Title :
Synchronization seeking in multi-agent dynamic systems with communication uncertainties
Author :
Han, Dongkun ; Chesi, Graziano ; Hung, Yeung Sam
Author_Institution :
Dept. of Electr. & Electron. Eng., Univ. of Hong Kong, Hong Kong, China
Abstract :
This paper addresses robust consensus problems among multiple agents with uncertain parameters constrained in a given set. Specifically, the network coefficients are supposed polynomial functions of an uncertain vector constrained in a set described by polynomial inequalities. First, the paper provides a necessary and sufficient condition for robust first-order consensus based on the eigenvalues of the uncertain Laplacian matrix. Based on this condition, a sufficient condition for robust first-order consensus is derived by solving a linear matrix inequality (LMI) problem built by exploiting sum-of-squares (SOS) polynomials. Then, the paper provides a necessary and sufficient condition for robust second-order consensus through the uncertain expanded Laplacian matrix and Lyapunov stability theory. Based on this condition, a sufficient condition for robust second-order consensus is derived by solving an LMI problem built by exploiting SOS matrix polynomials. Some numerical examples illustrate the proposed results.
Keywords :
Lyapunov matrix equations; eigenvalues and eigenfunctions; linear matrix inequalities; multi-agent systems; parameter estimation; polynomial matrices; uncertain systems; LMI problem; Lyapunov stability theory; SOS matrix polynomial; communication uncertainties; eigenvalues; linear matrix inequality; multiagent dynamic system; network coefficient; polynomial function; polynomial inequalities; robust first-order consensus problem; sum-of-squares polynomials; uncertain expanded Laplacian matrix; uncertain parameters; uncertain vector; Eigenvalues and eigenfunctions; Laplace equations; Linear matrix inequalities; Multiagent systems; Polynomials; Robustness; Symmetric matrices;
Conference_Titel :
Computer-Aided Control System Design (CACSD), 2011 IEEE International Symposium on
Conference_Location :
Denver, CO
Print_ISBN :
978-1-4577-1066-7
Electronic_ISBN :
978-1-4577-1067-4
DOI :
10.1109/CACSD.2011.6044567