γ-Iterative Dual Heuristic Dynamic Programming for Nonlinear Critical Surfaces With Strong Constraints
针对强约束非线性曲面问题，提出γ迭代双启发式动态规划算法，用神经网络重构梯度关系，避免高维偏导计算，仿真验证了算法在岩土临界滑面求解中的有效性。
In this article, the critical value problem of a class of model-free nonlinear surfaces with strong constraints is studied, and a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\gamma }$ </tex-math></inline-formula>-iterative dual heuristic dynamic programming algorithm is proposed. Considering the high coupling of nonlinear surface and the algorithm structure of traditional dual heuristic dynamic programming, this article directly uses neural network to reconstruct the gradient relationship between adjacent strips of the Janbu segmentation method, so as to reduce the superdimensional calculation of partial derivatives still needed by first fitting the model. The critical value of the strongly constrained nonlinear surface is transformed into the optimal control law for solving the input-constrained nonquadratic HJB equation with discount factor <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\gamma }$ </tex-math></inline-formula> and the cofunction is defined to avoid the need to calculate the integral term in the repeated iterative process. Finally, the simulation results show that the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\boldsymbol {\gamma }$ </tex-math></inline-formula>-iterative dual heuristic dynamic programming algorithm is effective in solving the critical sliding surface of a kind of rock and soil mass.