On The Compensation Of Imperfect Information In Dynamic Games

A linear pursuit-evasion game with first-order acceleration dynamics and bounded controls is considered. In this game, the pursuer has to estimate the state variables of the game, including the lateral acceleration of the evader, based on the noise-corrupted measurements of the relative position vector. The estimation process inherently involves some delay, rendering the information structure of the pursuer imperfect. If the pursuer implements the optimal strategy of the perfect information game, an evader with perfect information can take advantage of the estimation delay. However, the performance degradation is minimised if the pursuer compensates for its own estimation delay by implementing the optimal strategy derived from the solution of the imperfect (delayed) information game. In this paper the analytical solution of the delayed information game, allowing to predict the value of the game, is presented. The theoretical results are tested in a noise-corrupted scenario by Monte Carlo simulations, using a Kalman filter type estimator. The simulation results confirm the substantial improvement achieved by the new pursuer strategy.