A test platform for cognitive delays: target tracking problem with multiple time-delayed feedback control

Abstract

This paper studies a baseline 2-dimensional (2-D) target tracking problem from a new perspective. The dynamics entail two rationally independent time delays in an otherwise traditional feedback controller. A pursuer tries to track a moving target. When there are no time delays, capture is enabled using any stable control logic (for instance, LQR). If there are different delays in the sensing of position and velocity of the target, however, 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 recent cluster treatment of characteristic roots (CTCR) paradigm. It declares the complete stability outlook in the domain of the two delays. This method starts with the determination of all the potential stability switching curves in the domain of the delays. For this, a recent concept called the “spectral delay space (SDS)” is used. As a paradoxical outcome of this work, we show that the stability of the dynamics can be recovered by increasing the delays. The paper is accompanied by an interactive MATLAB-based game which is also available online.