Output-Feedback Homotopy-Based Policy Iteration for Performance Assurance of Unknown Linear Continuous-Time Systems

This study seeks to develop a data-driven output feedback homotopic policy iteration for assuring optimal performance of linear unknown continuous-time systems. Conventional policy iteration approaches often necessitate the availability of a stabilizing controller for initialization, posing constraints on output-feedback designs, particularly when dealing with partial measurements. To overcome such a constraint, we introduce a homotopy-based output-feedback policy iteration technique tailored for stabilizing continuous-time systems while guaranteeing performance. In comparison to the existing state-feedback result, a key difficulty arises due to the output-feedback framework only allows partial states for measurement, making full-state criteria insufficient. To address this issue, we make use of inputoutput data and a homotopic strategy, gradually adjusting a scalar, to compensate for the effect induced by the largest real part of the drift matrix concurrently fulfilling the criteria analogous to the state-feedback case. We validate the effectiveness of the proposed homotopy-based output-feedback policy iteration through a comprehensive case study.