基于伪谱法的自由采样实时最优反馈控制及应用

摘要

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.%利用高斯伪谱法收敛速率快、精度高的特点,基于通用伪谱优化软件包在线求解非线性系统的最优控制问题.将伪谱反馈控制理论与非线性最优控制理论结合起来,给出了一种自由采样实时最优反馈控制算法,该算法通过连续在线生成开环最优控制的方式提供闭环反馈.考虑计算误差、模型参数不确定性和干扰的作用,假定系统状态方程右侧的非线性向量函数关于状态、控制和系统参数是Lipschitz连续的,利用Bellman最优性原理对闭环控制系统的有界稳定性进行了分析和理论证明.最后,以高超声速再入飞行器为应用对象,研究了其再入制导问题,仿真结果验证了该算法的可行性和有效性.