Adaptive cooperative output regulation of discrete-time linear multi-agent systems by a distributed feedback control law

An approach based on the discrete-time adaptive distributed observer was recently proposed to solve the cooperative output regulation problem for discrete-time linear multi-agent systems. The validity of this approach relies on the assumptions that the solution to the regulator equations is unique and all the eigenvalues of the leader's system matrix are inside or on the unit circle. In this paper, we will first establish the existence condition of the discrete-time adaptive distributed observer without assuming that the eigenvalues of the leader's system matrix are inside or on the unit circle. Then we will further extend the existing adaptive control approach to the case where the solution to the regulator equations may not be unique. The new results in this paper have enlarged the systems that can be handled by the existing approach. The effectiveness of the proposed approach will be illustrated by an example.

[1]  Bruce A. Francis,et al.  The internal model principle of control theory , 1976, Autom..

[2]  Jie Huang,et al.  The Cooperative Output Regulation Problem of Discrete-Time Linear Multi-Agent Systems by the Adaptive Distributed Observer , 2017, IEEE Transactions on Automatic Control.

[3]  Guoqiang Hu,et al.  The adaptive distributed observer approach to the cooperative output regulation of linear multi-agent systems , 2017, Autom..

[4]  Jie Huang,et al.  Cooperative Output Regulation of Linear Multi-Agent Systems , 2012, IEEE Transactions on Automatic Control.

[5]  Jie Huang,et al.  A Discrete-Time Recurrent Neural Network for Solving Rank-Deficient Matrix Equations With an Application to Output Regulation of Linear Systems , 2018, IEEE Transactions on Neural Networks and Learning Systems.

[6]  Jie Huang,et al.  Nonlinear Output Regulation: Theory and Applications , 2004 .

[7]  Jiangping Hu,et al.  Leader-following coordination of multi-agent systems with coupling time delays , 2007, 0705.0401.

[8]  E. Davison.  The robust control of a servomechanism problem for linear time-invariant multivariable systems , 1976 .

[9]  Jie Huang,et al.  The Leader-Following Consensus for Multiple Uncertain Euler-Lagrange Systems With an Adaptive Distributed Observer , 2016, IEEE Transactions on Automatic Control.

[10]  Jie Lin,et al.  Coordination of groups of mobile autonomous agents using nearest neighbor rules , 2003, IEEE Trans. Autom. Control..

[11]  B. Francis.  The linear multivariable regulator problem , 1976, 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes.

[12]  C. Desoer,et al.  Linear Time-Invariant Robust Servomechanism Problem: A Self-Contained Exposition , 1980 .

[13]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[14]  Jie Huang,et al.  Cooperative output regulation of multi-agent systems , 2012, Proceedings of the 10th World Congress on Intelligent Control and Automation.

[15]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[16]  Jie Huang,et al.  Cooperative output regulation of discrete-time linear time-delay multi-agent systems , 2016 .