The design of distributed suboptimal controller for multi‐agent systems

Summary In this paper, the design of the distributed suboptimal controller for discrete-time multi-agent systems is considered. The distributed controllers, which only use the state information of itself and the relative states of its neighbors, are designed based on the topological structure of the system. The suboptimal feedback gain matrices of the distributed controllers are presented by using the ‘averaged’ optimization approach. It is showed that the distributed suboptimal controller is existent and unique. The design method of the distributed controller is obtained by the iteration procedure step by step. An example is given as an illustration of the proposed results. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  Fuzhen Zhang.  The Schur complement and its applications , 2005 .

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

[3]  Lihua Xie,et al.  Distributed Consensus With Limited Communication Data Rate , 2011, IEEE Transactions on Automatic Control.

[4]  Yongcan Cao,et al.  Optimal Linear-Consensus Algorithms: An LQR Perspective , 2010, IEEE Transactions on Systems, Man, and Cybernetics, Part B (Cybernetics).

[5]  Lihua Xie,et al.  Stochastic Approximation Approach for Consensus and Convergence Rate Analysis of Multiagent Systems , 2012, IEEE Transactions on Automatic Control.

[6]  Wenwu Yu,et al.  An Overview of Recent Progress in the Study of Distributed Multi-Agent Coordination , 2012, IEEE Transactions on Industrial Informatics.

[7]  Chang-Kyung Ryoo,et al.  Optimal cooperative control of dynamically decoupled systems , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[8]  B. Hassibi,et al.  A sub-optimal algorithm to synthesize control laws for a network of dynamic agents , 2005 .

[9]  Ian Postlethwaite,et al.  A distributed control law with guaranteed LQR cost for identical dynamically coupled linear systems , 2011, Proceedings of the 2011 American Control Conference.

[10]  G. Erickson.  Differential game models of advertising competition , 1995 .

[11]  Sanjay Lall,et al.  A Characterization of Convex Problems in Decentralized Control$^ast$ , 2005, IEEE Transactions on Automatic Control.

[12]  M. Athans,et al.  The design of suboptimal linear time-varying systems , 1968 .

[13]  Brian Chih-Hsiang Shu,et al.  Robust Longitudinal Control of Vehicle Platoons on Intelligent Highways , 1996 .

[14]  Sanjay Lall,et al.  Affine Controller Parameterization for Decentralized Control Over Banach Spaces , 2006, IEEE Transactions on Automatic Control.

[15]  Brian D. O. Anderson,et al.  Linear Optimal Control , 1971 .