Related papers: A shape optimal control problem and its probabilis…
This paper investigates the problem of optimal predictor design for distributed parameter systems using neural networks and shape optimization. Sensors with various shapes are placed on the domain of the distributed parameter system. Data…
This article investigates the numerical approximation of shape optimization problems with PDE constraint on classes of convex domains. The convexity constraint provides a compactness property which implies well posedness of the problem.…
In this article, we consider parabolic equations on a bounded open connected subset $\Omega$ of $\R^n$. We model and investigate the problem of optimal shape and location of the observation domain having a prescribed measure. This problem…
The paper studies a class of quadratic optimal control problems for partially observable linear dynamical systems. In contrast to the full information case, the control is required to be adapted to the filtration generated by the…
In this paper, we focus on the following general shape optimization problem: $$ \min\{J(\Om), \Om convex, \Om\in\mathcal S_{ad}\}, $$ where $\mathcal S_{ad}$ is a set of 2-dimensional admissible shapes and $J:\mathcal{S}_{ad}\to\R$ is a…
This paper provides necessary conditions of optimality for optimal control problems with time delays in both state and control variables. Different versions of the necessary conditions cover fixed end-time problems and, under additional…
The goal of this paper is to address some optimal control and shape optimisation problems arising from bulk-surface cooperative systems. The basic model under consideration is the following: letting $\Omega$ be a fixed domain, we assume…
We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic…
We are interested in the question of stability in the field of shape optimization, with focus on the strategy using second order shape derivative. More precisely, we identify structural hypotheses on the hessian of the considered shape…
We investigate a control process described by a linear system of ordinary differential equations with a noise of special type acting to the control parameter. As the cost functional the probability of the final state vector to enter to a…
This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…
Shape optimization models with one or more shapes are considered in this chapter. Of particular interest for applications are problems in which where a so-called shape functional is constrained by a partial differential equation (PDE)…
This paper deals with shape optimization for elastic materials under stochastic loads. It transfers the paradigm of stochastic dominance, which allows for flexible risk aversion via comparison with benchmark random variables, from…
We study optimal design problems involving variational inequalities with unilateral conditions in the domain and pointwise boundary observation. We use regularizing and penalization tehniques in the setting of the Hamiltonian approach to…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
We are interested in the optimization of convex domains under a PDE constraint. Due to the difficulties of approximating convex domains in $\mathbb{R}^3$, the restriction to rotationally symmetric domains is used to reduce shape…
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…
We consider an optimal control problem for the steady-state Kirchhoff equation, a prototype for nonlocal partial differential equations, different from fractional powers of closed operators. Existence and uniqueness of solutions of the…
We consider optimal control problems, where the control appears in the main part of the operator. We derive the Pontryagin maximum principle as a necessary optimality condition. The proof uses the concept of topological derivatives. In…
We prove a general existence result in stochastic optimal control in discrete time where controls take values in conditional metric spaces, and depend on the current state and the information of past decisions through the evolution of a…