γ-Iterative Dual Heuristic Dynamic Programming for Nonlinear Critical Surfaces With Strong Constraints

In this article, the critical value problem of a class of model-free nonlinear surfaces with strong constraints is studied, and a
$\boldsymbol {\gamma }$
-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
$\boldsymbol {\gamma }$
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
$\boldsymbol {\gamma }$
-iterative dual heuristic dynamic programming algorithm is effective in solving the critical sliding surface of a kind of rock and soil mass.