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Kernel-Based Hamilton-Jacobi Equations for Data-Driven Optimal and H-Infinity Control
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DOI：10.1109/ACCESS.2020.3009357.png)
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摘要
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This paper presents a data-driven method for designing optimal controllers and robust controllers for unknown nonlinear systems. Mathematical models for the realization of the control are difficult to develop owing to a lack of knowledge regarding such systems. The proposed multidisciplinary method, based on optimal control theory and machine learning with kernel functions, facilitates designing appropriate controllers using a data set. Kernel-based system models are useful for representing nonlinear systems. An optimal and an H-infinity controller can be designed by solving Hamilton-Jacobi (HJ) equations, which unfortunately, are difficult to solve owing to the nonlinearity and complexity of the kernel-based models. The objective of this study consists of overcoming two challenges. The first challenge is to derive exact solutions to the HJ equations for a class of kernel-based system models. A key technique in overcoming this challenge is to reduce the HJ equations to easily solvable algebraic matrix equations, from which optimal and H-infinity controllers are designed. The second challenge is to control an unknown system using the obtained controllers, wherein the system is identified as a kernel-based model. Additionally, this study analyzes probabilistic stability of the feedback system with the proposed controllers. Numerical simulations demonstrate control performances of both the derived optimal and H-infinity controllers and stability of the feedback system.
Keyword:
Mathematical model
Optimal control
Kernel
Computational modeling
Nonlinear dynamical systems
Gaussian processes
H-infinity control
optimal control
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期刊
IF:
3.6
论文数:
9.8W
被引数:
29.4W
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