The system-theoretic perspective developed in this work can be applied to analyze other classes of data-driven control algorithms beyond policy iteration in the following ways:
Reinforcement Learning Algorithms: The system-theoretic analysis can be extended to analyze reinforcement learning algorithms such as deep Q-learning, actor-critic methods, and policy gradient algorithms. By modeling these algorithms as dynamical systems and studying their convergence properties, robustness, and performance guarantees, insights can be gained into their behavior and design principles.
Model Predictive Control (MPC): The system-theoretic perspective can be applied to analyze MPC algorithms in data-driven control settings. By examining the closed-loop dynamics of MPC systems, stability properties, and optimization convergence, the analysis can provide a deeper understanding of the interaction between the controller and the system dynamics.
Adaptive Control Strategies: The system-theoretic framework can be used to analyze adaptive control strategies that dynamically adjust controller parameters based on online data. By studying the convergence and robustness properties of adaptive algorithms, the analysis can guide the design of effective adaptive control schemes in data-driven settings.
By applying the system-theoretic perspective to a broader range of data-driven control algorithms, researchers can gain valuable insights into the underlying principles, limitations, and performance characteristics of these algorithms.