基于网络上的动力系统的性能优化

This subject mainly studies the performance optimization for the (impulsive) multi-agent systems and the systems based on complex network by using of the method of the Pontryagin’s Minimum Principle, calculus of variations, dynamic programing and differential game theory. Firstly, we explore the optimal finite-time consensus for the generalized second-order multi-agent systems by using the optimal control theory. Secondly, we bring together stability and the inverse optimality theory to discuss the optimal consensus or synchronization for the impulsive multi-agent systems and the dynamic systems based on complex network. Moreover, we study the optimal tracker case for the leader-following systems. Lastly, in the case of performance for an individual agent, we investigate the Stackelberg strategy so as to make all the agents reach the state of the leader based on differential game theory.

本课题主要是利用庞特里亚金极值原理、变分法、动态规划、逆最优控制理论及微分博弈论等方法讨论（脉冲）多智能体系统和复杂网络系统的优化控制问题。首先, 我们利用最优控制理论探讨二阶广义多智能体系统的有限时间最优一致性控制策略；其次，我们综合利用稳定性理论和逆最优控制理论研究脉冲多智能体系统及复杂网络系统的最优一致性或同步性，进一步地，探讨有领导者的最优跟踪控制问题；最后我们针对每个个体分别设计相应的代价函数或效用函数的情形，利用微分博弈理论寻求Stackelberg策略同时保证所有个体与领导者达到同步状态。

基于庞特里亚金极值原理、变分法、动态规划、逆最优控制理论等方法，本课题探讨了（脉冲）多智能体系统和复杂网络系统的优化控制问题。首先, 我们利用稳定性理论和逆最优控制理论研究一阶脉冲多智能体系统及复杂网络系统的最优一致性或同步性，进一步地，我们探讨了具有脉冲效应的一阶多智能体系统L2增益性能分析；最后我们探讨了复杂网络SIS传染病模型最优反馈机制及随机斑块传染病模型的动力学行为。项目组成员在受资助期间共发表作学术论文12篇，其中SCI检索10篇，另有1篇为EI检索。