Nonlinear Control of Partially Unknown Systems based on Reinforcement Learning and Polynomial Representation

Yuta Tsuge, Kazuyuki Hyodo, Tatsuo Narikiyo, Michihiro Kawanishi, and Tanagorn Jennawasin


Reinforcement learning, polynomial system, Lyapunov function


This paper considers the problem of designing a controller for partially unknown plants. The new design method we propose is based on reinforcement learning and polynomial system representation. State space is divided into unknown space and polynomial space where the state equations are locally written by polynomial system. Stabilizing controller and domain of attraction in the polynomial space is derived from polynomial or rational Lyapunov functions. In the unknown space a reinforcement learning controller is synthesized by SARSA method. Reward of the reinforcement learning is given by Lyapunov function which is derived in the synthesis of stabilizing controller of the polynomial system. Since the reinforcement learning is driven by the Lyapunov function, the reinforcement learning controller can be connected to the stabilizing controller of the polynomial plant seamlessly on the domain of attraction. To demonstrate the usefulness and validity of the proposed method we apply to the stabilizing control of the Furuta pendulum.

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