Designing linear distributed algorithms with memory for fast convergence

International Journal of Robust and Nonlinear Control

Volumn 22, Issue 15, 2012, Pages 1691-1702

  Roy, Sandip ^a   Wan, Yan ^b   Saberi, Ali ^a   Xue, Mengran ^a  

^a Washington State University   (United States)

^b UNIVERSITY OF NORTH TEXAS   (United States)

Author keywords

decentralized control theory; distributed algorithms; large scale networks; numerical algorithms

Indexed keywords

DISTRIBUTED COMPUTATIONS; FAST CONVERGENCE; FASTER CONVERGENCE; ITERATIVE ALGORITHM; LARGE-SCALE NETWORK; LINEAR ITERATION; MEMORY ELEMENT; MEMORYLESS; NUMERICAL ALGORITHMS; SIMULATION EXAMPLE; SYSTEM OF LINEAR EQUATIONS;

DECENTRALIZED CONTROL; PARALLEL ALGORITHMS;

ALGORITHMS;

EID: 84866371780     PISSN: 10498923     EISSN: 10991239     Source Type: Journal    
DOI: 10.1002/rnc.1778     Document Type: Article

References (21)

1. Young DM,. A historical review of iterative methods. Proceedings of the ACM Conference on History of Scientific and Numeric Computation, Princeton, NJ, 13-15 May 1987; 117-123.
2. Fisher ME, Fuller AT,. On the stabilization of matrices and the convergence of linear iterative processes. Mathematical Proceedings of the Cambridge Philosophical Society 1958; 54 (4): 417-425.
3. Young DM,. Second-degree iterative methods for the solution of large linear systems. Journal of Approximation Theory 1972; 5 (2): 137-148.
4. Greenbaum A,. Iterative Methods for Solving Linear Systems. SIAM Press: Philadelphia, PA, 1997.
5. Boyd S, Ghosh A, Prabhakar B, Shah D,. Randomized gossip algorithms. IEEE Transactions on Information Theory 2006; 52 (6): 2508-2530. (Pubitemid 43898906)
6. Boyd S, Ghosh A, Prabhakar B, Shah D,. Gossip algorithms: design, analysis, and applications. Proceedings of the IEEE INFOCOM 2005, Miami, FL, 13-17 March 2005; 1653-1664. (Pubitemid 41390681)
7. Cao M, Spielman DA, Yeh EM,. Accelerated Gossip algorithms for distributed computation. Proceedings of the 44th Annual Allerton Conference on Communication Control and Computation, Montecelli, IL, 27-29 2006; 952-959.
8. Kempe D, Dobra A, Gehrke J,. Gossip-based computation of aggregate information. In 44th IEEE Symposium on Foundations of Computer Science (FOCS'03), Cambridge, MA, 11-14 October 2003.
9. Roy S, Herlugson K, Saberi A,. A control-theoretic approach on distributed discrete-valued decision-making in networks of sensing agents. IEEE Transactions on Mobile Computing 2006; 5 (8): 945-957. (Pubitemid 44109564)
10. Siljak D,. Decentralized Control Of Complex Systems. Academic Press: Boston, MA, 1994.
11. Roy S, Saberi A,. Scaling: a canonical design problem for networks. International Journal of Control 2007; 80 (8): 1342-1353. (Pubitemid 350021228)
12. Wan Y, Roy S, Saberi A, Stoorvogel A,. A multiple-derivative and multiple-delay paradigm for decentralized controller design: uniform rank systems. Journal of Discrete, Continuous, and Impulsive Systems, Special Issue in Honor of Hassan Khalil's 60th Birthday 2010; 17 (6): 883-907.
13. Wan Y, Roy S, Saberi A, Stoorvogel A,. The design of multi-lead- compensators for stabilization and pole placement in double-integrator networks. IEEE Transactions on Automatic Control 2010; 55 (12): 2870-2875.
14. Wan Y, Roy S,. An explicit formula for difference between Laplacian-eigenvector components using coalesced graphs. Linear Algebra and its Applications 2010; 433 (7): 1329-1335.
15. Wan Y, Roy S, Saberi A,. A new focus in the science of networks towards methods for design. Proceedings of the Royal Society 2008; 464 (2091): 513-535. (Pubitemid 351614504)
16. Boyd S,. Convex optimization of graph Laplacian eigenvalues. Proceedings of the International Congress of Mathematicians, Madrid, Spain, 22-30 August 2006; 1311-1319.
17. Rugh WJ,. Linear System Theory. Prentice Hall: Upper Saddle River, NJ, 1996.
18. Roy S, Saberi A, Herlugson K,. Formation and alignment of distributed sensing agents with double-integrator dynamics. IEEE Press Monograph on Sensor Network Operations 2006.
19. Corfmat JP, Morse AS,. Stabilization with decentralized feedback control. IEEE Transactions on Automatic Control 1976; 21 (1): 679-682.
20. Wan Y, Roy S, Saberi A,. Network design problems for controlling virus spread. Proceedings of 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, 12-14 December 2007; 3925-3932. (Pubitemid 351277761)
21. Olshevsky A, Tsitsiklis JN,. Convergence speed in distributed consensus and averaging. SIAM Journal on Control and Optimization 2009; 48 (1): 33-55.