Related papers: Some optimal control and shape optimisation proble…
We consider the unit ball $\Omega\subset \mathbb{R}^N$ ($N\ge2$) filled with two materials with different conductivities. We perform shape derivatives up to the second order to find out precise information about locally optimal…
We consider an optimal shape design problem for the plate equation, where the variable thickness of the plate is the design function. This problem can be formulated as a control in the coefficient PDE-constrained optimal control problem…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
Empirical observations show that ecological communities can have a huge number of coexisting species, also with few or limited number of resources. These ecosystems are characterized by multiple type of interactions, in particular…
We propose a semi-discrete numerical scheme and establish well-posedness of a class of parabolic systems. Such systems naturally arise while studying the optimal control of grain boundary motions. The latter is typically described using a…
This work studies shape filtering techniques, namely the convolution-based (explicit) and the PDE-based (implicit), and introduces an implicit bulk-surface filtering method to control the boundary smoothness and preserve the internal mesh…
Direct optimal control theory for quantum dynamical problems presents itself as an interesting alternative to the traditional indirect optimal control. The method relies on the first discretize and then optimize paradigm, where a…
The game interactions among individuals in nature are often uncertain and dynamically evolving, significantly influencing the persistence of cooperation. However, it remains a formidable challenge to effectively characterize these dynamic…
This paper deals with shape irregularity issues in discrete topology optimization algorithms whereby the design is created using the automated distribution of material in the design region. Graph theory is employed to derive appropriate…
Sustainable Development Goals are intrinsically competing, but their embedding into urban systems furthermore emphasises such compromises, due to spatial complexity, the non-optimal nature of such systems, and multi-objective aspects of…
To ensure preservation of local or global bounds for numerical solutions of conservation laws, we constrain a baseline finite element discretization using optimization-based (OB) flux correction. The main novelty of the proposed methodology…
In this article, we employ an input-output approach to expand the study of cooperative multi-agent control and optimization problems characterized by mean-field interactions that admit decentralized and selfish solutions. The setting…
The optimal offloading of tasks in heterogeneous edge-computing scenarios is of great practical interest, both in the selfish and fully cooperative setting. In practice, such systems are typically very large, rendering exact solutions in…
We present an optimal control problem to guide the selection of morphology classes arising in organic solar cells. The study focuses on phase separation processes in polymer solvent mixtures, with particular attention to solvent evaporation…
We optimize a selection of eigenvalues of the Laplace operator with Dirichlet or Neumann boundary conditions by adjusting the shape of the domain on which the eigenvalue problem is considered. Here, a phase-field function is used to…
We investigate a PDE-constrained optimization problem, with an intuitive interpretation in terms of the design of robust membranes made out of an arbitrary number of different materials. We prove existence and uniqueness of solutions for…
Swarm robotic systems utilize collective behaviour to achieve goals that might be too complex for a lone entity, but become attainable with localized communication and collective decision making. In this paper, a behaviour-based distributed…
The quest on how to collectively self-organize in order to maximize the survival chances of the members of a social group requires finding an optimal compromise between maximizing the well-being of an individual and that of the group. Here…
We study an optimal transport problem in a compact convex set $\Omega\subset\mathbb{R}^d$ where bulk transport is coupled to dynamic optimal transport on a metric graph $ \mathsf{G} = (\mathsf{V},\mathsf{E})$ which is embedded in $\Omega$.…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…