# SYSTeMS research

The research of the SYSTeMS research group is situated in different domains. Here, we give a short description of each of these domains.- Stability and stabilisation
- Optimization of dynamical systems
- Lagrangian and Hamiltonian systems: modeling and regulation
- Synchronisation of oscillators
- Control of discrete event systems
- Feedback control for on-line management of networks
- Imprecise probabilities as knowledge representations
- Machine Learning
- Modelling and Control in Biomedical Applications
- UAVs (Unmanned Aerial Vehicles)

## Stability and stabilisation

These notions are fundamental in the study of dynamical systems. The focus is on the development of new techniques in order to study the stability and the stabilization of nonlinear time-varying systems and in particular applications from engineering. The techniques are based on the method of Lyapunov or on averaging techniques, and take into account specific properties of the systems under study.

## Optimization of dynamical systems

By minimization of a cost function we may be able to design control algorithms with interesting properties. We are currently considering optimization principles in order to design optimal trajectories in space mission projects.

## Lagrangian and Hamiltonian systems: modeling and regulation

A large number of mechanical and electromechanical engineering systems can be modeled as Lagrangian or Hamiltonian systems. When developing control algorithms it is advised to take into account this specific structure since this leads to robustness of these algorithms. The classical Lagrangian/Hamiltonian framework may not accommodate particular applications (DC to DC power converters, interconnections of Lagrangian/Hamiltonian systems). The Hamiltonian framework has recently been extended in order to cope with more general systems. We are currently investigating extensions of the Lagrangian framework and the corresponding variational principle, with the Pontryagin maximum principle playing a central role. This approach has already been applied in the modeling of electrical networks.

## Synchronisation of oscillators

Coupled oscillators can be found throughout the natural world: pacemaker cells in the heart; neural networks in the brain and spinal cord that control rhythmic behaviours such as breathing, running. Particular applications in chemistry, biology and physics are other examples. Current research focuses on the understanding of the onset of synchronized behaviour.

## Control of discrete event systems

The modelling of complex systems, such as integrated production units, communication or transportation etworks, often requires the use of abstract models that represent only the successive discontinuous changes of the state of the plant. Petri nets can be used to represent such discrete event systems. Recent research has used both the graphical representation and the linear algebraic tools available for Petri net in order to synthesize supervisory controllers guaranteeing that the system always satisfies given specifications. The emphasis of the present research is on the improvement of the control ynthesis by using temporal information, on the synthesis of decentralised controllers, and on fault detection.

## Feedback control for on-line management of networks

Feedback concepts are very useful for the automatic synthesis of on-line managment systems for communication and transportation networks. Traffic loads throughout the network are observed by a decentralised controller in order to assign to each connection using the network its allocated capacity, in such a way that the network resources are used optimally. Recent work has investigated algorithms for estimating the gradient of performance measures on the basis of one single simulated trajectory. The estimated gradient can then be used in order to optimally adjust the controller parameters. Other recent research has developed adaptive predictors of the load, taking the long-range dependence load into account.

## Imprecise probabilities as knowledge representations

In modelling a system, it often occurs that some of its aspects, or some of the influences acting on it, are not well known. The uncertainty this produces about the system's behaviour is usually modelled by a probability measure, and treated using techniques from probability theory. Such a model will often not be adequate, for instance because not enough information is available in order to identify a unique probability measure. In that case, techniques from the theory of imprecise probabilities (a recent extension of probability theory) can be applied in order to represent and manipulate the really available knowledge about the system. Research is being conducted into the mathematical properties of important subclasses of imprecise probability models, into the dynamical behaviour of learning systems in which the existing (and evolving) knowledge is represented by an imprecise probability model, and into the optimal control of systems modelled using imprecise probabilities.

## Machine Learning

Machine learning investigates the mechanisms by which knowledge is acquired through experience. Research at UGent spans the spectrum of models for learning, including those based on statistics, mathematics, neural structures, information theory, and evolutionary search algorithms.

Our research involves the development and analysis of algorithms that identify patterns in observed data in order to make predictions about unseen data. New learning algorithms often result from research into the effect of problem properties on the accuracy and run-time of existing algorithms. We investigate learning from structured databases (for applications such as classifying malignant brain tumours), image data (for applications such as quality assesment).

Databases with millions of records and thousands of fields are now common in business, medicine, engineering, and the sciences. The problem of extracting useful information from such data sets is an important practical problem. Research on this topic focuses on key questions such as how can one build useful descriptive models that are both accurate and understandable? Probabilistic and statistical techniques in particular, play a key role in both analyzing the inference process from a theoretical viewpoint and providing a principled basis for algorithm development.

## Modelling and Control in Biomedical Applications

The human respiratory system is a complex structure, with a defined morphology and geometry. Symmetry of the respiratory system allows to develop geometrically-based parametric models which deliver physiological insight in non-invasive lung function tests (Forced Oscillation Technique).

Continuous efforts are directed towards optimal drug dosing control in Intensive Care Unit, for intra- or post-operatory patients. The level of anaesthesia in surgery and the optimal nociceptive parameters in Intensive Care are two of the most important measurements with deep impact on the patient healthcare. The blood glucose level is also important to ensure stability of the patient to the drug intake (which affects glycemia), especially for diabetic patients. Advanced (predictive) control techniques are developed and optimized to deliver stable and robust closed-loop performance.

## UAVs (Unmanned Aerial Vehicles)

An unmanned aerial vehicle is a remotely controlled or autonomous aircraft (rotorcraft, airship, etc.) used to perform a given mission. During the last 3 years, design, building, modelling and control of micro air vehicles have been carried out in UGent. Currently, new control algorithms are being tested on a 40 cm wingspan micro air vehicle. New ideas regarding reaching of specific missions involve theory of cooperative control and multi-agent systems, where more than one aircraft must be used. The developing of those ideas and their implementation on UAV swarms are the research challenge for the coming years.