A learning-based value iteration scheme for singularly perturbed systems and its application in RC ladder circuit

• The value-iteration-based guaranteed convergence control scheme is presented. • The learning-based approach can obtain a more accurate controller. • The proposed scheme is particularly suitable for practical engineering systems with high complexity or uncertainty. • The designed scheme is implemented through a data-driven approach. In this paper, a value iteration (VI) scheme considering the guaranteed state convergence rate (GSCR) is proposed for multi-input singularly perturbed systems (MISPSs) with unknown system dynamics. Unlike traditional reduced-order methods, a full-order modeling approach is adopted for MISPSs, thereby avoiding the suboptimality of reduction techniques. In contrast to classical differential games, this work explicitly considers the state convergence rate under multiple interacting inputs. Specifically, the control policy design is formulated as solving a guaranteed game algebraic Riccati equation (GGARE). To solve GGARE, an online model-free VI algorithm is developed, which obtains the solutions to Nash equilibrium in real-time using measured state and input data. Compared to existing algorithms, the proposed algorithm offers three key advantages: i) No initial stable control gain is needed; ii) Rapid state convergence is achieved; iii) The information on system dynamics is not required. Finally, the effectiveness of the proposed method is validated through an RC ladder circuit example.