Kernel-Based Hamilton-Jacobi Equations for Data-Driven Optimal Control: The General Case

抄録

Recently, control theory using machine learning, which is useful for the control of unknown systems, has attracted significant attention. This study focuses on such a topic with optimal control problems for unknown nonlinear systems. Because optimal controllers are designed based on mathematical models of the systems, it is challenging to obtain models with insufficient knowledge of the systems. Kernel functions are promising for developing data-driven models with limited knowledge. However, the complex forms of such kernel-based models make it difficult to design the optimal controllers. The design corresponds to solving Hamilton-Jacobi (HJ) equations because their solutions provide optimal controllers. Therefore, the aim of this study is to derive certain kernel-based models for which the HJ equations are solved in an exact sense, which is an extended version of the authors' former work. The HJ equations are decomposed into tractable algebraic matrix equations and nonlinear functions. Solving the matrix equations enables us to obtain the optimal controllers of the model. A numerical simulation demonstrates that kernel-based models and controllers are successfully developed.