Discrete-Time Optimal Control for Partially Unknown Nonlinear Systems with Asymmetry Input Constraints

This paper investigates the optimal control problem (OCP) of discrete-time nonlinear systems with asymmetry input constraints. First, a new cost function is designed to deal with asymmetry input constraints. Compared to existing cost functions for asymmetry input constraints, the designed cost function offers the advantage in guaranteeing the original optimality. Second, an approximate dynamic programming (ADP) method is developed to solve the investigated problem. The developed method can update the iterative control policy by utilizing historical data, eliminating the need for interaction with practical systems. This approach adds an extra layer of safety in preventing constraint violations. Third, we analyze the convergence and stability of the developed method with the designed cost function. At last, a simulation case is conducted to demonstrate the effectiveness of the developed method with the designed cost function in coping with asymmetry input constraints and guaranteeing the original optimality.