一类2-D不确定离散系统的弹性保成本控制

当被控系统的数学模型存在不确定性时,需要设计鲁棒控制器才能使得受控系统稳定,然而,如果控制器本身也存在不确定性时,系统就会变得复杂难以控制,使用传统的鲁棒控制方法很难达到期望的控制目标,甚至不能保证受控系统的稳定性.本研究就是针对当系统模型和控制器同时存在不确定性时,给出了设计稳定控制器的简便方法.通过将控制器的不确定性分别表示为加法式和乘法式摄动,研究了以上两种系统的弹性保成本控制问题,并给出了相应控制器的设计方法.在主要结果推导过程中,巧妙运用了各种矩阵不等式放缩和等价参数变换等数学方法,最终将主要结果表示为线性矩阵不等式(LMI),利用Matlab的LMI工具箱,可以很方便地设计所需要的控制器.最后,对同一个受控系统,分别施加利用本文结果和已有结果设计的控制器,发现前者可以很好地控制系统,而后者却不能使受控系统稳定,从而验证了所得结果的有效性.

Resilient guaranteed cost control for a class of 2-D uncertain discrete systems

When there exist uncertainties in the mathematical model of a controlled system, robust controller is needed to stabilize the controlled system. But if controller itself has uncertainties too, the controlled system will become complicated and difficult to control, at the same time, desirable control target is hard to achieve by traditional robust control methods, even stability can not be guaranteed either. For these reasons, the study was conducted to provide convenient methods to design stable controllers for those systems which have uncertainties in their models and controllers. By describing uncertainties as additive and multiplicative perturbations respectively, two resilient guaranteed cost control problems were considered, and the design methods for corresponding controllers were given simultaneously. During the study, the main results were expressed as LMIs by employing various mathematical techniques, such as zooms of matrix inequalities, equivalent parameter transformations etc. Using LMI tool box of Matlab software, it is very easy to design the appropriate controllers. Finally, through employing one controller designed by results in this paper and the other one designed by existed methods on the same controlled system, it is found that the former could stabilize the system perfectly, but the latter fails, which proveed the effectiveness of the derived results.