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

Abstract

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.