A gradient-enhanced functional tensor train cross approximation method for the resolution of the Hamilton-Jacobi-Bellman (HJB) equations associated to optimal feedback control of nonlinear dynamics is presented. The procedure uses samples of both the solution of the HJB equation and its gradient to obtain a tensor train approximation of the value function. The collection of the data for the algorithm is based on two possible techniques: Pontryagin Maximum Principle and State Dependent Riccati Equations. Several numerical tests are presented in low and high dimension showing the effectiveness of the proposed method and its robustness with respect to inexact data evaluations, provided by the gradient information. The resulting tensor train approximation paves the way towards fast synthesis of the control signal in real-time applications.
翻译:该程序使用HJB方程式及其梯度的解决方案样本,以获得价值函数的数列列近似值。为算法收集的数据以两种可能的技术为基础:Pontryagin 最大原理和州Dependent Riccati Equation。若干数字测试以低高尺度进行,显示拟议方法的有效性及其在梯度信息提供的不精确数据评价方面的稳健性。由此产生的高压列近似值为快速合成实时应用的控制信号铺平了道路。