Polynomial optimization and control
Organizer(s): Didier Henrion, Milan Korda, Jean B. Lasserre and Mihai Putinar
The mini-course focuses on polynomial optimization and control, with a focus on semidefinite relaxation techniques exploiting duality between moment problems and representations of polynomials nonnegative on semialgebraic sets.
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Quantum systems: measurement and feedback
Organizer(s): Mazyar Mirrahimi and Pierre Rouchon
The goal of this mini-course is to present some of the particular features of the quantum systems that one needs to study with extra care while discussing system theory concepts such as state and parameter estimation, feedback control, active and passive stabilization. More precisely we will overview the following subjects
- Two-level quantum system, Quantum harmonic oscillator, composite spin-spring system, Jaynes-Cummings model.
- Discrete-time dynamical models and generalized measurements: hidden Markov chain and Kraus maps, state estimation via quantum filtering and Bayes law.
- Stabilization scheme relying on active measurement-based feedback and control Lyapunov techniques.
- Dissipation and continuous-time Lindblad master equation.
- Stabilization scheme relying on passive reservoir (dissipation) engineering.
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Automated verification and synthesis of complex systems
Organizer(s): Majid Zamani, Ilya Tkachev, Manuel Mazo and Alessandro Abate
The objective of this mini-course is to introduce the participants to the topics of correct-by-design synthesis and verification of embedded control software. The main objectives are:
- Make participants new to the topic familiar with relevant concepts and techniques in computer science such as: temporal logics, automata, simulation relations, safety/reachability games, etc.
- Introduce abstraction techniques to construct finite-state models of infinite (stochastic) hybrid systems.
- Introduce algorithmic techniques to automatically synthesize hybrid controllers satisfying some specifications of interest.
- Illustrate the introduced concepts on the MATLAB-based toolbox Pessoa and on a newly developed toolbox for stochastic hybrid systems.
- Exhibit the audience to new directions and areas in formal methods with applications in control.
- Suggest novel applications of the discussed formal techniques.
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Role of graph theory in modeling, analysis and control of electric power systems
Organizer(s): Aranya Chakrabortty and Thomas Nudell
The goal of this mini-course is to educate control engineers about recent advancements of network and control-theoretic research in the field of electric power systems. Our discussion will be particularly geared towards one of the most critical aspect of power system modeling and control, namely - graph theory. Graphs and networks play an ubiquitous role in power system dynamics. Starting from simple electro-mechanical oscillation models of interconnected synchronous generators and loads to more complex nonlinear mechanisms of bifurcation, voltage collapse and cascading failure, almost every aspect of how a power system reacts to external disturbances depends on the characteristics of its underlying network graph. Therefore, a perennial question of interest to power system operators is how this network graph may be designed during planning, or manipulated during operation to guarantee stability, robustness and quality-of-service following large disturbances.
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Stability and stabilization of distributed port-Hamiltonian systems
Organizer(s): Alessandro Macchelli and Markus Schöberl
This mini-course is devoted at illustrating the latest results on the stability analysis, and on the (boundary) stabilisation of distributed port-Hamiltonian systems. Several related topics will be discussed in five short lessons. More in detail, at the beginning, the problems of well-posedness of distributed port-Hamiltonian systems, existence of solutions for the associated systems of PDEs, and definition of a boundary control system in port-Hamiltonian form are addressed. These topics can be seen as the foundations of the remaining part of the course, that is more focused on stability criteria in case of static and dynamic boundary control, and on the energy-based control of this class of infinite dimensional systems. The emphasis is on linear systems with one-dimensional domain, but it is worth mentioning that most of the proposed techniques can be in principal adapted to the nonlinear scenario. However, this extension is not trivial, and it is still an open problem.
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Geometric structures for the modelling, analysis and discretization of infinite-dimensional port-Hamiltonian systems
Organizer(s): Alessandro Macchelli and Markus Schöberl
This mini-course deals with geometric structures that arise in the modelling of infinite-dimensional port-Hamiltonian systems. In four short lessons different geometric structures as well as their system theoretic consequences will be analyzed. This includes symplectic, polysymplectic as well as Stokes-Dirac structures, where the focus is put on the latter class, especially also with regard to diffusion systems and to higher order differential operators.
Additionally, the structure preserving discretization by using simplicial Dirac structures will be discussed by applying tools from discrete exterior calculus. Finally, the connection to functional analytic concepts on Hilbert spaces will be presented.
