TY - BOOK ID - 7540183 TI - Stochastic averaging and stochastic extremum seeking AU - Liu, Shujun. AU - Krstic, Miroslav. PY - 2012 SN - 1447140869 1447161858 9786613767950 128099634X 1447140877 PB - London : Springer-Verlag, DB - UniCat KW - Hybrid systems. KW - Stochastic processes KW - Average KW - Mathematics KW - Mechanical Engineering KW - Engineering & Applied Sciences KW - Physical Sciences & Mathematics KW - Mathematical Statistics KW - Mechanical Engineering - General KW - Automatic control. KW - Adaptive control systems. KW - Self-adaptive control systems KW - Control engineering KW - Control equipment KW - Engineering. KW - Systems biology. KW - System theory. KW - Calculus of variations. KW - Control engineering. KW - Robotics. KW - Automation. KW - Economic theory. KW - Control. KW - Calculus of Variations and Optimal Control; Optimization. KW - Economic Theory/Quantitative Economics/Mathematical Methods. KW - Systems Biology. KW - Robotics and Automation. KW - Systems Theory, Control. KW - Artificial intelligence KW - Feedback control systems KW - Self-organizing systems KW - Control theory KW - Engineering instruments KW - Automation KW - Programmable controllers KW - Mathematical optimization. KW - Biological models. KW - Systems theory. KW - Control and Systems Theory. KW - Models, Biological KW - Economic theory KW - Political economy KW - Social sciences KW - Economic man KW - Optimization (Mathematics) KW - Optimization techniques KW - Optimization theory KW - Systems optimization KW - Mathematical analysis KW - Maxima and minima KW - Operations research KW - Simulation methods KW - System analysis KW - Systems, Theory of KW - Systems science KW - Science KW - Automatic factories KW - Automatic production KW - Computer control KW - Engineering cybernetics KW - Factories KW - Industrial engineering KW - Mechanization KW - Assembly-line methods KW - Automatic control KW - Automatic machinery KW - CAD/CAM systems KW - Robotics KW - Machine theory KW - Computational biology KW - Bioinformatics KW - Biological systems KW - Molecular biology KW - Isoperimetrical problems KW - Variations, Calculus of KW - Philosophy UR - https://www.unicat.be/uniCat?func=search&query=sysid:7540183 AB - Stochastic Averaging and Stochastic Extremum Seeking develops methods of mathematical analysis inspired by the interest in reverse engineering  and analysis of bacterial  convergence by chemotaxis and to apply similar stochastic optimization techniques in other environments. The first half of the text presents significant advances in stochastic averaging theory, necessitated by the fact that existing theorems are restricted to systems with linear growth, globally exponentially stable average models, vanishing stochastic perturbations, and prevent analysis over infinite time horizon. The second half of the text introduces stochastic extremum seeking algorithms for model-free optimization of systems in real time using stochastic perturbations for estimation of their gradients. 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. The Communications and Control Engineering series reports major technological advances which have potential for great impact in the fields of communication and control. It reflects research in industrial and academic institutions around the world so that the readership can exploit new possibilities as they become available. ER -