Abstract:
This paper deals with robust synchronization of uncertain multi-agent networks. Given a network with for each of the agents identical nominal linear dynamics, we allow un...Show MoreMetadata
Abstract:
This paper deals with robust synchronization of uncertain multi-agent networks. Given a network with for each of the agents identical nominal linear dynamics, we allow uncertainty in the form of additive perturbations of the transfer matrices of the nominal dynamics. The perturbations are assumed to be stable and bounded in H∞-norm by some a priori given desired tolerance. We derive state space formulas for observer based dynamic protocols that achieve synchronization for all perturbations bounded by this desired tolerance. It is shown that a protocol achieves robust synchronization if and only if each controller from a related finite set of feedback controllers robustly stabilizes a given, single linear system. Our protocols are expressed in terms of real symmetric solutions of certain algebraic Riccati equations and inequalities, and also involve weighting factors that depend on the eigenvalues of the graph Laplacian. For undirected network graphs we show that within the class of such dynamic protocols, a guaranteed achievable tolerance can be obtained that is proportional to the quotient of the second smallest and the largest eigenvalue of the Laplacian. We also extend our results to additive nonlinear perturbations with L2-gain bounded by a given tolerance.
Published in: IEEE Transactions on Automatic Control ( Volume: 58, Issue: 6, June 2013)
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, Netherlands
Harry L. Trentelman (SM'98) received the Ph.D. degree in mathematics from the University of Groningen Groningen, The Netherlands, in 1985.
He is a Full Professor in Systems and Control at the Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen in the Netherlands. From 1991 to 2008 he was an Associate Professor and later an Adjunct Professor at the same institute. From 1985 to 1991 he wa...Show More
Harry L. Trentelman (SM'98) received the Ph.D. degree in mathematics from the University of Groningen Groningen, The Netherlands, in 1985.
He is a Full Professor in Systems and Control at the Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen in the Netherlands. From 1991 to 2008 he was an Associate Professor and later an Adjunct Professor at the same institute. From 1985 to 1991 he wa...View more
Department of Electrical and Electronic Engineering, College of Science and Engineering, Ritsumeikan University, Ritsumeikan, Japan
Kiyotsugu Takaba (M'93) received the B.Eng., M.Eng., and Dr.Eng. degrees from Kyoto University, Japan, in 1989, 1991, and 1996, respectively.
From 1991 to 1998, he was a Research Associate at the Department of Applied Mathematics and Physics, Kyoto University. From 1998 to 2012, he was an Associate Professor at the same department. In 2000, he was a Visiting Researcher with the University of Groningen, Groningen, The Nethe...Show More
Kiyotsugu Takaba (M'93) received the B.Eng., M.Eng., and Dr.Eng. degrees from Kyoto University, Japan, in 1989, 1991, and 1996, respectively.
From 1991 to 1998, he was a Research Associate at the Department of Applied Mathematics and Physics, Kyoto University. From 1998 to 2012, he was an Associate Professor at the same department. In 2000, he was a Visiting Researcher with the University of Groningen, Groningen, The Nethe...View more
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, Netherlands
Nima Monshizadeh was born in Tehran, Iran, in 1983. He received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, the M.Sc. degree in control engineering from K.N. Toosi University of Technology, and is currently pursuing the Ph.D. degree at the Systems and Control Group, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlan...Show More
Nima Monshizadeh was born in Tehran, Iran, in 1983. He received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, the M.Sc. degree in control engineering from K.N. Toosi University of Technology, and is currently pursuing the Ph.D. degree at the Systems and Control Group, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlan...View more
Contents Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, Netherlands
Harry L. Trentelman (SM'98) received the Ph.D. degree in mathematics from the University of Groningen Groningen, The Netherlands, in 1985.
