Multi-pursuer single-evader differential games with limited observations

In this paper, closed-loop Nash equilibrium strategies for an N-pursuer single-evader differential game over a finite time horizon with limited observations is considered. The game setting is such that each pursuer has limited sensing range and can observe the state vector of another player only if that player is within the pursuer\u27s sensing range. The evader, on the other hand, has unlimited sensing range which allows it to observe the state of all pursuers at all times and implement a standard closed-loop Nash strategy. To derive strategies for the pursuers, a new concept of best achievable performance indices is proposed. These indices are derived in a way to be the closest to the original performance indices and such that the resulting pursuers\u27 collective strategy satisfies a Nash equilibrium against the evader\u27s strategy. The strategies obtained by such an approach are independent of the initial state vector. An illustrative example is solved and simulation results corresponding to different sensing ranges and performance indices of the game are presented. © 2013 AACC American Automatic Control Council

Differential Games For Multi-agent Systems Under Distributed Information

In this dissertation, we consider differential games for multi-agent systems under distributed information where every agent is only able to acquire information about the others according to a directed information graph of local communication/sensor networks. Such games arise naturally from many applications including mobile robot coordination, power system optimization, multiplayer pursuit-evasion games, etc. Since the admissible strategy of each agent has to conform to the information graph constraint, the conventional game strategy design approaches based upon Riccati equation(s) are not applicable because all the agents are required to have the information of the entire system. Accordingly, the game strategy design under distributed information is commonly known to be challenging. Toward this end, we propose novel open-loop and feedback game strategy design approaches for Nash equilibrium and noninferior solutions with a focus on linear quadratic differential games. For the open-loop design, approximate Nash/noninferior game strategies are proposed by integrating distributed state estimation into the open-loop global-information Nash/noninferior strategies such that, without global information, the distributed game strategies can be made arbitrarily close to and asymptotically converge over time to the global-information strategies. For the feedback design, we propose the best achievable performance indices based approach under which the distributed strategies form a Nash equilibrium or noninferior solution with respect to a set of performance indices that are the closest to the original indices. This approach overcomes two issues in the classical optimal output feedback approach: the simultaneous optimization and initial state dependence. The proposed open-loop and feedback design approaches are applied to an unmanned aerial vehicle formation control problem and a multi-pursuer single-evader differential game problem, respectively. Simulation results of several scenarios are presented for illustration