执行器饱和的离散时间多智能体系统有限时域一致性控制  

Finite-horizon Consensus Control of Discrete-time Multi-agent Systems With Actuator Saturation

作　　者：王巍 王珂 黄自鑫 王乐君 穆朝絮 WANG Wei;WANG Ke;HUANG Zi-Xin;WANG Le-Jun;MU Chao-Xu(School of Information Engineering,Zhongnan University of Economics and Law,Wuhan 430073;School of Electrical and Information Engineering,Tianjin University,Tianjin 300072;School of Electrical and Information Engineering,Wuhan Institute of Technology,Wuhan 430205;School of Automation,Chongqing University of Posts and Telecommunications,Chongqing400065;Engineering Research Center of Autonomous Unmanned System Technology,Ministry of Education,Anhui University,Hefei 230601)

机构地区：[1]中南财经政法大学信息工程学院,武汉430073 [2]天津大学电气自动化与信息工程学院,天津300072 [3]武汉工程大学电气信息学院,武汉430205 [4]重庆邮电大学自动化学院,重庆400065 [5]安徽大学自主无人系统技术教育部工程研究中心,合肥230601

出　　处：《自动化学报》2025年第3期617-630,共14页Acta Automatica Sinica

基　　金：国家自然科学基金(62203009,62473003);安徽省重点研发计划(2022i01020013);安徽省高校协同创新计划(GXXT-2021-010);安徽省自然科学基金(2108085QF275)资助。

摘　　要：针对执行器饱和的离散时间线性多智能体系统(Multi-agent systems,MASs)有限时域一致性控制问题,将低增益反馈(Low gain feedback,LGF)方法与Q学习相结合,提出采用后向时间迭代的模型无关控制方法.首先,将执行器饱和的有限时域一致性控制问题的求解转化为执行器饱和的单智能体有限时域最优控制问题的求解,并证明可以通过求解修正的时变黎卡提方程(Modified time-varying Riccati equation,MTVRE)实现有限时域最优控制.随后,引入时变参数化Q函数(Time-varying parameterized Q-function,TVPQF),并提出基于Q学习的模型无关后向时间迭代算法,可以更新低增益参数,同时实现逼近求解MTVRE.另外,证明所提迭代求解算法得到的LGF控制矩阵收敛于MTVRE的最优解,也可以实现全局有限时域一致性控制.最后,通过仿真实验结果验证了该方法的有效性.A model-free control method using backward-in-time iteration by combining the low gain feedback(LGF)method with Q-learning is proposed for the finite-horizon consensus control problem for discrete-time linear multi-agent systems(MASs)with actuator saturation.First,the solution of the finite-horizon consensus control problem with actuator saturation is transformed into the solution of the finite-horizon optimal control problem of single agent with actuator saturation,and it is proved that the finite-horizon optimal control can be realized by solving the modified time-varying Riccati equation(MTVRE).Then,a time-varying parameterized Q-function(TVQPF)is introduced,and a model-free backward-in-time iteration algorithm based on Q-learning is proposed to update the low gain parameter and simultaneously approximate the solution of the MTVRE.In addition,it is demonstrated that the LGF control matrix obtained by the proposed iterative solution algorithm converges to the optimal solution of the MTVRE,and the global finite-horizon consensus control can also be realized.Finally,the effectiveness of the proposed method is verified by simulation results.

关 键 词：有限时域一致性控制 执行器饱和 Q函数 模型无关 多智能体系统 

分 类 号：TP13[自动化与计算机技术—控制理论与控制工程]