A Nonlinear Critical Surface With Input Constraints on Costate-Adaptive Dynamic Programming

Abstract

In this brief, a costate-adaptive dynamic programming algorithm is presented to solve a class of nonlinear critical surface problems with input constraints. Different from the traditional-dual heuristic dynamic programming, costate-ADP does not rely on the exact system model, and can incubate the model-neural network through data catalysis, avoiding the super-dimensional calculation in the iterative process. Furthermore, the critical nonlinear surface with input constraints is transformed into the optimal action sequence for solving the non-quadratic HJB equation with discount factor. The costate function replaces the integral term in the repeated iterations. The algorithm is proved to be effective in determining the security properties of a class of structures.