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Optimal Strategies for Uncertain Differential Games with Applications

The major goal of this project is to develop and test ingenious solutions for controlling multiple unmanned vehicles having a common goal under the influence of external disturbances and uncertainties. The external disturbances can include winds (in the case of aerial vehicles), water currents (in the case of marine vehicles), traffic flow (in the case of self-driving cars). The difference in the actual and perceived behavior of other adversarial agents (asymmetric information) in the environment account to the uncertainties part of the research. More specifically, the project intends to find decentralized strategies for the players in a multi-player pursuit-evasion game with external disturbances and uncertainties using algorithms that are computationally efficient.

As a part of initial study, two-pursuer/single-evader pursuit-evasion problems with different information structures, assuming both pursuers to be superior to the evader in terms of their speed capabilities, and no external disturbances are examined. The time optimal evading strategies have been identified. The regions of non-degeneracy proposed in this research can be used to investigate the utility of employing two pursuers to more efficiently capture the evader. If the initial positions of the players are such that the problem is degenerate, then one of the pursuers does not play any role in the game, and the optimal evading strategy is pure evasion from the other pursuer. Optimal evading strategies against relay pursuit are also investigated by keeping one pursuer stationary. These results provide a potential framework for solving larger classes of multi-player time-optimal pursuit-evasion games under different information structures.

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Figure 1: Regions of degeneracy and non-degeneracy in the case of pursuers' strategy being constant bearing

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Figure 2: Regions of degeneracy and non-degeneracy in the case of pursuers' strategy being pure pursuit

Sponsors

This project is supported by NSF.

Selected Publications


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