Dynamical Systems, Control and Optimization

Identification of dynamical systems is one of the first steps in the study of dynamical systems, since it addresses the issue of finding an appropriate model for its input/output behavior. Much of our work on identification has focused on understanding the connections between, identifiability, informative experiments, the information matrix and the minimization of a prediction error criterion.

Several new multi-agent models have been proposed and studied with behavior reminiscent of the partial entrainment behavior of the Kuramoto-Sakaguchi model, but with a greater potential for analysis and with applications to systems not related to coupled oscillators. The main emphasis on these dynamic models is to analyze the asymptotic clustering behavior. The analysis of such models is relevant in the study of opinion formation, interconnected water basins, platoon formation in cycling races, and the minimum cost flow problem.

We study fundamental issues in modeling, control design and stability analysis of physical networks described by hyperbolic systems of conservation laws and by distributed parameter systems modeling e.g. tubular reactors. We also study problems related to optimal prediction of nonlinear systems, such as the flow in channels (modeled by Saint-Venant equations), the modeling of the water level in water basins in order to prevent flooding and the prediction and control of traffic jams.

Optimization techniques play a fundamental role in the area of dynamical systems and they are being developed and analyzed at several levels, depending on the type of variables one wishes to optimize. Variables can be discrete (as in graph theoretic problems) or continuous (as in parametric optimization), but can also be infinite dimensional (as in optimal control over function spaces) and constrained (as in optimization on manifolds or on cones). The group has activities in each of these areas and also develops special purpose numerical techniques for dealing efficiently with such problems.

The activities here include microbial ecology and the modeling of wastewater treatment, including applications to various biological wastewater systems. We developed population balance models covering a large spectrum of applications in the industry of polymer production, crystallization, biotechnology or any process in which the size distribution of particles is essential for process quality. We also study the design and application of observers converging in finite time for a class of fed-batch processes.

We combine theoretical and experimental approaches to investigate the neural control of movement and its interactions with our environment. The mathematical models that are developed are based on experimental results from both normal and pathological subjects (clinical studies) and focus on the interaction between different types of eye movements and on eye/hand coordination. Our main research objective is to gain further insight into the nature and characteristics of high-level perceptual and motor representations in the human brain.