Stochastic averaging and stochastic extremum seeking
This book deals with two topics: (i) stochastic averaging, which refers to approximating the evolution of an ordinary or stochastic differential equation with a noise input on a `fast' timescale by a simpler system wherein the effect of the 'fast' timescale dynamics is averaged out, and, (ii) stochastic extremum seeking, which refers to designing systems with rapidly varying noise so that their averaged system achieves a desired goal, typically a solution to a control problem. Stochastic averaging is considered in chapters 1, 3 and 4, for finite time horizon, for tracking the asymptotic behavior of systems with strong stability properties, and finally for situations under weaker hypotheses, respectively. The remainder of the book develops single- and multi-parameter stochastic extremum seeking techniques and discusses various specific classes of applications. These are: stochastic source seeking by tuning angular or forward velocity, stochastic gradient seeking and its Newton-based counterpart, and Nash equilibrium seeking in games, with special focus on quadratic games and their application to oligopoly markets and multi-agent deployment in the plane. The theoretical analysis is supported by simulations. Much of the book is based on the authors' own research.
scientific article; zbMATH DE number 6048955