Scheduling algorithm of observation and controlling for multi-agent systems to guarantee structural controllability

This paper addresses how to select observed agents and controlled agents in a multi-agent system such that the system is structurally controllable with minimum cost of control and measurement. Firstly, we model the design issue as a minimum cost control configuration (MCCC) design problem of a bilinear system. Next, a necessary condition for the solvability of MCCC is derived. Then, an algorithm is given to provide the optimal solution to MCCC. This algorithm is based on the directed acyclic graph decomposition of the system graph, the Dulmage-Mendelson decomposition of the system bipartite graph, and verifying coprime paths. We use a new graph called dynamic graph to verify the coprime paths, which can avoid infinite verification loops when there are cycles in the system graph. We also prove that this algorithm has polynomial computational complexity. Finally, an example is given to illustrate the validity of the algorithm.

[1]  Christian Commault,et al.  The single-input Minimal Controllability Problem for structured systems , 2015, Syst. Control. Lett..

[2]  Christian Commault,et al.  Input addition and leader selection for the controllability of graph-based systems , 2013, Autom..

[3]  Mohsen Zamani,et al.  Structural controllability of multi-agent systems , 2009, 2009 American Control Conference.

[4]  H.G. Tanner,et al.  On the controllability of nearest neighbor interconnections , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[5]  Alexander Olshevsky.  The Minimal Controllability Problem , 2013, ArXiv.

[6]  Amir G. Aghdam,et al.  Structural controllability of multi-agent networks: Robustness against simultaneous failures , 2013, Autom..

[7]  K. Murota.  Systems Analysis by Graphs and Matroids: Structural Solvability and Controllability , 1987 .

[8]  Christian Commault,et al.  Generic properties and control of linear structured systems: a survey , 2003, Autom..

[9]  Ginestra Bianconi,et al.  Network controllability is determined by the density of low in-degree and out-degree nodes. , 2014, Physical review letters.

[10]  Yu-Ping Tian,et al.  Leader selection for strong structural controllability of single-integrator multi-agent systems , 2017, J. Syst. Sci. Complex..

[11]  Alexander Olshevsky,et al.  Minimal Controllability Problems , 2013, IEEE Transactions on Control of Network Systems.

[12]  Ching-tai Lin.  Structural controllability , 1974 .

[13]  Xiang Li,et al.  Structural Controllability of Temporally Switching Networks , 2016, IEEE Transactions on Circuits and Systems I: Regular Papers.

[14]  Supratim Ghosh,et al.  Structural control of single-input rank one bilinear systems , 2016, Autom..

[15]  Amir G. Aghdam,et al.  Leader localization in multi-agent systems subject to failure: A graph-theoretic approach , 2011, Autom..

[16]  Soummya Kar,et al.  On the complexity of the constrained input selection problem for structural linear systems , 2014, Autom..

[17]  Soummya Kar,et al.  Minimum cost constrained input-output and control configuration co-design problem: A structural systems approach , 2015, 2015 American Control Conference (ACC).

[18]  Derek Ruths,et al.  Control Profiles of Complex Networks , 2014, Science.

[19]  J. Pearson,et al.  Structural controllability of multiinput linear systems , 1976 .

[20]  Zhen Wang,et al.  Interconnection topologies for multi-agent coordination under leader-follower framework , 2009, Autom..

[21]  Albert-László Barabási,et al.  Controllability of complex networks , 2011, Nature.

[22]  D. Murthy,et al.  Controllability of a class of discrete time bilinear systems , 1977 .

[23]  Soummya Kar,et al.  Minimum cost input/output design for large-scale linear structural systems , 2014, Autom..

[24]  Soummya Kar,et al.  A Framework for Structural Input/Output and Control Configuration Selection in Large-Scale Systems , 2013, IEEE Transactions on Automatic Control.