He is a Full Professor in Systems and Control at the Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen in the Netherlands. From 1991 to 2008 he was an Associate Professor and later an Adjunct Professor at the same institute. From 1985 to 1991 he was an Assistant Professor, and later an Associate Professor with the Mathematics Department, University of Technology, Eindhoven, The Netherlands. He is a co-author of the textbook Control Theory for Linear Systems (Springer, 2001). He is an Associate Editor for Systems and Control Letters and is past Associate Editor of the SIAM Journal on Control and Optimization. His research interests are the behavioral approach to systems and control, robust control, model reduction, multi-dimensional linear systems, hybrid systems, analysis and control of networked systems, and the geometric theory of linear systems.
Dr. Trentelman is an Associate Editor of the IEEE Transactions on Automatic Control.
Harry L. Trentelman (SM'98) received the Ph.D. degree in mathematics from the University of Groningen Groningen, The Netherlands, in 1985.
He is a Full Professor in Systems and Control at the Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen in the Netherlands. From 1991 to 2008 he was an Associate Professor and later an Adjunct Professor at the same institute. From 1985 to 1991 he was an Assistant Professor, and later an Associate Professor with the Mathematics Department, University of Technology, Eindhoven, The Netherlands. He is a co-author of the textbook Control Theory for Linear Systems (Springer, 2001). He is an Associate Editor for Systems and Control Letters and is past Associate Editor of the SIAM Journal on Control and Optimization. His research interests are the behavioral approach to systems and control, robust control, model reduction, multi-dimensional linear systems, hybrid systems, analysis and control of networked systems, and the geometric theory of linear systems.
Dr. Trentelman is an Associate Editor of the IEEE Transactions on Automatic Control.View more
Department of Electrical and Electronic Engineering, College of Science and Engineering, Ritsumeikan University, Ritsumeikan, Japan
Kiyotsugu Takaba (M'93) received the B.Eng., M.Eng., and Dr.Eng. degrees from Kyoto University, Japan, in 1989, 1991, and 1996, respectively.
From 1991 to 1998, he was a Research Associate at the Department of Applied Mathematics and Physics, Kyoto University. From 1998 to 2012, he was an Associate Professor at the same department. In 2000, he was a Visiting Researcher with the University of Groningen, Groningen, The Netherlands. From 2012, he has been a Professor with the Department of Electrical and Electronic Engineering, College of Science and Engineering, Ritsumeikan University. His current research interests include robust control, multi-agent control systems, behavioral approach to systems and control.
Dr. Takaba is a member of ISCIE and SICE.
Kiyotsugu Takaba (M'93) received the B.Eng., M.Eng., and Dr.Eng. degrees from Kyoto University, Japan, in 1989, 1991, and 1996, respectively.
From 1991 to 1998, he was a Research Associate at the Department of Applied Mathematics and Physics, Kyoto University. From 1998 to 2012, he was an Associate Professor at the same department. In 2000, he was a Visiting Researcher with the University of Groningen, Groningen, The Netherlands. From 2012, he has been a Professor with the Department of Electrical and Electronic Engineering, College of Science and Engineering, Ritsumeikan University. His current research interests include robust control, multi-agent control systems, behavioral approach to systems and control.
Dr. Takaba is a member of ISCIE and SICE.View more
Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, Netherlands
Nima Monshizadeh was born in Tehran, Iran, in 1983. He received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, the M.Sc. degree in control engineering from K.N. Toosi University of Technology, and is currently pursuing the Ph.D. degree at the Systems and Control Group, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands.
His research interests include model order reduction, switched systems, control configuration selection, decentralized control, networks and multi-agent systems.
Nima Monshizadeh was born in Tehran, Iran, in 1983. He received the B.Sc. degree in electrical engineering from the University of Tehran, Tehran, Iran, the M.Sc. degree in control engineering from K.N. Toosi University of Technology, and is currently pursuing the Ph.D. degree at the Systems and Control Group, Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, Groningen, The Netherlands.
His research interests include model order reduction, switched systems, control configuration selection, decentralized control, networks and multi-agent systems.View more
