Nonlinear Signal Processing and Team Differential Games

摘要

Team pursuit-evasion games are studied here with one performance index for the team as a unit in competition with one common opponent. Particular structures of team games are discussed after a brief introduction of the two-player differential games. The classical calculus of variations is used to derive the feedback strategies for team linear, quadratic pursuit-evasion games. Several definitions of the performance index that correspond to different levels of cooperation and hierarchical organization in the team are investigated. The game of kind analysis partitions the players and the space according to their role in the team. Practical solutions to these complex problems rely best on suboptimal schemes. Thus a structural analysis is presented with the intent to simplify the computation of optimal decision and communication processes. Then approximated solutions as well as suboptimal hierarchies for linear quadratic team games are derived. Two-player games provide a great deal of information concerning the solution team games, allowing to compute an approximate solution of a three-player game using a composition method and to derive exactly the solution of a complex linear quadratic team game from a controllability study by providing terminal-time criteria of selection of unknowns. Hierarchical structures naturally arise; in particular, different filtering structures for a stochastic team game are compared.