A design method with differentiability for optimal control problems with non-differential Hamilton-Jacobi equations

3rd International Conference on Manufacturing, Optimization, Industrial and Material Engineering

Imae, Joe^1 ; Kanda, Norito^1 ; Kobayashi, Tomoaki^1

Osaka Prefecture University, Osaka, Japan^1

关键词: Design method;    Design process;    Differentiability;    Hamilton Jacobi equations;    Non-differentiable;    Optimal control problem;    Optimal Feedback;   

Others  :  https://iopscience.iop.org/article/10.1088/1757-899X/83/1/012009/pdf
DOI  :  10.1088/1757-899X/83/1/012009

来源: IOP

【 摘 要 】

As far as optimal feedback controllers for nonlinear systems are concerned, Hamilton-Jacobi(HJ) equations play a key role in the design process. However, we sometimes meet the HJ equations in non-differential situations, which are extremely difficult to solve analytically/numerically. This paper proposes a simple design method to attack such optimal control problems using differentiable solutions of the associated HJ equations. By simulation, we demonstrate the proposed method useful in a non-differentiable situation.