Stochastic and adaptive optimal control of uncertain interconnected systems: A data-driven approach

This paper provides a novel non-model-based, data-driven stochastic H∞ control design for linear continuous-time stochastic interconnected systems with unknown dynamics. Our contributions are three-fold. First, we develop a tool to show how to assign an arbitrarily small input-to-output stochastic L2 gain of the closed-loop system, by combining the gain assignment technique with the zero-sum dynamic game-based H∞ control design. Second, robustness to dynamic uncertainties is tackled using the small-gain theory. Third, we develop a non-model-based stochastic robust adaptive dynamic programming (RADP) algorithm for adaptive optimal controller design. In sharp contrast to the existing methods, the obtained algorithm is based on value iteration (VI), and the knowledge of an initial stabilizing control policy is no longer needed. An example of a power electronic system is adopted to illustrate the obtained results.