Control of a Wheeled Vehicle Using the Viscosity Solution of the Hamiton-Jacobi Partial Differential Equation
Control of a Wheeled Vehicle Using the Viscosity Solution of the Hamiton-Jacobi Partial Differential Equation
复制标题
使用 Hamiton-Jacobi 偏微分方程的粘度解控制轮式车辆
DOI：
10.7210/jrsj.17.689
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
H. Nishitani
中科院分区：
文献类型：
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作者：
K. Imafuku;Y. Yamashita;H. Nishitani
为了构造非线性系统的最优调节器，我们需要求解一个哈密顿-雅可比偏微分方程（HJ-PDE）。然而，如果系统具有非完整约束，HJ-PDE有一个非光滑的解决方案，因为非光滑的最优成本函数。在这种情况下，粘性解，一个非光滑的弱解的HJ-PDE，本文中，我们处理的轮式车辆，这是一个非完整系统，并提出了一种数值方法来获得粘性解的HJ-PDE的动态规划原理（DPP）。DPP可用于获得HJ-PDE的非光滑解。我们还构造了一个最优控制律使用的HJ-PDE的粘度溶液的导数。仿真结果表明了该方法的有效性。
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.