Prescribed-rate target tracking for time-delayed systems using output measurements

This paper investigates target tracking systems with input time delays using output measurements and reinforcement learning to ensure tracking performance at a prescribed rate. We demonstrate that the delayed tracking problem can be addressed within the framework of robust output regulation theory by incorporating the desired convergence rate. The solution involves tackling two learning-based tasks: developing an optimal control policy to achieve the prescribed rate of convergence and predicting the system's future state to compensate for input delays. Our approach, called Future State Prediction by Input-Output Measurements, unifies input time delays and output-feedback tracking under a single framework. Using output regulation theory, the prescribed control policy is determined, while the system's future state is estimated from historical data. Based on this, we propose off-policy reinforcement learning algorithms for time-delayed tracking that rely solely on output measurements, without requiring an accurate system model. Numerical results confirm the effectiveness of the proposed algorithms for target tracking.