Related papers: Shape turnpike for linear parabolic PDE models
The concept of turnpike connects the solution of long but finite time horizon optimal control problems with steady state optimal controls. A key ingredient of the analysis of the turnpike is the linear quadratic regulator problem and the…
We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on…
This paper is concerned with the problem of shape optimization of two-dimensional flows governed by the time-dependent Navier-Stokes equations. We derive the structures of shape gradients with respect to the shape of the variable domain for…
This paper is concerned with a shape optimization problem governed by a non-smooth PDE, i.e., the nonlinearity in the state equation is not necessarily differentiable. We follow the functional variational approach of [40] where the set of…
We consider a shape optimization problem written in the optimal control form: the governing operator is the $p$-Laplacian in the Euclidean space $\R^d$, the cost is of an integral type, and the control variable is the domain of the state…
Considering a general nonlinear dissipative finite dimensional optimal control problem in fixed time horizon T , we establish a two-term asymptotic expansion of the value function as $T\rightarrow+\infty$. The dominating term is T times the…
Recent studies have explored finite-time dissipation-minimizing protocols for stochastic thermodynamic systems driven arbitrarily far from equilibrium, when granted full external control to drive the system. However, in both simulation and…
A central goal of thermodynamics is to identify optimal processes during which the least amount of energy is dissipated into the environment. Generally, even for simple systems, such as the parametric harmonic oscillator, optimal control…
We propose a time domain decomposition approach to optimal control of partial differential equations (PDEs) based on semigroup theoretic methods. We formulate the optimality system consisting of two coupled forward-backward PDEs, the state…
We use the continuation and bifurcation package pde2path to numerically analyze infinite time horizon optimal control problems for parabolic systems of PDEs. The basic idea is a two step approach to the canonical systems, derived from…
We use non-equilibrium dynamical mean field theory and a real-time diagrammatic impurity solver to study the heating associated with time-dependent changes of the interaction in a fermionic Hubbard model. Optimal ramp shapes U(t) which…
Optimal transport has gained significant attention in recent years due to its effectiveness in deep learning and computer vision. Its descendant metric, the Wasserstein distance, has been particularly successful in measuring distribution…
This paper presents first results for near optimality in expectation of the closed-loop solutions for stochastic economic MPC. The approach relies on a recently developed turnpike property for stochastic optimal control problems at an…
In this article, we establish exponential turnpike theorems for a class of nonlinear deterministic meanfield optimal control problems. We carry out our analysis simultaneously in the so-called Lagrangian and Eulerian frameworks. In the…
We consider a vibrating string that is fixed at one end with Neumann control action at the other end. We investigate the optimal control problem of steering this system from given initial data to rest, in time T , by minimizing an objective…
A crucial problem in shape deformation analysis is to determine a deformation of a given shape into another one, which is optimal for a certain cost. It has a number of applications in particular in medical imaging. In this article we…
We extend the time-dependent variational principle to the setting of dissipative dynamics. This provides a locally optimal (in time) approximation to the dynamics of any Lindblad equation within a given variational manifold of mixed states.…
We present a method to extract temporal hypergraphs from sequences of 2-dimensional functions obtained as solutions to Optimal Transport problems. We investigate optimality principles exhibited by these solutions from the point of view of…
We consider two-dimensional homogeneous shear turbulence within the context of optimal control, a multi-scale turbulence model containing the fluctuation velocity and pressure correlations up to the fourth order; The model is formulated on…
In this paper we analyze the relaxed form of a shape optimization problem with state equation $\{{array}{ll} -div \big(a(x)Du\big)=f\qquad\hbox{in}D \hbox{boundary conditions on}\partial D. {array}.$ The new fact is that the term $f$ is…