H ∞ consensus control of multi-agent systems with input delay and directed topology

In this study, the consensus problem for linear multi-agent systems with general directed graph in the presence of constant input delay and external disturbances is addressed. To deal with input delay, a truncated prediction of the agent state over the delay period is approximated by the finite-dimensional term of the classical state predictor. The truncated predictor feedback method is used for the consensus protocol design. By exploring certain features of the Laplacian matrix, the H ∞ consensus analysis is put in the framework of Lyapunov analysis. The integral terms that remain in the transformed systems are carefully analysed using Krasovskii functional. Sufficient conditions are derived for the multi-agent systems to guarantee the H ∞ consensus in the time domain. The feedback gain is then designed by solving these conditions with an iterative linear matrix inequality procedure. A simulation study is carried out to validate the proposed control design.

[1]  O. J. M. Smith,et al.  A controller to overcome dead time , 1959 .

[2]  A. Olbrot,et al.  Finite spectrum assignment problem for systems with delays , 1979 .

[3]  Wook Hyun Kwon,et al.  Feedback stabilization of linear systems with delayed control , 1980 .

[4]  Z. Artstein.  Linear systems with delayed controls: A reduction , 1982 .

[5]  Dirk Roose,et al.  Limitations of a class of stabilization methods for delay systems , 2001, IEEE Trans. Autom. Control..

[6]  Vladimir L. Kharitonov,et al.  Stability of Time-Delay Systems , 2003, Control Engineering.

[7]  Richard M. Murray,et al.  Information flow and cooperative control of vehicle formations , 2004, IEEE Transactions on Automatic Control.

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

[9]  William S. Levine,et al.  The Control Handbook , 2010 .

[10]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[11]  Jiangping Hu,et al.  Tracking control for multi-agent consensus with an active leader and variable topology , 2006, Autom..

[12]  Zongli Lin,et al.  On Asymptotic Stabilizability of Linear Systems With Delayed Input , 2006, IEEE Transactions on Automatic Control.

[13]  Kevin L. Moore,et al.  High-Order and Model Reference Consensus Algorithms in Cooperative Control of MultiVehicle Systems , 2007 .

[14]  Z. Qu,et al.  Cooperative Control of Dynamical Systems: Applications to Autonomous Vehicles , 2009 .

[15]  Yingmin Jia,et al.  Robust h ∞ consensus analysis of a class of second-order multi-agent systems with uncertainty , 2010 .

[16]  Daizhan Cheng,et al.  Leader-following consensus of multi-agent systems under fixed and switching topologies , 2010, Syst. Control. Lett..

[17]  Zongli Lin,et al.  Stabilization of linear systems with input delay and saturation—A parametric Lyapunov equation approach , 2010 .

[18]  Lin Huang,et al.  Consensus of Multiagent Systems and Synchronization of Complex Networks: A Unified Viewpoint , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

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

[20]  Zhisheng Duan,et al.  On H∞ and H2 performance regions of multi-agent systems , 2011, Autom..

[21]  Z. Duan,et al.  On H ∞ and H 2 performance regions of multi-agent systems ✩ , 2011 .

[22]  Lihua Xie,et al.  Global H∞ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics , 2012, ArXiv.

[23]  Lihua Xie,et al.  Global $H_\infty$ Consensus of Multi-Agent Systems with Lipschitz Nonlinear Dynamics , 2012 .

[24]  Guang-Ren Duan,et al.  Truncated predictor feedback for linear systems with long time-varying input delays , 2012, Autom..

[25]  Yang Liu,et al.  H ∞ consensus control for multi-agent systems with linear coupling dynamics and communication delays , 2012, Int. J. Syst. Sci..

[26]  Mengyin Fu,et al.  Consensus of Multi-Agent Systems With General Linear and Lipschitz Nonlinear Dynamics Using Distributed Adaptive Protocols , 2011, IEEE Transactions on Automatic Control.

[27]  Guangming Xie,et al.  Consensus for multi-agent systems with inherent nonlinear dynamics under directed topologies , 2013, Syst. Control. Lett..

[28]  Zongli Lin,et al.  An LMI approach to the control of exponentially unstable systems with input time delay , 2013, 52nd IEEE Conference on Decision and Control.

[29]  Zongli Lin,et al.  Truncated predictor feedback control for exponentially unstable linear systems with time-varying input delay , 2013, 2013 American Control Conference.

[30]  Zhengtao Ding,et al.  Consensus Output Regulation of a Class of Heterogeneous Nonlinear Systems , 2013, IEEE Transactions on Automatic Control.

[31]  Wenwu Yu,et al.  Synchronization via Pinning Control on General Complex Networks , 2013, SIAM J. Control. Optim..

[32]  Antoine Girard,et al.  Multiagent Flocking Under General Communication Rule , 2014, IEEE Transactions on Control of Network Systems.

[33]  Zhisheng Duan,et al.  Cooperative Control of Multi-Agent Systems: A Consensus Region Approach , 2014 .

[34]  Khashayar Khorasani,et al.  $H_{\infty}$ Consensus Achievement of Multi-Agent Systems With Directed and Switching Topology Networks , 2014, IEEE Transactions on Automatic Control.

[35]  Zhengtao Ding,et al.  Truncated state prediction for control of Lipschitz nonlinear systems with input delay , 2014, 53rd IEEE Conference on Decision and Control.

[36]  Bin Zhou,et al.  Consensus of high-order multi-agent systems with large input and communication delays , 2014, at - Automatisierungstechnik.

[37]  Bin Zhou.  Consensus of delayed multi-agent systems by reduced-order observer-based truncated predictor feedback protocols , 2014 .

[38]  Guoqiang Hu,et al.  Distributed ${\cal H}_{\infty}$ Consensus of Higher Order Multiagent Systems With Switching Topologies , 2014, IEEE Transactions on Circuits and Systems II: Express Briefs.

[39]  Guanghui Wen,et al.  Distributed H ∞ and H 2 consensus control in directed networks , 2014 .

[40]  X. Dong,et al.  Time-varying formation control for high-order linear swarm systems with switching interaction topologies , 2014 .

[41]  Zhengtao Ding,et al.  Consensus Disturbance Rejection With Disturbance Observers , 2015, IEEE Transactions on Industrial Electronics.

[42]  Zhengtao Ding,et al.  Consensus Control of a Class of Lipschitz Nonlinear Systems With Input Delay , 2014, IEEE Transactions on Circuits and Systems I: Regular Papers.

[43]  Zhengtao Ding,et al.  Adaptive consensus output regulation of a class of nonlinear systems with unknown high-frequency gain , 2015, Autom..