Hierarchical Decentralized Controller Synthesis for Heterogeneous Multi-Agent Dynamical Systems by LQR

This paper is concerned with systematic ways of designing hierarchical decentralized controllers for heterogeneous multi-agent dynamical systems. Given a bunch of independent agents or subsystems with a class of information networks, the aim of the paper is to propose a systematic design procedure for hierarchical decentralized controllers, where each subsystem cooperatively interacts with each other as well as controls it locally to achieve both the local and global goals in some senses. It is shown that employing the LQR (Linear Quadratic Regulator) method with properly chosen weighting matrices in the performance index, both the local and global objectives can be achieved by the desired hierarchical decentralized structure which fits the given information network. The effectiveness of the proposed design method is confirmed through an illustrative example and its application to a velocity consensus problem in vehicle platoons.

[1]  Michel Verhaegen,et al.  Distributed Control for Identical Dynamically Coupled Systems: A Decomposition Approach , 2009, IEEE Transactions on Automatic Control.

[2]  H. Shimizu,et al.  Cyclic pursuit behavior for hierarchical multi-agent systems with low-rank interconnection , 2008, 2008 SICE Annual Conference.

[3]  Shinji Hara,et al.  Consensus in hierarchical multi-agent dynamical systems with low-rank interconnections: Analysis of stability and convergence rates , 2009, 2009 American Control Conference.

[4]  Shinji Hara,et al.  Eigenvector-based intergroup connection of low rank for hierarchical multi-agent dynamical systems , 2012, Syst. Control. Lett..

[5]  B. Anderson,et al.  Optimal control: linear quadratic methods , 1990 .

[6]  Mireille E. Broucke,et al.  A hierarchical cyclic pursuit scheme for vehicle networks , 2005, Autom..

[7]  Francesco Borrelli,et al.  Distributed LQR Design for Identical Dynamically Decoupled Systems , 2008, IEEE Transactions on Automatic Control.

[8]  T. Samad,et al.  Formations of formations: hierarchy and stability , 2004, Proceedings of the 2004 American Control Conference.

[9]  Makan Fardad,et al.  The operator algebra of almost Toeplitz matrices and the optimal control of large-scale systems , 2009, 2009 American Control Conference.

[10]  Lu Liu,et al.  Hierarchical network synthesis for output consensus by eigenvector-based interlayer connections , 2011, IEEE Conference on Decision and Control and European Control Conference.

[11]  Mireille E. Broucke,et al.  Patterned linear systems: Rings, chains, and trees , 2010, 49th IEEE Conference on Decision and Control (CDC).

[12]  Shinji Hara,et al.  Hierarchical consensus for multi-agent systems with low-rank interconnection , 2009, 2009 ICCAS-SICE.

[13]  Shinji Hara,et al.  An algebraic approach to hierarchical LQR synthesis for large-scale dynamical systems , 2013, 2013 9th Asian Control Conference (ASCC).

[14]  Shinji Hara,et al.  Performance analysis of decentralized cooperative driving under non-symmetric bidirectional information architecture , 2010, 2010 IEEE International Conference on Control Applications.

[15]  Santo Fortunato,et al.  Community detection in graphs , 2009, ArXiv.

[16]  A. Jadbabaie,et al.  On decentralized optimal control and information structures , 2008, 2008 American Control Conference.

[17]  Shinji Hara,et al.  Hierarchical decentralized stabilization for networked dynamical systems by LQR selective pole shift , 2014 .