不确定时滞系统的全局鲁棒最优滑模控制

针对一类不确定性时滞系统, 研究线性二次型最优调节器的鲁棒性设计问题. 首先基于级数近似方法, 将原标称时滞系统的最优调节器问题转化为迭代求解一族不含时滞的两点边值问题, 从而获得标称时滞系统最优控制的近似解. 然后将滑模控制理论应用于最优调节器的设计, 使得系统对于不确定性具有全局的鲁棒性, 并且其理想滑动模态与标称系统的最优闭环控制系统相一致, 从而实现了全局鲁棒最优滑模控制. 仿真示例将所提出的方法与相应的二次型最优控制进行比较, 验证了该方法的有效性和优越性.

Global robust optimal sliding-mode control for uncertain systems with time-delay

The design problem of robust optimal linear quadratic regulators(LQRs) for a class of uncertain systems with time-delay is considered. By using a series-based approximation approach, we transform the solution of a LQR problem into an iterative solution of a linear two-point-boundary-value problem without time-delay. After the approximate solution to the LQR problem for the original system with time-delay is obtained, we apply the sliding-mode control theory to design the LQR controller. Thus, a global robust optimal sliding-mode control(GROSMC) system is developed. This system is globally robust to uncertainties, and maintains the same sliding-mode dynamics as the original optimal LQR system. The simulation results of the proposed approach are compared with those of the original optimal LQR, successfully demonstrating the efficiency and other advantages of the proposed approach.