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.
Optimal Control Applications and Methods – Wiley
Published: Jan 1, 2018
Keywords: ; ; ; ; ;
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