Stochastic Averaging and Stochastic Extremum Seeking

  • Shu-Jun Liu
  • Miroslav Krstic

Part of the Communications and Control Engineering book series (CCE)

Table of contents

  1. Front Matter
    Pages I-XI
  2. Shu-Jun Liu, Miroslav Krstic
    Pages 1-10
  3. Shu-Jun Liu, Miroslav Krstic
    Pages 11-20
  4. Shu-Jun Liu, Miroslav Krstic
    Pages 21-55
  5. Shu-Jun Liu, Miroslav Krstic
    Pages 57-78
  6. Shu-Jun Liu, Miroslav Krstic
    Pages 79-93
  7. Shu-Jun Liu, Miroslav Krstic
    Pages 95-119
  8. Shu-Jun Liu, Miroslav Krstic
    Pages 121-128
  9. Shu-Jun Liu, Miroslav Krstic
    Pages 129-146
  10. Shu-Jun Liu, Miroslav Krstic
    Pages 181-199
  11. Back Matter
    Pages 201-224

About this book


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.


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

Authors and affiliations

  • Shu-Jun Liu
    • 1
  • Miroslav Krstic
    • 2
  1. 1.Department of MathematicsSoutheast UniversityNanjingChina, People's Republic
  2. 2.Dept. Mechanical & Aerospace Engin.University of California, San DiegoLa JollaUSA

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