A data‐driven approximate solution to the model‐free HJB equation

A data‐driven approximate solution to the model‐free HJB equation It is generally impossible to analytically solve the Hamilton‐Jacobi‐Bellman (HJB) equation of an optimal control system. With the coming of the big‐data era, this paper first derives a new data‐driven and model‐free Hamilton function for the HJB equation. Then, a data‐driven tracking differentiator method is proposed to solve the Hamilton function. Finally, the simulation for a classic example shows that the optimal control policy can be approximated with the proposed method. Thus, an online data‐driven model‐free approximate solution to the HJB equation is achieved. This method is only driven by the measured system states. All other variables and derivatives can be derived from the data‐driven model‐free Hamilton function and tracking differentiator. The method has a complete mathematical support and works like a controller. It does not need neural networks and has no training or iterative convergence problem. Thus, this paper adds an online data‐driven model‐free method to the existing literature on the approximate solution to the HJB equation. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Optimal Control Applications and Methods Wiley

A data‐driven approximate solution to the model‐free HJB equation

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Publisher
Wiley Subscription Services, Inc., A Wiley Company
Copyright
Copyright © 2018 John Wiley & Sons, Ltd.
ISSN
0143-2087
eISSN
1099-1514
D.O.I.
10.1002/oca.2381
Publisher site
See Article on Publisher Site

Abstract

It is generally impossible to analytically solve the Hamilton‐Jacobi‐Bellman (HJB) equation of an optimal control system. With the coming of the big‐data era, this paper first derives a new data‐driven and model‐free Hamilton function for the HJB equation. Then, a data‐driven tracking differentiator method is proposed to solve the Hamilton function. Finally, the simulation for a classic example shows that the optimal control policy can be approximated with the proposed method. Thus, an online data‐driven model‐free approximate solution to the HJB equation is achieved. This method is only driven by the measured system states. All other variables and derivatives can be derived from the data‐driven model‐free Hamilton function and tracking differentiator. The method has a complete mathematical support and works like a controller. It does not need neural networks and has no training or iterative convergence problem. Thus, this paper adds an online data‐driven model‐free method to the existing literature on the approximate solution to the HJB equation.

Journal

Optimal Control Applications and MethodsWiley

Published: Jan 1, 2018

Keywords: ; ; ; ; ;

References

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