具有广义齐次性的非线性切换系统的镇定及正性化设计

This project intends to investigate the stabilization and positization design of switched nonlinear systems with generalized homogeneity. The research content includes the followings: to derive the conditions on the stability with positive property under arbitrary switchings and constraint switchings, respectively; when both stabilization and positization for each subsystem are not solvable by designing the individual control of subsystem, to seek the conditions on the stabilization and positization, and to simultaneously design both the individual controller for the subsystems and the switching signal to achieve both stabilization and positization; when the uncertainties exist in both the switching signal channel and the individual subsystem, to understand the uncertainties are how the impact of positization, and to study the robust design method for stabilization and positization. Also, the research results are expected to be applied to the consensus with positiveness of homogeneous multi-agent systems with switching topologies...The successful implementation of the proposed project will extend the scope of the study of switched systems, provide new methods for studying on switched nonlinear systems with generalized homogeneity, reveal the mechanism of the interaction between uncertainties and positization, and reveal the impact on the positization of the whole switched system when uncertainties existing in the switching signal channel and the individual subsystem, establish a variety criterions for stabilization and positization, obtain the design methods of both the controller and the switching law, and enrich and develop the theory of both switched systems and positive systems.

本项目研究具有广义齐次性的非线性切换系统的镇定及正性化设计问题。以具有广义齐次性结构的非线性切换系统为主要系统模型，研究内容包括：在任意切换信号和约束切换信号下切换系统带有正性的稳定性分析；在各子系统的镇定及正性化都不可解的前提下，研究在子系统控制器和切换信号双重设计下系统镇定及正性化的可解性条件和设计方案；当不确定性同时出现在切换信号通道和子系统的状态方程时，研究不确定性对切换系统正性化的影响规律，获得切换系统的鲁棒镇定及正性化的设计方案；将上述研究结果应用于具有切换拓扑结构的多智能体系统带有正性化的一致性控制。..项目的成功实施将扩大切换系统的研究范围，为切换系统的镇定及正性化研究提供一种全新的思路和方法，揭示不确定性对系统正性化的影响规律，获得系统可镇定及正性化的各种判据及控制器和切换信号的设计方法，进一步发展和完善切换系统理论和正系统理论。

由于切换系统广泛的应用背景及在实际中系统对正性的要求，对切换正系统的研究得到关注。为扩大切换系统的研究范围，获得切换系统的镇定及正性化方法，本项目研究了非线性切换系统的镇定及正性化设计问题。 在密切关注、分析、研究国内外相关研究发展状况基础上，以切换正系统为主要系统模型，研究切换正系统的稳定性分析与镇定设计，获得切换系统带有正性的稳定性条件及分析方案；提出在子系统控制器和切换信号双重设计任务下切换正系统可镇定的判据、设计方案及各种算法；发现不确定性、连续动态与离散动态之间的相互作用机理及对切换系统的正性、稳定性等性能的影响。 研究成果具有一定的创新性，丰富了切换系统的研究理论。.. 围绕上述研究，在本领域重要期刊和会议共发表和录用论文14篇，其中在国际SCI期刊上发表论文13篇，包括IEEE Transactions on Automatic Control 3篇、SCIENCE CHINA Information Sciences 1篇、IEEE/CAA Journal of Automatica Sinica 1篇。出版英文专著1部。培养硕士毕业生10人，在读硕士研究生7人。