Output-Feedback Stabilizing Policy Iteration for Convergence Assurance of Unknown Discrete-Time Systems with Unmeasurable States

This note proposes a data-driven output-feedback stabilizing policy iteration for unknown linear discrete-time systems with unmeasurable states. Existing policy iteration methods for optimal control must start from a stabilizing control policy, which is particularly challenging to obtain for unknown systems, especially when states are unavailable. In such cases, it is more difficult to guarantee stability and convergence performance. To address this problem, an output-feedback stabilizing policy iteration framework is developed to learn closed-loop stabilizing control policies while ensuring convergence performance. Specifically, cumulative scalar parameters are introduced to compress the original system to a stable scale. Then, by integrating modified policy iteration with parameter update rules, the system is gradually amplified/restored to the original system while preserving stability such that the stabilizing control policy is obtained. The entire process is driven solely by input-output data. Moreover, a stability analysis is provided for output-feedback. The proposed approach is validated by simulations.