Input Delay Compensation in Multi-Agent Systems via Piecewise Constant Control

Abstract We consider a multi-agent system with time-invariant topology containing several agents governed by similar linear time-invariant ODEs with constant delay in actuation. Piecewise constant (PWC) control with sampling time larger than the delay value is applied. Assuming the delay-free version of the system can be brought to consensus by the PWC feedback, we design a predictive PWC feedback achieving consensus in the system with delayed input. During prediction, PWC structure is employed to determine future input to the system from its past output. This input is then used to predict the future state and compensate for the delay.

[1]  Anton Ponomarev.  Nonlinear Predictor Feedback for Input-Affine Systems With Distributed Input Delays , 2016, IEEE Transactions on Automatic Control.

[2]  Iasson Karafyllis,et al.  Nonlinear Stabilization Under Sampled and Delayed Measurements, and With Inputs Subject to Delay and Zero-Order Hold , 2012, IEEE Transactions on Automatic Control.

[3]  Sonia Martínez,et al.  Robust rendezvous for mobile autonomous agents via proximity graphs in arbitrary dimensions , 2006, IEEE Transactions on Automatic Control.

[4]  Daizhan Cheng,et al.  Leader-following consensus of second-order agents with multiple time-varying delays , 2010, Autom..

[5]  Delphine Bresch-Pietri,et al.  Delay-Adaptive Predictor Feedback for Systems With Unknown Long Actuator Delay $ $ , 2010, IEEE Transactions on Automatic Control.

[6]  Yisheng Zhong,et al.  Time-varying formation control for unmanned aerial vehicles with switching interaction topologies , 2014, 2014 International Conference on Unmanned Aircraft Systems (ICUAS).

[7]  Rogelio Lozano,et al.  Semiglobal stabilization of continuous systems with bounded delayed inputs , 2002 .

[8]  V. Kharitonov.  Time-Delay Systems: Lyapunov Functionals and Matrices , 2012 .

[9]  Nikolaos Bekiaris-Liberis,et al.  Compensation of state-dependent input delay for nonlinear systems , 2011, IEEE Conference on Decision and Control and European Control Conference.

[10]  Zhiyong Chen,et al.  Consensus Acceleration in a Class of Predictive Networks , 2014, IEEE Transactions on Neural Networks and Learning Systems.

[11]  F. Bullo,et al.  Motion Coordination with Distributed Information , 2007 .

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

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

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

[15]  Reza Olfati-Saber,et al.  Flocking for multi-agent dynamic systems: algorithms and theory , 2006, IEEE Transactions on Automatic Control.

[16]  Leonid Mirkin,et al.  On the approximation of distributed-delay control laws , 2004, Syst. Control. Lett..

[17]  Tao Zhou,et al.  Ultrafast consensus via predictive mechanisms , 2008 .

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

[19]  Miroslav Krstic,et al.  Input Delay Compensation for Forward Complete and Strict-Feedforward Nonlinear Systems , 2010, IEEE Transactions on Automatic Control.

[20]  Jonathan Chauvin,et al.  Adaptive control scheme for uncertain time-delay systems , 2012, Autom..

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

[22]  Vladimir L. Kharitonov,et al.  Time-Delay Systems , 2013 .

[23]  Yisheng Zhong,et al.  Time-Varying Formation Control for Unmanned Aerial Vehicles: Theories and Applications , 2015, IEEE Transactions on Control Systems Technology.

[24]  Vladimir L. Kharitonov,et al.  An extension of the prediction scheme to the case of systems with both input and state delay , 2014, Autom..