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ResearchBernoulli InstituteDepartmentsSystems, Control and Applied Analysis

Description

The research program Systems, Control and Applied Analysis (SCAA) is devoted to the analysis, control and optimization of complex large-scale dynamical systems. The mathematical research in this program is motivated by a wide range of applications in the engineering and natural sciences.

Mathematical systems and control theory deals with the mathematical modeling, analysis and control of open systems evolving in time. The dynamics is described by ordinary or partial differential equations, or can be a mixture of continuous and discrete dynamics. This dynamical behavior is not only sought to be analyzed, but to be influenced (controlled) and optimized as well; by the addition of feedback loops, and by the interconnection to other dynamical systems (controller design). Furthermore, dynamical data are used to identify the underlying model, or to approximate it by a model of lower dimension.

Typically, the system models under consideration are described by under-determined sets of equations. As a result, there are free variables in the system description (corresponding to 'inputs'), which together with information about the current state of the system (corresponding to 'outputs') model the interaction with other systems or the environment. Furthermore, the systems point of view is emphasized, in the sense that large-scale dynamical systems are viewed as networks of interconnected systems, where the overall dynamics is determined by the dynamics of the system components plus the network and feedback structure. This point of view is prevailing in many areas of engineering science and economics, and is receiving increasing attention in the life sciences ('reverse engineering'). The modeling, control, and optimization of complex dynamics brings together a variety of mathematical theories and tools, from analysis, geometric control, multi-physics modeling and stability theory, to algebraic graph theory, Hamiltonian systems and (distributed) optimization.

The members of the program have close collaboration and joint projects with colleagues working in other scientific disciplines such as control engineering, smart energy systems, robotics, transportation systems, and systems biology. In particular, there is a close collaboration with the control engineering groups DTPA and SMS at the neighboring Engineering and Technology Institute (ENTEG), under the umbrella of the Jan C. Willems Center for Systems and Control.

Although the focus in the program is on fundamental mathematical developments, the research is motivated by a number of application areas, and applied to these in collaboration with colleagues. Present day application topics include energy systems (stability and control of power networks, dynamic pricing, systems integration), systems biology (chemical reaction networks, regulation), and transportation systems (e.g., vehicle platooning).

Systems, Control and Applied Analysis
Systems, Control and Applied Analysis

The main research themes in the program are:
  1. Network dynamics and control (Kanat Camlibel, Harry Trentelman, Arjan van der Schaft, Bart Besselink, Oleksandr Ivanov, Mark Jeeninga, Monika Jozsa, Jia Jiajia, Junjie Jiao, Pooya Monshizadeh, Li Wang, Henk van Waarde).
    Network dynamics and dynamical multi-agent systems arise in many fields of engineering and natural sciences. Systems and control theory contributes to this area by providing concepts and tools for the study of structural properties such as controllability (leader-follower networks) and model reduction, and for their control including synchronization and consensus dynamics. This entails a close interplay between geometric systems and control theory on the one hand, and algebraic graph theory on the other. Applications include power and sensor networks, dynamical distribution networks, as well as large-scale chemical reaction networks in systems biology.

  2. Geometric modeling and control of multi-physics systems (Arjan van der Schaft, Filip Koerts, Pooya Monshizadeh, Rodolfo Reyes Baez, Tjerk Stegink, Li Wang).
    Port-Hamiltonian systems constitute an extension of Hamiltonian systems where external interaction and energy-dissipating ports are taken into account, and the underlying geometry is derived from the interconnectionstructure of the complex system. The aim of this research is to provide a systematic geometric theory for the modeling, analysis and simulation of multi-physics, lumped- and distributed parameter, systems. Current focal themes include the geometric modeling and analysis of power systems and of thermodynamical systems. The port-Hamiltonian formulation is employed for controller design, leading to physically inspired and robust control strategies. Applications include stabilization and demand-supply matching in power systems, control of robotic systems and distribution networks, and analysis and control of chemical reaction networks.

  3. Mathematical systems theory (Kanat Camlibel, Harry Trentelman, Bart Besselink, Stephan Trenn, Arjan van der Schaft, Junjie Jiao, Monika Jozsa, Jaap Eising, Noorma Yulia Megawati).
    Mathematical systems theory deals with the modeling and analysis of open and interconnected systems. This naturally leads to models containing differential and algebraic equations, called DAE systems. Current research themes concern equivalence and minimality notions, and model reduction. Furthermore, physical systems often do not exhibit an a priori fixed information flow direction. In the behavioral approach, all external system variables are therefore in first instance treated on an equal footing. Hybrid systems are a mixture of interacting continuous and discrete dynamics, and arise naturally in embedded systems and physical systems modeling, including switched DAE systems and convex processes. Important research issues concern the analysis of solution trajectories, and the structural properties of controllability and stabilizability, as well as the design of controllers. The mathematical analysis of switched and piecewise-affine and systems is heavily intertwined with convex optimization theory and non-smooth analysis. Another line of research concerns the compositional analysis and design of interconnected systems, developing notions and tools of assume-guarantee reasoning and contract-based design using geometric control theory.

  4. Modeling, control and optimization of energy systems (Arjan van der Schaft, Kanat Camlibel, Stephan Trenn, Mark Jeeninga, Filip Koerts, Pooya Monshizadeh, Tjerk Stegink).
    Power networks, from high-voltage distribution networks to AC or DC micro-grids, constitute an application area of growing importance and interest. Furthermore, there is an increasing trend for integration with other energy systems such as gas distribution networks. The aim of this theme is to develop a sound mathematical framework for the modeling, optimization and control of large-scale energy systems. This includes the systematic modeling of components such as synchronous generators and converters, as well as of the transmission line network. Based on these models fundamental problems of stability and power sharing are addressed, as well as optimal demand-supply matching by dynamic pricing, coupling physical dynamics to market dynamics. Furthermore, integration of power networks with other energy systems leads to large-scale distributed optimization problems. This research is mostly carried out in a collaborative effort with colleagues from ENTEG.

  5. Control of distributed-parameter systems and inverse problems (Alden Waters, Arjan van der Schaft).
    This research theme is concerned with the analysis, control and estimation of systems described by partial differential equations. Current themes of interest are approximations to solutions for coupled systems of hyperbolic wave equations, and issues of short time well-posedness and parameter recovery from solution waves. Structure-preserving spatial discretization and model reduction for control.

    Further information can be found on the local web pages maintained by the research group.

Last modified:17 July 2019 1.48 p.m.