The Homicidal Chauffeur Problem with Multiple Time Delayed Feedback

Abstract

This paper studies a conventional pursuit-evasion game within a new perspective. The dynamics entail two rationally independent time delays in the otherwise traditional feedback controller. A pursuer (the homicidal chauffeur) tries to capture an evasive victim in a 2-dimensional space. When there are no time delays, capture is enabled using an LQR optimal control logic. When we introduce two delays in the measurement of position and velocity of the evader the performance of the pursuit changes dramatically. We explore the stability of the dynamics for a broad range of delay compositions. An exhaustive and exact determination of those stable delay combinations is achieved using The Cluster Treatment of Characteristic Roots (CTCR) paradigm. Under those conditions the capture of the evader by the pursuer is guaranteed. As a paradoxical outcome of this work, it is shown that the stability of the system can be recovered by increasing the delays. The paper is accompanied by an interactive MATLAB demo which will be at the disposal of the attendees.