Solutions of Continuous-Time Preview Two-Player Differential Games

Abstract

The continuous-time two-player preview game problems are studied in this paper. A preview game problem is formulated when the input signals generated by one of the two players are delayed (e.g., by actuator dynamics), and are previewed by the other player. In accordance with the control terminology, these two players are referred to as the control player and the disturbance player, respectively. Both control-advantaged and disturbance-advantaged game solutions are presented. When the solution of an infinite horizon problem exists, the response of the closed-loop system can be analyzed in the frequency domain. A vehicle handling problem is used as an example for the analysis. It is shown that the preview action of the advantaged player effectively reduces the authority of the disadvantaged player, and results in significantly improved performance compared with feedback-only game algorithms.