Adaptive minimax control of a~pursuit process with many pursuers in discrete dynamical systems

A. F. Shorikov

Trudy Instituta matematiki i mehaniki, Dynamical systems and control problems, Tome 11 (2005) no. 1, pp. 225-240

Résumé

An adaptive minimax control of a pursuit process with several controlled objects whose dynamics are described by discrete recursive vector equations is considered. It is assumed that the past realizations of the control signals of objects $I_i$ ($i=1,2,\dots,n$) controlled by $n$ pursuers and signals containing an incomplete information about an object II controlled by an evader are known. The sets of values of all a priori unknown parameters of the dynamical systems considered are convex polyhedra in the corresponding finite-dimensional vector spaces. Under these assumptions, the problem of adaptive minimax control of the pursuit process is stated and solved. A recursive procedure for organizing a minimax pursuit control in a certain class of feasible adaptive control strategies is suggested; each step of this procedure is based on implementation of a posteriori minimax nonlinear filtering and on solution of linear and convex programming problems. The results obtained can be used in computer modeling of real-life dynamical processes and in designing optimal navigational and control devices for various transportation systems.