Workshop # 1
Time Delays in Networks: Models, Stability Theory, Control, and Numerical Methods
Organizers: Fatihcan M. Atay, Wim Michiels, Silviu-Iulian Niculescu, Hitay Ozbay, Rifat Sipahi
Background & Significance: Time delays are all around us, from engineering and operations research, to biology, manufacturing, economics, human factors. The presence of delays in many examples found in these applications cannot be neglected, especially when a “feedback system” is used to regulate system behavior. In such cases, delays may cause poor performance, and even invite instability. Delays are not necessarily destabilizing however; in many examples, we may find situations where delays could also be beneficial for the closed loop system. For instance, “wait before act” is an effective strategy to control a dynamical system, first by waiting to see what happens, and then acting accordingly to counter act destabilization.
One of the major issues in investigating systems with delays is their inherent infinite dimensionality. In linear systems, this could be seen as delay bringing about infinitely many eigenvalues, all of which must be managed for stability and control design – a nontrivial task. This is probably one of the many reasons these types of systems attracted significant amount of interest in the past six decades, with increasing intensity in the past two decades, including journal and book publications in theoretical and applied fields, presentations at major control systems conferences sponsored by IFAC, IEEE, and ASME, the dedicated IFAC Workshop on Time Delay Systems, and two articles that appeared on the topic in the last three years in IEEE Control Systems Magazine.
Interestingly, we notice that time delay systems arise in various network settings, whether engineered by humans, or built by nature. Examples are many; traffic flow networks in which humans’ physiological delays affect flow behavior; supply chains in which transport and manufacturing delays affect inventory regulation; biological systems in which delays exist in neural transmissions, in reproduction processes of cells, and physiology of humans; and tele-operation systems, e.g., tele-surgery technology, in which dynamical systems are coupled via control and delayed sensory information due to a communication medium, such as Internet.
Synopsis of the Workshop Talks: The workshop will present various network systems examples from traffic flow, supply chains, biology, and synchronization problems. The coverage will include stability theory, graph theory, approaches to analyze stability and to synthesize controllers, and numerical techniques to be used for moderately large scale networks. Some of the details on these techniques will be demonstrated on Linear Time-Invariant Time Delay Systems.
Fatihcan M. Atay
Duration & date
Full-day: June 24, 2014
From Basics of Graph Theory to Synchronization Issues in Networks with Delays, Fatihcan M. Atay
Methods for Stability and Relative Stability Problems with Application to Neuronal Networks Analysis, Wim Michiels
Traffic Flow Networks with Human Reaction Delays, Silviu-Iulian Niculescu
Networks, Delays, and Stability in Biological Systems, Hitay Ozbay
Supply Networks and Logistics Systems with Delays, Rifat Sipahi