线性系统反馈镇定的时滞裕度理论研究

Time delay system can describe control objects of most engineering practice. As one of the important research area on the theory and application of control, feedback stabilization of time-delay systems has attracted attentions from scholars in and abroad. Among them, the delay margin, which describing a system can be stabilized, is a direct reflection of controller merit and a important factor affecting the implementation of a project. It is worth noting that the existing results only examine the case of continuous systems with constant input delay, without other time delay and other system types, this have obvious limitations. As for linear system with constant input delay, the applicant and collaborator have excellently solved the calculation problem of time delay margin of feedback stabilization. This project will be based on the previous work, focus on continuous systems and/or discrete systems with time-varying input time-delay, adopt static/dynamic feedback control, based on frequency domain theory, small-gain theory, stability theory, and integral inequality, to study the stability of closed-loop control system, and provide a effective method to calculate the delay margin. Finally, the proposed method is applied to the consensus of the multi-agent system, which will provide some technical support and theoretical guarantee for the related applications.

时滞系统可以描述大量工程中的控制对象，作为控制理论及应用的一个重要研究领域，时滞系统的反馈镇定已得到了国内外学者的广泛关注。其中刻画系统可被反馈镇定的时滞裕度，更是能直接反映控制器的优劣、影响工程完善实施的重要因素。值得注意的是，已有结果仅考察了含定长输入时滞的连续系统情形，对其他时滞和系统类型还没有涉及，这具有明显的局限性。针对含定常输入时滞的线性系统，申请人和合作者利用所提出的双线性变换方法，已很好地解决其反馈镇定时滞裕度的计算问题。本项目将在前期工作的基础上，重点针对含时变输入时滞的连续系统和/离散系统，采取静态/动态反馈控制，利用频域理论、小增益原理、稳定性理论、以及积分不等式等方法，研究闭环控制系统稳定性，并设计有效的时滞裕度计算方法。最后将所提出的方法用于多智能体系统的趋同控制中，期望为相关应用提供一定的技术支持和理论保证。

研究线性系统中与时滞界限有关的控制和优化问题。在前面我们研究线性系统含多个不稳定实极点，和多个不稳定虚极点，获得时滞界限的基础上。项目主要考察了含有两个不稳定极点的线性系统，在采用经典的PID控制时，系统能被镇定时，时滞的最大时滞界限。给出了系统可镇定的充要条件，即在所求出的时滞界限内，系统都存在一个PID控制器使得系统可镇定。相反的，若系统可被一PID控制器镇定，则其时滞一定在所求出的时滞界限内。.其次，对含有时滞线性系统的最优控制和鲁棒线性二次微分博弈等问题进行研究。另外，还针对一般性的大系统和博弈问题作探讨。研究了一类控制受限大系统的控制和镇定问题，得到系统可控和可镇定的充要条件。还研究了控制信息部分分享的随机博弈问题。在含外界未知干扰的博弈问题，给出其最优线性反馈策略。.