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Engineering - Control Engineering | Stochastic Averaging and Stochastic Extremum Seeking

Stochastic Averaging and Stochastic Extremum Seeking

Liu, Shu-Jun, Krstic, Miroslav

2012, XII, 224 p.

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  • For engineers the text develops a stochastic version of increasingly popular deterministic extremum-seeking algorithms
  • Demonstrates to the mathematician how stochastic averaging theory can be used as a tool for studying stability rather than just approximation
  • Stochastic algorithms are intuitive and connect with the huge field of stochastic optimization
  • Shows how control ideas derived from study of a biological system can be generalized into other widely-different fields of application

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.

Content Level » Research

Keywords » Adaptive Control - Extremum Seeking - Game Theory - Gradient-based Algorithm - Nash Equilibria - Newton-based Algorithm - Optimization - Stochastic Averaging - Systems Biology

Related subjects » Applications - Control Engineering - Game Theory / Mathematical Methods - Mathematics - Robotics

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