Nonlinear Optimal Control With Control Constraints Based on FBDEs and Its Application to AGV

This article focuses on optimal control problems for a class of continuous-time affine nonlinear systems with control constraints. Most of the existing optimal control algorithms face challenges in achieving a balance between computational efficiency and control performance. To address this problem, first, the nonlinear optimal control problem is transformed into a novel optimization problem with the aid of forward and backward differential equations derived from the maximum principle, where the constraints are addressed through the introduction of a nonquadratic function. Second, an innovative and effective algorithm for solving optimal control is proposed based on the concept of receding horizon control. This algorithm offers the potential advantage of reducing the dimensionality of optimization problems. Finally, the proposed algorithm is applied for the trajectory tracking control of automated guided vehicles. Simulation and experimental results demonstrate that this control scheme achieves accurate tracking and exhibits high computational efficiency compared to the existing methods.