A survey on cross-discipline of control and game

关键词:  Control-oriented game, game-based control, evolutionary game, potential game, logical-Newtonian control system

Key words:  Control-oriented game, game-based control, evolutionary game, potential game, logical-Newtonian control system

摘要:

In recent years, the cross discipline of game theory and the control theory has been emerging. This paperwill survey this newly growing direction. First, the development from optimization of control systems to games consisting of multi-purpose controls is introduced, which demonstrates the close relationship between control theory and game theory. Secondly, the control-oriented game is considered. Three kinds of problems are discussed in details: i) Learning strategy in game theory, which is basically the same as the adaptive control; ii) state space approach for control systems is applied to evolutionary games; and iii)machine-human game is treated as the optimal control problem. Finally, after introducing some new results on potential games, the game-based control is studied. Three kind of control problems using potential games are investigated: i) The consensus of multi-agent systems is considered; ii) the maximization of the distributed coverage of multi-agents on a graph is discussed; and iii) the congestion control is investigated using congestion game technology. Some other game-based control problems are also briefly introduced. A prediction for the control systems in next generation is presented in conclusion.

Abstract:

In recent years, the cross discipline of game theory and the control theory has been emerging. This paperwill survey this newly growing direction. First, the development from optimization of control systems to games consisting of multi-purpose controls is introduced, which demonstrates the close relationship between control theory and game theory. Secondly, the control-oriented game is considered. Three kinds of problems are discussed in details: i) Learning strategy in game theory, which is basically the same as the adaptive control; ii) state space approach for control systems is applied to evolutionary games; and iii)machine-human game is treated as the optimal control problem. Finally, after introducing some new results on potential games, the game-based control is studied. Three kind of control problems using potential games are investigated: i) The consensus of multi-agent systems is considered; ii) the maximization of the distributed coverage of multi-agents on a graph is discussed; and iii) the congestion control is investigated using congestion game technology. Some other game-based control problems are also briefly introduced. A prediction for the control systems in next generation is presented in conclusion.