线性时滞系统的离散最优控制

介绍了对线性时滞系统进行最优控制的设计，将具有时滞控制的线性系统离散后引入增广状态向量。获得不显含时滞的差分方程，根据时滞量的两种分类情况采用连续和离散形式的性能指标函数导出了最优控制律。控制律包含当前状态和此前若干步状态向量的叠加，最优控制律直接从时滞方程中得到，可保证系统的稳定性，此方法亦适用于大时滞的情况。数值算例验证了控制策略的有效性。

Discrete-time optimal control method for linear time-delay systems

A discrete-time optimal control method for linear systems with time-delay is proposed, in which a numerical algorithm for control implementation is presented. The controller is designed in terms of two cases that the time delay is respectively integer and non-integer times of the sampling period. The motion equation of system with time delay is transformed into standard discrete form that contains no time delay. Then, the optimal controller is designed by using the classical optimal control theory. The discrete quadratic function is used as objective function in design of the controller to guarantee good control efficiency on sampling points. In every step of computation of the deduced controller, it contains not only current step of state feedback but also linear combination of some former steps of control. Since the optimal controller is obtained directly from the time-delay differential equation, the control method proposed is prone to guarantee stability of the controlled structures. Instability in responses might occur if the system with time delay is controlled by the optimal controller designed with no consideration of time delay. Furthermore, the control method presented is available for the case of large time delay. Simulation results demonstrate that the continuous time performance index is superior to that of discrete-time and the control method presented ensures the stability of the controlled structures as well as the desired reduction in the maximum responses. The performance of the proposed control method under different sampling periods is investigated numerically to illustrate the feasibility for application to seismically excited linear systems.