Robust Policy Iteration of Uncertain Interconnected Systems with Imperfect Data

This paper investigates the robust optimal control problem of a class of continuous-time, partially linear, inter- connected systems. In addition to the dynamic uncertainties resulted from the interconnected dynamic system, unknown bounded disturbances and computational errors are taken into account throughout the learning process, wherein the system’s dynamics are also assumed unknown. These challenges lead the collected online data to be imperfect. In this scenario, traditional data-driven control techniques, such as adaptive dynamic programming (ADP) and robust ADP, encounter a challenge in learning the optimal control policy precisely due to imperfect data. In this paper, a novel data-driven robust policy iteration method is proposed to solve the robust optimal control problems. Without relying on the knowledge of the system’s dynamics, the external disturbances or the complete state, the implementation of the proposed method only needs to access the input and partial state information. Based on the small-gain theorem, the notions of strong unboundedness observability and input-to-output stability, it is guaranteed that the learned robust optimal control gain is stabilizing and that the solution of the closed-loop system is uniformly ultimately bounded despite the existence of dynamic uncertainties and unknown external disturbances. The simulation results reveal the efficiency and practicality of the proposed data-driven control method.