2019/11/23 by Junjie Jiao, Jiao, Junjie, Harry L. Trentelman +3 · 1 citation
Computer Science · Mathematics · Medicine · #Algorithm #Bounded function #Computer science #Control (management) #Control theory (sociology) #Dimension (graph theory) #Discrete mathematics #Distributed Control Multi-Agent Systems #Eigenvalues and eigenvectors #FOS: Mathematics #Graph #Linear system #Mathematical and Theoretical Epidemiology and Ecology Models #Mathematics #Multi-agent system #Neural Networks Stability and Synchronization #Norm (philosophy) #Optimization and Control (math.OC) #Pure mathematics #Quadratic equation #State (computer science) #Strongly connected component #math.OC
paper · pdf · doi:10.48550/arxiv.1911.11611
published in arXiv (Cornell University) (Cornell University) · 7 pages, 3 figures, submitted to a conference. arXiv admin note: text overlap with arXiv:1803.02682
arxiv created 2019/11/23 · openalex publication_date 2019/11/23 · arxiv updated 2019/11/27 · openalex created_date 2019/12/05 · openalex updated_date 2026/08/05
In this paper, we extend the results from Jiao et al. (2019) on distributed linear quadratic control for leaderless multi-agent systems to the case of distributed linear quadratic tracking control for leader-follower multi-agent systems. Given one autonomous leader and a number of homogeneous followers, we introduce an associated global quadratic cost functional. We assume that the leader shares its state information with at least one of the followers and the communication between the followers is represented by a connected simple undirected graph. Our objective is to design distributed control laws such that the controlled network reaches tracking consensus and, moreover, the associated cost is smaller than a given tolerance for all initial states bounded in norm by a given radius. We establish a centralized design method for computing such suboptimal control laws, involving the solution of a single Riccati inequality of dimension equal to the dimension of the local agent dynamics, and the smallest and the largest eigenvalue of a given positive definite matrix involving the underlying graph. The proposed design method is illustrated by a simulation example.