Adaptive Optimal Control for Input-constrained Nonlinear Discrete-time System With Stage Cost Learning

This paper investigates the problem of input-constrained optimal control for nonaffine nonlinear discrete-time systems in the presence of an inaccurate model. To address this problem, a bounded function is used to convert the input-constrained optimal control problem into an unconstrained counterpart. Additionally, an optimal stage cost function is introduced to quantify the discrepancy between the inaccurate model and the true system dynamics. Subsequently, a policy iteration based stage cost learning (PISCL) algorithm is proposed to obtain the optimal stage cost function and the convergence of the algorithm is proved. The proposed approach provides a new framework for addressing input-constrained control problems of nonaffine nonlinear systems with an inaccurate model, bridging the gap between model-based and data-based approximate dynamic programming techniques. Numerical experiments validate the effectiveness of the PISCL algorithm in obtaining the constrained optimal control policies for nonaffine nonlinear discrete-time systems without precise system models.