DyCon project identifies and focuses on six key topics that play a central role in most of the processes arising in applications, but which are still poorly understood, namely: control of parameter dependent problems, long time horizon control…

#### Optimal control applied to collective behaviour

The standard approach for solving a driving problem is a leadership strategy, based on the attraction that a driver agent exerts on other agent. Repulsion forces are mostly used for collision avoidance, defending a target or describing the need for personal space. We present a “guidance by repulsion” model describing the behaviour of two agents, a driver and an evader…

#### Greedy Control

Control of a parameter dependent system in a robust manner. Fix a control time , an arbitrary initial data , and a final target …

#### From finite to infinite-dimensional models (FI)

Our team has made some high impact contributions in the description of the limit, as the mesh sizes tend to zero, of numerical schemes for wave equations. These results also provide insight into the link between conservative finite and infinite-dimensional dynamical systems. We have also developed the theoretical control consequences of these facts, which show…

#### Models involving memory terms & hybrid PDE+ODE systems (MHM)

Control theory for PDEs has been quite exhaustively developed for model problems (heat and wave equations). But other important models in applications, of hybrid nature, remain poorly understood: models involving memory terms in viscoelasticity. Our team recently made key contributions in this area, inspired in the work by P. Martin, L. Rosier and P. Rouchon…

#### Inverse design and control in the presence of singularities (SINV)

Some important PDE models in Continuum Physics, such as hyperbolic conservation laws, represent a major challenge from a control viewpoint for two (closely related) reasons: solutions lack regularity properties and develop shock discontinuities in finite time, making linearization methods inapplicable the property of backward uniqueness is lost in the absence of viscosity effects and the…

#### Control under constraints (CC)

Most of the existing theory of controllability for PDEs has been developed in the absence of constraints on the states. Thus, in practice, most of the available controllability results do not ensure that controlled trajectories fulfil the physical constraints of the process under consideration. Nevertheless, these constraints, often formulated as unilateral bounds on the controlled…

#### Long time horizon control (LTHC)

Control problems for evolution PDEs are most often considered in finite time intervals, without paying attention to the length of the control horizon and how it affects the optimal trajectories and controls. However, the effective available time horizon is one of the critical factors in applications, as it occurs in the design of medical therapies,…

#### Control of parameter dependent problems (PDC)

In applications, models are not completely known, since the relevant parameters (deterministic or stochastic) are subject to uncertainty. It is therefore essential to develop robust analytical and computational methods that not only allow a given realisation of the model to be controlled, but also to deal with parameter-dependent families of systems in a stable and…

#### About the Project

DyCon project aims at making a breakthrough contribution in the broad area of Control of Partial Differential Equations (PDE) and their numerical approximation methods by addressing key unsolved issues appearing systematically in real-life applications…