Related papers: Nonuniqueness of minimizers for semilinear optimal…
We consider a linear-quadratic optimization problem with pointwise bounds on the state for which the constraint is given by the Laplace-Beltrami equation (to have uniqueness we add an lower order term) on a two-dimensional surface . By…
An optimal control problem with an infinite horizon quadratic cost functional for a linear system with a known additive disturbance is considered. The feature of this problem is that a weight matrix of the control cost in the cost…
In this paper, we carry out the analysis of the semismooth Newton method for bilinear control problems related to semilinear elliptic PDEs. We prove existence, uniqueness and regularity for the solution of the state equation, as well as…
The analysis of an optimal control problem of nonlocal type is analyzed. The results obtained are applied to the study the corresponding local optimal control problems. The state equations are governed by p-laplacian elliptic operators, of…
We study optimal control problems that are governed by semilinear elliptic partial differential equations that involve non-Lipschitzian nonlinearities. It is shown that, for a certain class of such PDEs, the solution map is Fr\'{e}chet…
In this paper, we investigate optimal control problems subject to a semilinear elliptic partial differential equations. The cost functional contains a term that measures the size of the support of the control, which is the so-called…
We establish the turnpike property for linear quadratic control problems for which the control operator is admissible and may be unbounded, under quite general and natural assumptions. The turnpike property has been well studied for bounded…
We study the small-regularisation limit of the entropic optimal transport problem on the line with distance cost. While convergence of entropic minimizers is well understood in the discrete setting and in the case where the cost is…
When applying methods of optimal control to motion planning or stabilization problems, some theoretical or numerical difficulties may arise, due to the presence of specific trajectories, namely, singular minimizing trajectories of the…
A large-scale complex system comprising many, often spatially distributed, dynamical subsystems with partial autonomy and complex interactions are called system of systems. This paper describes an efficient algorithm for model predictive…
Nonconvex functionals with spherical symmetry are studied. Existence of one and radial symmetry of all global minimizers is shown with an approach based on convex relaxation.
In this paper, we consider the problem of multi-objective optimal control of a dynamical system with additive and multiplicative noises with given second moments and arbitrary probability distributions. The objectives are given by quadratic…
This paper considers an optimal control problem for a linear mean-field stochastic differential equation having regime switching with quadratic functional in the large time horizons. Our main contribution lies in establishing the strong…
We study the turnpike phenomenon for optimal control problems with mean field dynamics that are obtained as the limit $N\rightarrow \infty$ of systems governed by a large number $N$ of ordinary differential equations. We show that the…
An open question contributed by Yu. Orlov to a recently published volume "Unsolved Problems in Mathematical Systems and Control Theory", V.D. Blondel, A. Megretski (eds), Princeton Univ. Press, 2004, concerns regularization of optimal…
We establish a polynomial turnpike estimate for an optimal control problem consisting of a system of infinitely many controlled oscillators, considered as an abstract differential equation in a Hilbert space, with a quadratic cost. Our…
In this work, we investigate a neural network based solver for optimal control problems (without / with box constraint) for linear and semilinear second-order elliptic problems. It utilizes a coupled system derived from the first-order…
In this paper, we consider a linear quadratic (LQ) optimal control problem in both finite and infinite dimensions. We derive an asymptotic expansion of the value function as the fixed time horizon T tends to infinity. The leading term in…
The classical problem of optimal transportation can be formulated as a linear optimization problem on a convex domain: among all joint measures with fixed marginals find the optimal one, where optimality is measured against a cost function.…
In the contest of optimal control problems, regularity results for optima are known when addressing fiber-strictly convex Lagrangian. For infinite time horizons, or for settings with infinite dimensional dynamics, the equivalence between…