Cao Mengjuan, Liao Fucheng
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China ; School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing 100083, China.
School of Mathematics and Physics, University of Science and Technology Beijing, Beijing 100083, China.
ScientificWorldJournal. 2014 Jan 23;2014:965915. doi: 10.1155/2014/965915. eCollection 2014.
The linear discrete-time descriptor noncausal multirate system is considered for the presentation of a new design approach for optimal preview control. First, according to the characteristics of causal controllability and causal observability, the descriptor noncausal system is constructed into a descriptor causal closed-loop system. Second, by using the characteristics of the causal system and elementary transformation, the descriptor causal closed-loop system is transformed into a normal system. Then, taking advantage of the discrete lifting technique, the normal multirate system is converted to a single-rate system. By making use of the standard preview control method, we construct the descriptor augmented error system. The quadratic performance index for the multirate system is given, which can be changed into one for the single-rate system. In addition, a new single-rate system is obtained, the optimal control law of which is given. Returning to the original system, the optimal preview controller for linear discrete-time descriptor noncausal multirate systems is derived. The stabilizability and detectability of the lifted single-rate system are discussed in detail. The optimal preview control design techniques are illustrated by simulation results for a simple example.
本文考虑线性离散时间广义非因果多速率系统，以提出一种最优预见控制的新设计方法。首先，根据因果能控性和因果能观性的特点，将广义非因果系统构造为广义因果闭环系统。其次，利用因果系统的特性和初等变换，将广义因果闭环系统变换为正规系统。然后，利用离散提升技术，将正规多速率系统转换为单速率系统。通过使用标准预见控制方法，构建广义增广误差系统。给出了多速率系统的二次性能指标，该指标可转换为单速率系统的性能指标。此外，得到了一个新的单速率系统，并给出了其最优控制律。回到原系统，推导了线性离散时间广义非因果多速率系统的最优预见控制器。详细讨论了提升后的单速率系统的能稳性和能检测性。通过一个简单例子的仿真结果说明了最优预见控制设计技术。
