Action group on numerical methods in the behavioral setting
Chair: Ivan Markovsky, Co-chair: Paolo Rapisarda
The activities of this action group have been subsumed into the activities of the
Introduction
The behavioral approach to systems theory revises the classical input-output map notion of a dynamical system. A system is defined abstractly as a collection of legitimate trajectories. No a priori separation of the variables into inputs and outputs is imposed (but deduced from the system). Analysis and synthesis of systems in the behavioral setting still heavily relies on concrete representations. Among the representations used, the input/state/output and the vector difference equation ones play central role. Therefore, the familiar state space and polynomial linear algebra analysis tools are still the main tools for system analysis and synthesis. In the behavioral setting, however, the analysis and synthesis goals are defined on the higher level of the set of trajectories, which might lead to more adequate problem formulations and clearer solutions. Examples are the behavioral definition of controllability, the quadratic differential forms theory for the study of dissipative systems, and the interpretation of control as interconnection.
What is currently missing in the behavioral approach, at least from the applications point of view, are numerical methods derived from and devoted to this setting. Many algorithms are proposed in papers employing the behavioral approach but very little software based on these algorithms is currently developed. Particular problems studied in the behavioral setting that lead to algorithms are:
- Modeling from first principles
- Modeling from data (time series)
- Synthesis of dissipative systems
- Control as interconnection
- Control of distributed systems
Goals
The goals of the action group on numerical methods in the behavioral setting are to collect, classify, and present (on this web page) information about progress in the research on the behavioral approach and in particular in the software implementation of the resulting theories. Our ultimate goal is to popularize the behavioral paradigm to the level of making it the standard approach to systems and control theory.
The activities of the Action Group on Numerical Methods in the Behavioral Setting overlap with those of the IEEE Technical Committee on Behavioral Systems and Control Theory.
People
- Jan C. Willems - Department of Electrical Engineering, K.U. Leuven
- Harry L. Trentelman - Department of Mathematics and Computing Science, University of Groningen
- Arjan van der Schaft - Department of Mathematics and Computing Science, University of Groningen
- Jan Willem Polderman - Department of Applied Mathematics, University of Twente
- H. K. Pillai - Electrical Engineering Department, Indian Institute Of Technology, Bombay
- Eric Rogers School of Electronics and Computer Science, University of Southampton, United Kingdom
- Mark C. French School of Electronics and Computer Science, University of Southampton, United Kingdom
- Maria Elena Valcher - Universita` di Padova
- Athanasios C. Antoulas - Electrical and Computer Engineering, Rice University
- P. Rocha - Department of Mathematics University of Aveiro Portugal
- Siep Weiland - Department of Electrical Engineering, Eindhoven University of Technology
- B. Roorda - University of Twente
- Paolo Rapisarda - School of Electronics and Computer Science, University of Southampton, United Kingdom
- Ivan Markovsky - School of Electronics and Computer Science, University of Southampton, United Kingdom
- Agung Julius - Department of Applied Mathematics, University of Twente
- Fagnani Fabio - Dipartimento di Matematica, Politecnico di Torino
- Achim Ilchmann - Fakultet fur Mathematik und Naturwissenschaften, TU Ilmenau
- Mark Opmeer - Department of Mathematics and Computing Science, University of Groningen
- Sandro Zampieri - Dipartimento di Elettronica ed Informatica, University of Padova
Software
Invited sessions, Minicourses, and Workshops
Books