时变正系统稳定性理论及其在多智能体协同控制中的应用

In the real world, many systems are time varying. The dynamic properties of time-varying positive systems are much more complicated than that of the time-invariant systems. As one of the most important dynamic characteristics, the study of the stability of time-varying systems has important theoretical significance and practical value. This project will intensively study stability and practical stability of time-varying positive systems, and meanwhile explore its application in the cooperative control of multi-agents. The planned research contents include as follows: Based on the Copositive Lyapunov functional method, it plans to establish asymptotic stability criteria for linear and nonlinear time-varying positive systems in both continuous-time and discrete-time cases, and the effect of time-varying delay on the stability of the system will be explained clearly. By using the non-Lyapunov functional method such as differential inequality and comparison principle, practical stability criteria for linear and nonlinear time-varying positive systems will be given. Finally, it plans to extend the corresponding theory to the general time-varying system and build the inherent relation between stability of time-varying systems and consensus of multi-agent systems, and then discuss the consensus problem of multi-agent systems from a new point of view. The project will further complement and improve the stability theory of time-varying systems, and provide an effective theoretical tool for the cooperative control of multi-agent systems.

现实中很多系统都是时变的，时变系统的动力学性质远比定常系统复杂，而稳定性又是系统的非常重要的动力学特性。因此，研究时变系统的稳定性具有重要的理论意义和实际应用价值。本项目将重点针对时变正系统的渐近稳定性和实用稳定性进行深入研究，同时探索相关理论在多智能体协同控制中的应用。拟研究的内容包括：基于余正Lyapunov函数方法，分别在连续时间和离散时间情形下，建立线性和非线性时变正系统的渐近稳定性准则，并解释时变时滞对系统稳定性的影响机理；基于微分不等式和比较原理等非Lyapunov函数方法，分别得到线性和非线性时变正系统的实用稳定性准则；最后，拓展相关理论成果到一般时变系统，构建其稳定性和多智能体系统一致性之间的内在联系，从新的角度探讨多智能体系统的一致性问题。本项目的研究将进一步丰富和完善时变系统的稳定性理论体系，为多智能体系统的协同控制提供有效的理论工具。

现实中很多系统都是时变的，时变系统的动力学性质远比定常系统复杂，而稳定性又是系统的非常重要的动力学特性。因此，研究时变系统的稳定性具有重要的理论意义和实际应用价值。正系统是现实世界中普遍存在的一类系统，其在很多领域具有重要的应用。相比于时不变正系统，时变正系统的稳定性要复杂的多且具有十分重要的理论意义和实际应用价值。本项目聚焦几类时变正系统的渐近稳定性和实用稳定性开展深入研究，并探索其在多智能体系统一致性问题中的应用。首先，基于余正Lyapunov函数方法，建立线性和非线性切换正系统渐近稳定和实用稳定的新准则，并在子系统不稳定的前提下刻画切换信号对系统稳定性的影响机理。其次，基于微分不等式和比较原理等非Lyapunov函数方法，得到线性和非线性切换正系统渐近稳定和实用稳定的新判据。最后，拓展相关理论成果到非正时变系统，构建时变正系统和多智能体系统之间的内在联系，进而从新的角度探讨多智能体系统的一致性问题。本项目的研究成果丰富和完善了时变正系统的稳定性理论体系，为多智能体系统的分布式协同控制提供有效的理论工具。