动态时延网络的镇定控制与自适应控制研究

Since time-delay dynamic networks can be expressed as the nonlinear system models of complicated forms and it presents abundant dynamic behaviors and application expectation, the research on such systems will become one heated topic in the control area more and more. Presently, as for studies on delay dynamic networks home and abroad, most results have used the techniques, such as integral inequality, free-weighting matrix and so on, much important information has been unconsidered when estimating the derivative of Lyapunov functional, which led to the conservatism, Based on the existent relevant results and methods, this project will use those effective tools such as primary matrix transformation and multi-Lyapunov functional to establish some novel results and both lower and upper bounds on delay derivative will be fully considered, which help to reduce the conservatism of the proposed results. The main contents of this project can be illustrated as follows: 1) through choosing some new Lyapunov functionals based on addressed systems, the global stabilization and its control will be studied for continuous-time delay dynamic networks and the east-to-test stability criteria and control design will be obtained; 2) as for the networks with uncertain delay and unknown delay parameters, the adaptive stabilization and its control will be discussed; 3) the cases including distribution delay and neutral one will be extended; 4) on the basis on above methods, the discrete-time case also will be extended. Overall, the results derived by this project will be less conservative and easy-to-test. Furthermore, some restriction conditions in present literatures will be removed, which can help to extend the application area of the obtained results.

时延动态网络是一种形式复杂的非线性系统模型, 具有丰富的动力学行为与研究前景，对该类系统的研究日益成为控制理论界的研究热点。目前国内外对于时延动态网络的研究，大都使用多重Lypunov泛函等方法，但往往在估计其导函数上界时，会丢失很多重要项，因而造成结论的保守性。本项目结合国内外的研究成果，基于初等变换矩阵、Kronecker 积等手段，建立新型的泛函，使得在对其进行分析时能够重现变时滞导数上界等重要信息，减小结论的保守性。主要研究内容如下：1通过初等变换矩阵设计新型的泛函，研究连续时延动态网络的全局镇定控制问题，获得了保守性较小且易于验证的稳定性判据及控制器；2对不确定时滞条件包含未知时延参数的时延动态网络，研究自适应镇定控制问题；3 加入分布与中立时延环节的结论；4将上述结论推广到离散域的系统。本项目不仅结论保守性较小，且所研究的系统模型去除了某些限制条件，较之以往结论更符合实践需要。

本项目针对动态时延网络分析时易丢失重要项的缺陷，通过初等变换矩阵设计新型的泛函，研究连续时延动态网络的全局镇定控制问题，获得了保守性较小且易于验证的稳定性判据及控制器；对不确定时滞条件包含未知时延参数的时延动态网络，研究自适应镇定控制问题；加入分布与中立时延环节的结论；将上述结论推广到离散域的系统。本项目不仅结论保守性较小，且所研究的系统模型去除了某些限制条件，较之以往结论更符合实践需要。