Related papers: Controllability of evolution equations with memory
In this paper, we obtain a null controllability result for a coupled fourth order parabolic system based on the Stackelberg-Nash strategies. For this purpose, we first prove the existence and uniqueness of Nash equilibrium pair of the…
The goal of the present article is to study controllability properties of mixed systems of linear parabolic-transport equations, with possibly non-diagonalizable diffusion matrix, on the one-dimensional torus. The equations are coupled by…
We investigate control problems for wave-Petrovsky coupled systems in the presence of memory terms. By writing the solutions as Fourier series, we are able to prove Ingham type estimates, and hence reachability results. Our findings have…
In this paper it is considered a class of infinite-dimensional control systems in a variational setting. By using a Faedo-Galerkin method, a sequence of approximating finite dimensional controlled differential equations is defined. On each…
This review examines classical and recent results on controllability and inverse problems for hyperbolic and dispersive equations with dynamic boundary conditions. We aim to illustrate the applicability of Carleman estimates to establish…
Differential balancing theory for nonlinear model reduction relies on differential controllability and observability functions. In this paper, we further investigate them from two different perspectives. First, we establish novel…
We study the minimum energy null-controllability problem for differential equations with point-wise delays. For the equations of both neutral and retarded type we reduce the problem of finding the optimal control to a Volterra integral…
We investigate the well-posedness and solution regularity of an evolution equation with non-positive type variable-exponent memory, which describes multiscale viscoelasticity in materials with memory. The perturbation method is applied for…
In this paper we consider a fourth order nonlinear parabolic delayed problem modelling a quasi-instantaneous turn-over of linkages in the context of cell-motility. The model depends on a small parameter $\epsilon$ which represents a typical…
This paper presents a closed-form notion of controllability and observability for systems with communication delays, actuation delays, and locality constraints. The formulation reduces to classical notions of controllability and…
Quantum control is traditionally expressed through bilinear models and their associated Lie algebra controllability criteria. But, the first order approximation are not always sufficient and higher order developpements are used in recent…
This work is concerned with the time optimal control problem for evolution equations in Hilbert spaces. The attention is focused on the maximum principle for the time optimal controllers having the dimension smaller that of the state…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
The verification theorem serving as an optimality condition for the optimal control problem, has been expected and studied for a long time. The purpose of this paper is to establish this theorem for control systems governed by stochastic…
We study several aspects of the dynamic programming approach to optimal control of abstract evolution equations, including a class of semilinear partial differential equations. We introduce and prove a verification theorem which provides a…
In this paper we investigate the Hierarchical null controllability of a coupled degenerate semilinear parabolic equation in domains which are moving in time. We show the local null controllability of the semilinear system using Liusternik's…
We investigate a backward anisotropic stochastic parabolic equation with general dynamic boundary conditions, where the drift involves both $\mathbb{L}^2$ and $\mathbb{H}^{-1}$ bulk--surface terms. We first establish the well-posedness of…
The purpose of this paper is to establish first and second order necessary optimality conditions for optimal control problems of stochastic evolution equations with control and state constraints. The control acts both in the drift and…
As Evolutionary Dynamics moves from the realm of theory into application, algorithms are needed to move beyond simple models. Yet few such methods exist in the literature. Ecological and physiological factors are known to be central to…
In this paper, we prove the null controllability of a one-dimensional fourth-order degenerate parabolic equation with a singular potential. Here, we analyze cases where boundary control conditions are applied at the left endpoint. We…