EVENTS
Dover Publications paperback reprint of the book
LARGE SCALE DYNAMIC SYSTEMS: International Journal of Robust and Nonlinear Control Academician Vladimir A. Yakubovich: A Tribute Ever since A. I. Lur'e introduced the absolute stability problem of nonlinear automatic control systems in his book in 1951, numerous researchers have proposed solutions and extensions of the problem, thus making it one of the most - researched problems in control theory. In my opinion, there are three crucial contributions that stand above all others. The frequency method introduced by V. M. Popov in 1960, the method of linear matrix inequalities proposed by V. A. Yakubovich in 1962, and Kalman's version of the positive real lemma formulated in 1963 via the concepts of controlability and observability. It has been the concept of matrix inequalities, however, that achieved special significance in a large number of areas in control theory and beyond. Supported by the recent advances in convex optimization, the matrix inequalities methods of Yakubovich have dramatically changed the way we approach problems in control theory and applications. It is with great respect and pleasure that I offer to professor Yakubovich my best wishes for his health and happiness on the occasion of his 80th birthday. Dragoslav D. Siljak Abstract:
STABILITY AND STRUCTURE
North Holland, Amsterdam, 1978
appears in November 2007
THE PAPERBACK FRONT COVER
Volume 17, Issue No. 5 - 6, 2007, p. 361
Special Issue Dedicated to the 80th Birthday od V. A. Yakubovich
Santa Clara University,
Santa Clara, California, U.S.A.
Dynamic Graphs in Modeling of Complex Systems
Drago Siljak
Santa Clara University
Friday, June 1st, 2007 3:00pm-4:00pm ESB 2001
Dynamic graphs are defined in a linear graph space as one-parameter group of transformations of the space into itself. Stability of equilibrium graphs is formulated in the sense of Liapunov to study motions of positive graphs in the nonnegative orthant of the graph space. In transportation and communication problems, the edges of a dynamic graph representing the network can be considered as goods of a multiple market system where economic agents choose the edges with their weights taken as given prices to come up with the shortest paths which minimize cost. The edges are regarded as gross substitute goods and conditions are provided for stability of the resulting competitive equilibrium. When a complex system is represented as an interconnection of dynamic subsystems (agents), a dynamic graph is used by a coordinator to make sure that a desired level of interconnections between the subsystems is preserved as a connectively stable equilibrium. The equilibrium remains stable despite uncertain structural perturbations whereby the coupling between subsystems changes during the time-evolution of the overall system. The coordinator can be used to adaptively adjust the interconnection levels in multi-agent systems in order to assign the prescribed state as a stable equilibrium point of the overall system. The equilibrium assignment is achieved by solving an optimization problem involving a two-time-scale system; the coordinator action is slow compared to the fast dynamics of the agents. Polytopic connective stability of the multi-agent systems is established by applying the concept of vector Liapunov functions and the theory of M-matrices.
About the Speaker:
Drago Siljak received the Ph.D degree in 1963 from the University of Belgrade, Belgrade, Yugoslavia. Since 1964 he has been with Santa Clara University, where he is the B & M Swig University Professor in the School of Engineering and teaches courses in system theory and applications. His research interests are in the theory of large scale systems and its applications to problems in control engineering, power systems, economics, aerospace, and model ecosystems. He is the author of Nonlinear Systems (Wiley, 1969), Large-Scale Dynamic Systems (North Holland, 1978), and Decentralized Control of Complex Systems (Academic Press, 1991). He is an honorary member of the Serbian Academy of Sciences and Arts and is a Life Fellow of IEEE.
