分数阶时滞非线性多智能体系统的自适应控制

Adaptive control of fractional order delay nonlinear multi-agent systems

中文关键词  分数阶多智能体系统  一致性  时滞  自适应控制  分数阶Halanay不等式稳定性定理

英文关键词  fractional multi-agent system  uniformity  delay: adaptive control  fractional Halanay inequality stability theorem

中文摘要

      针对分数阶多智能体系统中存在时滞和非线性特性, 时滞往往会引起控制系统的性能下降甚至出现系统 不稳定等问题, 提出了一种含时滞非线性的分数阶多智能体系统自适应控制方法. 对于多智能体系统的控制协议, 设计了基于领导者和相邻智能体状态信息的自适应控制协议, 减小了过大常数控制增益带来的能源浪费. 对于一 致性, 利用图论基础、分数阶Halanay不等式稳定性定理、Kronecker积和Schur补引理, 获得了分数阶时滞非线性多 智能体系统的LMI一致性条件. 仿真结果验证了本文算法的正确性和有效性. 由于整数阶系统是分数阶系统的特殊 形式, 本文结论可以直接推广到整数阶多智能体系统中.

英文摘要

      For the problems of time delay and nonlinearity in fractional order multi-agent system, which often leads to the performance degradation and even system instability of the control system, an adaptive control method for fractional order multi-agent system with time delay nonlinearity is proposed. For the control protocol of multi-agent system, an adaptive control protocol based on the state information of leaders and adjacent agents is designed to reduce the energy waste caused by too large constant control gain. For consistency, the LMI consistency conditions of fractional delay nonlinear multi-agent systems are obtained by using the basis of graph theory, the stability theorem of fractional Halanay inequality, the Kronecker product and the Schur complement lemma. Simulation results verify the correctness and effectiveness of the proposed algorithm. Because integer order system is a special form of fractional order system, the conclusion of this paper can be directly extended to the integer order multi-agent system.