Abstract
To construct an optimal regulator for nonlinear systems, we need to solve a Hamilton-Jacobi partial differential equation (HJ-PDE) . However, if the system has nonholonomic constraints, the HJ-PDE has a nonsmooth solution because of the nonsmoothness of the optimal cost function. In such a case, the viscosity solution, a nonsmooth weak solution of the HJ-PDE, is obtained.
In this paper, we deal with a wheeled vehicle, which is a nonholonomic system, and propose a numerical method to achieve a viscosity solution of the HJ-PDE using the dynamic programming principle (DPP) . The DPP can be applied to acquire a nonsmooth solution of the HJ-PDE. We also construct an optimal control law using derivatives of the viscosity solution of the HJ-PDE. The effectiveness of the proposed method is shown through simulations.
