Distributed optimal coordination for multiple heterogeneous Euler-Lagrangian systems

Abstract In this paper, we consider the distributed optimal coordination (DOC) problem for multi-agent systems with the agents in the form of Euler–Lagrangian (EL) dynamics. We propose two different distributed protocols for the heterogeneous continuous-time EL agents to achieve the optimization task. By constructing suitable Lyapunov functions, we prove the global convergence to the optimal coordination of the EL systems in the case with parametric uncertainties, and the global exponential convergence in the case without parametric uncertainties. Furthermore, we estimate the regret bound for an uncertain DOC problem with time-varying cost functions and inexact gradients. Finally, we provide a numerical example to validate the theoretical results.

[1]  Sonia Martínez,et al.  Distributed convex optimization via continuous-time coordination algorithms with discrete-time communication , 2014, Autom..

[2]  Yurii Nesterov,et al.  First-order methods of smooth convex optimization with inexact oracle , 2013, Mathematical Programming.

[3]  Mehran Mesbahi,et al.  Online distributed optimization via dual averaging , 2013, 52nd IEEE Conference on Decision and Control.

[4]  Karl Henrik Johansson,et al.  Approximate Projected Consensus for Convex Intersection Computation: Convergence Analysis and Critical Error Angle , 2014, IEEE Transactions on Automatic Control.

[5]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[6]  Lihua Xie,et al.  Distributed Projection-Based Algorithms for Source Localization in Wireless Sensor Networks , 2015, IEEE Transactions on Wireless Communications.

[7]  R. Tyrrell Rockafellar,et al.  Convex Analysis , 1970, Princeton Landmarks in Mathematics and Physics.

[8]  Silvia Ferrari,et al.  Distributed optimal control for multi-agent trajectory optimization , 2014, Autom..

[9]  Yiguang Hong,et al.  Distributed optimization design for second-order multi-agent systems , 2014, Proceedings of the 33rd Chinese Control Conference.

[10]  Dezhen Song,et al.  Cooperative Search of Multiple Unknown Transient Radio Sources Using Multiple Paired Mobile Robots , 2014, IEEE Transactions on Robotics.

[11]  Asuman E. Ozdaglar,et al.  Distributed Subgradient Methods for Multi-Agent Optimization , 2009, IEEE Transactions on Automatic Control.

[12]  Yiguang Hong,et al.  Distributed optimization design for high-order multi-agent systems , 2015, 2015 34th Chinese Control Conference (CCC).

[13]  Xuan Zhang,et al.  Distributed optimal steady-state control using reverse- and forward-engineering , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[14]  Andrea Gasparri,et al.  Decentralized estimation of Laplacian eigenvalues in multi-agent systems , 2012, Autom..

[15]  Feng Yan,et al.  Distributed Autonomous Online Learning: Regrets and Intrinsic Privacy-Preserving Properties , 2010, IEEE Transactions on Knowledge and Data Engineering.

[16]  Xinghu Wang,et al.  Dynamic optimization for multi-agent systems with external disturbances , 2014 .

[17]  Jie Huang,et al.  Leader-following consensus of multiple uncertain Euler–Lagrange systems under switching network topology , 2014, Int. J. Gen. Syst..

[18]  Feng Liu,et al.  Initialization-free distributed algorithms for optimal resource allocation with feasibility constraints and application to economic dispatch of power systems , 2015, Autom..

[19]  Mark W. Spong,et al.  Robot dynamics and control , 1989 .

[20]  Jing Wang,et al.  A control perspective for centralized and distributed convex optimization , 2011, IEEE Conference on Decision and Control and European Control Conference.

[21]  Ziyang Meng,et al.  Cooperative Set Aggregation for Multiple Lagrangian Systems , 2014, ArXiv.

[22]  Yiguang Hong,et al.  Multi-Agent Optimization Design for Autonomous Lagrangian Systems , 2016, Unmanned Syst..