Cooperative robust output regulation of linear uncertain multiple multivariable systems with performance constraint

This paper is to pursue a general investigation of cooperative robust output regulation for linear continuous-time multiple multivariable systems with unknown system parameters and unmodeled external disturbances. We show that, under standard minimum-phase and relative degree like assumptions, an internal model principle based output-feedback protocol can be constructed by incorporating suitable dynamic compensators, even when the parametric uncertainties are arbitrarily large in some sense. Moreover, we are able to establish a redesigned protocol by means of adapting the H∞ control method. It assures a desired robustness property for the closed-loop system of attenuating external unmodeled disturbances. Hence, our study offers a performance-constrained robust control solution in a distributed control fashion.

[1]  Markus Mueller,et al.  Normal form for linear systems with respect to its vector relative degree , 2009 .

[2]  Kevin L. Moore,et al.  Disturbance Attenuation in a Consensus Network of Identical Linear Systems: An $ {\cal H}_{\infty }$ Approach , 2014, IEEE Transactions on Automatic Control.

[3]  A. Isidori Nonlinear Control Systems , 1985 .

[4]  Frank L. Lewis,et al.  Adaptive cooperative tracking control of higher-order nonlinear systems with unknown dynamics , 2012, Autom..

[5]  Daizhan Cheng,et al.  Consensus of multi-agent linear dynamic systems† , 2008 .

[6]  Frank L. Lewis,et al.  Optimal Design for Synchronization of Cooperative Systems: State Feedback, Observer and Output Feedback , 2011, IEEE Transactions on Automatic Control.

[7]  Robert J. Plemmons,et al.  Nonnegative Matrices in the Mathematical Sciences , 1979, Classics in Applied Mathematics.

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

[9]  Eduardo D. Sontag,et al.  Mathematical Control Theory: Deterministic Finite Dimensional Systems , 1990 .

[10]  Giorgio Picci,et al.  A variational integrators approach to second order modeling and identification of linear mechanical systems , 2014, Autom..

[11]  Markus Mueller,et al.  Time-Varying Linear Systems: Relative Degree and Normal Form , 2007, IEEE Transactions on Automatic Control.

[12]  Wei Ren On Consensus Algorithms for Double-Integrator Dynamics , 2008, IEEE Trans. Autom. Control..

[13]  Yingmin Jia,et al.  Distributed robust Hinfinity consensus control in directed networks of agents with time-delay , 2008, Syst. Control. Lett..

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

[15]  Youfeng Su,et al.  Output Feedback Cooperative Control for Linear Uncertain Multi-Agent Systems With Nonidentical Relative Degrees , 2016, IEEE Transactions on Automatic Control.

[16]  Guanghui Wen,et al.  Distributed H ∞ consensus of multi-agent systems: a performance region-based approach , 2012, Int. J. Control.

[17]  Meirong Zhang,et al.  ${\cal H}_{\infty}$ Almost Output Synchronization for Heterogeneous Networks Without Exchange of Controller States , 2015, IEEE Transactions on Control of Network Systems.

[18]  Graziano Chesi,et al.  Robust Synchronization via Homogeneous Parameter-Dependent Polynomial Contraction Matrix , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[19]  Hyungbo Shim,et al.  Output Consensus of Heterogeneous Uncertain Linear Multi-Agent Systems , 2011, IEEE Transactions on Automatic Control.

[20]  Petros A. Ioannou,et al.  Robust Adaptive Control , 2012 .

[21]  Kiyotsugu Takaba,et al.  Robust Synchronization of Uncertain Linear Multi-Agent Systems , 2013, IEEE Transactions on Automatic Control.

[22]  Xudong Ye,et al.  Cooperative Output Regulation of Heterogeneous Multi-Agent Systems: An $H_{\infty}$ Criterion , 2014, IEEE Transactions on Automatic Control.

[23]  Lorenzo Marconi,et al.  Robust output synchronization of a network of heterogeneous nonlinear agents via nonlinear regulation theory , 2013, 52nd IEEE Conference on Decision and Control.

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

[25]  Huijun Gao,et al.  Network-Induced Constraints in Networked Control Systems—A Survey , 2013, IEEE Transactions on Industrial Informatics.

[26]  Tao Li,et al.  Consensus control for leader-following multi-agent systems with measurement noises , 2010, J. Syst. Sci. Complex..

[27]  Frank Allgöwer,et al.  An internal model principle is necessary and sufficient for linear output synchronization , 2011, Autom..

[28]  Zhong-Ping Jiang,et al.  A Distributed Control Approach to A Robust Output Regulation Problem for Multi-Agent Linear Systems , 2010, IEEE Transactions on Automatic Control.

[29]  Jan Lunze,et al.  Synchronization of Heterogeneous Agents , 2012, IEEE Transactions on Automatic Control.

[30]  Achim Ilchmann,et al.  Non-Identifier-Based High-Gain Adaptive Control , 1993 .

[31]  Xinghu Wang,et al.  Robust almost output consensus in networks of nonlinear agents with external disturbances , 2016, Autom..

[32]  Zhong-Ping Jiang,et al.  Decentralized nonlinear output-feedback stabilization with disturbance attenuation , 2001, IEEE Trans. Autom. Control..