1. N-Player Games with Quadratic Payoff Functions -- 10.1.1. General Quadratic Games -- 10.1.2. Symmetric Quadratic Games -- 10.2. Oligopoly Price Games -- 10.3. Multi-agent Deployment in the Plane -- 10.3.1. Vehicle Model and Local Agent Cost -- 10.3.2. Control Design -- 10.3.3. Stability Analysis -- 10.3.4. Simulation -- 10.4. Notes and References -- 11. Newton-Based Stochastic Extremum Seeking -- 11.1. Single-parameter Newton Algorithm for Static Maps -- 11.2. Multi-parameter Newton Algorithm for Static Maps -- 11.2.1. Problem Formulation -- 11.2.2. Algorithm Design and Stability Analysis -- 11.3. Newton Algorithm for Dynamic Systems -- 11.4. Simulation -- 11.5. Notes and References Summary Annotation 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 Analysis Engineering Biological models Systems theory Mathematical optimization Economics, Mathematical Control Calculus of Variations and Optimal Control; Optimization Game Theory/Mathematical Methods Systems Biology Robotics and Automation Systems Theory, Control calculus optimalisatie optimization automatisering automation systeembiologie controle speltheorie game theory wiskunde mathematics regeltheorie control theory optimalisatiemethoden optimization methods Engineering (General) Techniek (algemeen) Bibliography Includes bibliographical references and index Subject Stochastic processes. Average. Stochastic Processes mean. MATHEMATICS -- Applied. MATHEMATICS -- Probability & Statistics -- General. Ingénierie. Average Stochastic processes Form Electronic book Author Krstić, Miroslav. ISBN 9781447140870 1447140877

  Permalink