Differential games involves multi-person decision making under conflicts in the context of dynamical systems. It has found its application on a large range of areas, including aeronautics, biology, ecology, economics, engineering, management science, operations research, etc. The decisions made by the players that join the differential game are susceptible to uncertainties that are pervasive in realistic differential game scenarios. The uncertainties that enters the system can be divided into three main categories, namely, exogenous/environmental uncertainties, endogenous/dynamical uncertainties and observation uncertainties. In this research, we provide methods to deal with environmental and dynamical uncertainties. In particular, we solve pursuit-evasion games under external flow fields to demonstrate how to cope with differential games under environmental uncertainties. We first recast the multiplayer pursuit-evasion problem into a relay pursuer-target assignment problem and utilize generalized Voronoi diagrams to guide the assignment. Then we present an analytical approach to solve a pursuit-evasion game in a linear flow field and a numerical approach that is based on reachability sets and the level set method to deal with pursuit-evasion games in general flow fields. Extension of our numerical approach towards 3-dimensional space and stochastic environmental disturbance are also discussed. Finally, we present an efficient algorithm to solve general differential game problems and extend to cases subject to stochastic dynamics to handle dynamical uncertainties.
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Pursuit-evasion and differential games under uncertainties
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