Structural Methods in the Study of Complex Systems
Elena Zattoni, Alma Mater Studiorum – University of Bologna
Anna Maria Perdon, Università Politecnica delle Marche
Giuseppe Conte, Università Politecnica delle Marche
The workshop provides a forum for a comprehensive exposition and discussion on how paradigmatic analysis and synthesis problems formulated for complex dynamical systems can be effectively investigated and solved through methodological approaches primarily grounded on structural views.
Complex dynamical systems emerge in a variety of disciplines and domains, ranging from those that deal with physical processes (biology, genetics, environmental sciences, etc.) to those that concern man-made systems (engineering, energy, finance, etc.). Indeed, in these fields, it is more and more common to refer to dynamical structures such as systems of systems, hybrid systems and multimodal systems. In brief, the former ones consist of many interconnected dynamical systems with various topological patterns and hierarchical relations; the second ones are dynamical systems that exhibit dynamics of a different nature, both continuous and discrete; the third ones are dynamical systems whose behavior may vary during their lifecycle owing to different operating conditions or depending on the occurrence of some events. The dynamical structures with these characteristics are currently modelled as, e.g., multi-agent systems, hybrid impulsive systems, switching systems, implicit switching systems, and so forth.
Consequently, control design techniques have changed to adapt to the ever-increasing system complexity. In this scenario, structural methodologies — i.e., those methods which have evolved from original graph theories, differential-algebraic techniques and geometric approaches to linear and nonlinear control—have proven to be particularly powerful for several reasons. Beforehand, the structural approaches privilege the essential features of dynamical systems and their interconnections, thus yielding abstractions that can fit a wide variety of situations. Meanwhile, the geometric perspective, which is often at the basis of the structural approaches, introduces a relevant visual and intuitive component which fosters research advancements. Nevertheless, the formalization of the structural and geometric concepts is rendered with algebraic tools, which, in turn, have a direct correspondence with computational algorithms, thus paving the way to actual implementation in engineering applications.
During the latest years, relevant theoretical achievements have been obtained within the scope of each of the methodologies encompassed in the sphere of the structural approaches (i.e., graph theoretic methods, geometric methods, differential-algebraic methods) in respect of fundamental control and observation problems stated for complex systems (e.g., multi-agent systems, hybrid impulsive systems, switching systems, implicit switching systems). Moreover, computational algorithms and specific applications have been developed together with the theoretical accomplishments. Thus, the corpus of consolidated results (both theoretical and practical/computational ones) presently available motivates the intention to share and disseminate the status of the art by a thorough presentation. Furthermore, the discussion among the participants is expected to establish fruitful relations between the various approaches, to emphasize pros and cons in connection with specific contexts or applications and to point out merging opportunities. Although these are definitely nontrivial tasks, the efforts made to these ends are expected to develop new sensibility towards the selection of the most suitable tools in relation to the problems at issue as well as to outline new directions for solving the open problems both in the theory and in the applications.
The workshop is organized in such a way that the discussion starts from a general description of complexity and structural attitudes towards it, then it focuses on some fundamental problems and, finally, it dwells on applications. In more detail, an overview on the complex systems emerging in the various fields, on the new challenges of engineering design and on how these can be mastered by means of the structural approaches is provided first. A novel geometric view, based on transformations which maintain the invariance of global properties, such as stability or H-infinity norm, is described and shown to provide new tools to investigate stability and to parametrize the set of the stabilizing controllers. A graph-theoretic-based approach is then shown to be an effective tool to analyze controllability in leader/follower multi-agent systems and to understand the effects of the underlying network structure. How solvability of the output regulation problem in hybrid linear systems with periodic state jumps can be investigated by structural methods is then illustrated. A mixed digraph-theory and geometric approach is exploited to solve another classic problem of system and control theory, i.e. disturbance decoupling, for a special class of hybrid switching systems. Furthermore, the synthesis of unknown-input state observers with minimum-complexity is tackled by structural tools in the context of linear impulsive systems: necessary and sufficient solvability conditions are derived once a set of essential requirements has been disentangled. The disturbance decoupling problem is also investigated for a class of implicit switching systems through geometric considerations inspired to the behavioral approach. In particular, the theoretical results are applied to the synthesis of a Beard-Jones filter. Finally, another meaningful application is considered in depth: a structural perspective is adopted to analyze Huygens synchronization over distributed media and it reveals a complex, but structured behavior, behind a seemingly chaotic one.
The workshop is intended for systems and control researchers who are interested in developing theoretical and practical computational tools for analysis and synthesis problems in the area of complex systems. Due to the emerging importance of dealing with and governing complexity of dynamical structures, we believe that the workshop may attract a large audience of conference attendees, including students as well as experienced researchers. Presentations aim at giving a comprehensive picture of available results together with a stimulating view of possible new directions of investigation and research in the field. Since the workshop will emphasize methodologies supported by a solid computational background and it will illustrate concrete applications, scientists who either focus on practical engineering aspects or are mainly involved in theoretical issues are equally welcome.
Morning Session I:
– 9:00: Opening Elena Zattoni (Alma Mater Studiorum – University of Bologna, Italy), Anna Maria Perdon (Polytechnic University of Marche, Italy) and Giuseppe Conte (Polytechnic University of Marche, Italy)
– 9:00–9:45: “Structure evolving systems and engineering design: Structural problems”, Nicos Karcanias (City University of London, UK)
– 9:45–10:30: “Stability and the Kleinian view of geometry”, Zoltán Szabó (Hungarian Academy of Sciences, Hungary) and Jozsef Bokor (Hungarian Academy of Sciences, Hungary)
10:30-11:00: Coffee break
Morning Session II:
– 11:00–11:45: “Controllability of networks”, Kanat Camlibel (University of Groningen, The Netherlands)
– 11:45–12:30: “Output regulation of hybrid linear systems: Solvability conditions and structural implications”, Sergio Galeani (University of Rome “Tor Vergata”, Italy) and Mario Sassano (University of Rome “Tor Vergata”, Italy)
12:30-14:00: Lunch break
Afternoon Session I:
– 14:00–14:45: “A stratified geometric approach to the disturbance decoupling problem with stability for switched discrete-time systems over digraphs”, Andrea Serrani (The Ohio State University, USA) and Junqiang Zhou (GE Global Research, USA)
– 14:45–15:30: “The unknown-input observation problem for hybrid dynamical structures”, Giuseppe Conte (Polytechnic University of Marche, Italy), Anna Maria Perdon (Polytechnic University of Marche, Italy) and Elena Zattoni (Alma Mater Studiorum – University of Bologna, Italy)
15:30-16:00: Coffee Break
Afternoon Session II:
– 16:00–16:45: “Advances of implicit description techniques in modelling and control of complex systems”, Moisés Bonilla (Control Automatico, CINVESTAV IPN and UMI LAFMIA CNRS, Mexico), Michel Malabre (Laboratoire des Sciences du Numérique de Nantes, France) and Vadim Azhmyakov (Department of Basic Science, University of Medellin, Colombia)
– 16:45–17:30: “Huygens synchronization over distributed media – Structure versus complex behavior” Vladimir Rasvan (University of Craiova, Romania)
– 17:30: Closing Elena Zattoni, Anna Maria Perdon and Giuseppe Conte
(* The name of the confirmed speakers is underlined)
Extended abstracts of the talks and brief bios of the speakers can be found here.