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From sampled-data control to signal processing
Organizer(s):Yutaka Yamamoto and Masaaki Nagahara
There has been remarkable progress in sampled-data control theory in the last two decades. The main achievement here is that there exists a digital (discrete-time) control law that takes the intersample behavior into account and makes the overall analog (continuous-time) performance optimal, in the sense of H-infinity norm. This naturally suggests its application to digital signal processing where the same hybrid nature of analog and digital is always prevalent. A crucial observation here is that the perfect band-limiting hypothesis, widely accepted in signal processing, is often inadequate for many practical situations. In practice, the original analog signals (sounds, images, etc.) are neither fully band-limited nor even close to be band-limited in the current processing standards. Sampled-data control theory provides an ideal platform for dealing with these problems, and our new design method has become highly successful in commercial applications of sound processing chips (45 million chips produced to date) and AAC/MP3 sound processing audio players applications (iPhone/iPod App).
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Harmonic influence in large-scale networks: Analysis, optimization, and applications to opinion dynamics and distributed control
Organizer(s): Giacomo Como, Fabio Fagnani and Paolo Frasca
Discrete harmonic functions have long proved to be a fundamental analytical tool in applications as diverse as electrical networks, random walks, and mechanical systems of springs. Recently, they have emerged as models for the stationary state of some ergodic opinion dynamics over social networks. This mini-course will provide an introduction to such models and an overview of some recent results in the field. We will illustrate emerging phenomena in large-scale social networks such as homogeneous influence in highly fluid networks, and persistent disagreement and fluctuations. Other current applications will be presented in problems of distributed control and estimation, such as leader-follower models in robotics and estimation from relative measurements.
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System identification in the behavioral setting: A low-rank approximation approach
Organizer(s): Ivan Markovsky, Konstantin Usevich and Mariya Ishteva
Established data modeling approaches are often derived in a stochastic setting. An alternative deterministic approximation approach, known in the systems and control literature as the behavioral approach, has been developed since the 80's by Jan C. Willems and co-workers. The behavioral approach differentiates between the abstract notion of a model and the concrete notion of a model representation. This distinction proves to be important for developing a coherent theory and effective algorithms for system identification, analysis, and control. The mini-course presents a behavioral approach to system identification. The highlight of the mini-course is the low-rank approximation problem, which is a practical tool for modeling in the behavioral setting. A matrix constructed from the data being rank deficient implies that there is an exact low complexity linear model for the data. Moreover, the rank of the data matrix corresponds to the complexity of the model. In the generic case when an exact low-complexity model does not exist, the aim is to find a model that fits the data approximately. The corresponding computational problem is low-rank approximation. In the case of linear time-invariant dynamical models, the data matrix is, in addition, Hankel structured and the approximation should have the same structure.
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Well-posed systems – linear and with nonlinear feedback
Organizer(s): Marius Tucsnak, George Weiss and Hans Zwart
This minicourse is an introduction to well-posed linear time-invartiant (LTI) systems on Hilbert spaces for non-specialists, while also giving a glimse into nonlinear well-posed systems.
In part I (GW) we recall the more general concept of a system node, classical and generalized solutions of system equations, criteria for well-posedness, the subclass of regular linear systems, some of the available linear feedback theory. Motivated by physical examples, we recall the concepts of impedance passive and scattering passive systems, conservative systems and systems with a special structure that belong to these classes. We illustrate this theory by examples of systems governed by heat and wave equations.
In part II (MT) We develop local and global well-posedness results for LTI systems with nonlinear (in particular, bilinear) feedback, by extracting the abstract idea behind various proofs in the literature. We apply these abstract results to derive well-posedness results for the Burgers and Navier-Stokes equations.
In part III (HZ) we present the main results about a special class of well-posed linear systems: those that are port-Hamiltonian systems in one space dimension, including 1D Schrodinger equations and the Euler Bernoulli beam equation.
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Neuronal behaviors
Organizer(s): Rodolphe Sepulchre, Guillaume Drion, Alessio Franci and Julie Dethier
The foundation of today’s computational neuroscience is the 1952 paper of Hodgkin and Huxley. This paper is a model of behavioral modeling. It uses an exquisite combination of parsimonious experiments, biophysical principles, and curve fitting, to reduce the mechanism of the action potential to an elementary switching RC circuit. Yet the default textbook presentation of Hodgkin Huxley model is an obscure set of four nonlinear differential equations that produce oscillations for a well chosen set of parameters. The talk will review the basics of this historical model and emphasizes the importance of regarding this model as a behavior, that is, an open system, regulated by elementary but fundamental feedback principles.
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The mini-course “Quantum Systems: Measurement and Feedback” (Mirrahimi, Rouchon), as well as the Invited Sessions “Quantum Control: Controllability Issues and Modern Control Design Techniques”, Part 1 and 2 (organizer P. Mason), have been organized as a joint activity with the EU Network of Excellence HYCON2 (Highly-complex and networked control systems).