Pseudospectral-based free sampling real-time optimal feedback control and its application
基于伪谱法的自由采样实时最优反馈控制及应用

Owing to fast convergence and high accuracy of Gauss pseudospectral method, we solve nonlinear optimal control problems subject to constraints by online using the general pseudospectral optimization software (GPOPS). Combining pseudospectral feedback control with nonlinear optimal control, we develop a real-time optimal feedback control algorithm with free sampling frequency, which continuously generates the open-loop optimal control for closed-loop feedback control application. Considering computational errors, model parameter uncertainties and disturbances, and assuming that the nonlinear vector function in the system state-equation is Lipschitz continuous on states, controls and parameters, we prove the bounded stability of the closed-loop control systems by using the principle of Bellman optimality. The above algorithm has been applied to solve reentry guidance problems for hypersonic vehicles. Simulation results show the validity of the algorithm.