Related papers: Control and numerical approximation of fractional …
We examine the minimization of a quadratic cost functional composed of the output and the final state of abstract infinite-dimensional evolution equations in view of existence of solutions and optimality conditions. While the initial value…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We study a nonlinear elliptic problem defined in a bounded domain involving fractional powers of the Laplacian operator together with a concave-convex term. We characterize completely the range of parameters for which solutions of the…
In this work, we study the control constrained distributed optimal control of a stationary doubly diffusive flow model. For the control problem, we use a well-posedness analysis based on minimal assumptions on data and domain. We show the…
In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
In this article, the piecewise-linear finite element method (FEM) is applied to approximate the solution of time-fractional diffusion equations on bounded convex domains. Standard energy arguments do not provide satisfactory results for…
The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…
This article addresses the inverse source problem for a nonlocal heat equation involving the fractional Laplacian. The primary goal is to reconstruct the spatial component of the source term from partial observations of the system's state…
We study the controllability to trajectories, under positivity constraints on the control or the state, of a one-dimensional heat equation involving the fractional Laplace operator $ (-\partial_x^2)^s$ (with $0<s<1$) on the interval…
H-infinity optimal control and estimation are addressed for a class of systems governed by partial differential equations with bounded input and output operators. Diffusion equations are an important example in this class. Explicit formulas…
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order $\alpha\in(0,1)$ in time, due to their many successful applications in engineering, physics, biology…
The goal of this work is to compute a boundary control of reaction-diffusion partial differential equation. The boundary control is subject to a constant delay, whereas the equation may be unstable without any control. For this system…
We provide a novel approach to the numerical solution of the family of nonlocal elliptic equations $(-\Delta)^su=f$ in $\Omega$, subject to some homogeneous boundary conditions $\mathcal{B}(u)=0$ on $\partial \Omega$, where $s\in(0,1)$,…
Fractional equations have become the model of choice in several applications where heterogeneities at the microstructure result in anomalous diffusive behavior at the macroscale. In this work we introduce a new fractional operator…
Dual control explicitly addresses the problem of trading off active exploration and exploitation in the optimal control of partially unknown systems. While the problem can be cast in the framework of stochastic dynamic programming, exact…
We investigate the exact enlarged controllability and optimal control of a fractional diffusion equation in Caputo sense. This is done through a new definition of enlarged controllability that allows us to extend available contributions.…
The current paper initially studies the optimal control of linear $\psi$-Hilfer fractional derivatives with state-dependent control constraints and optimal control for a particular type of cost functional. Then, we investigate the…
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…
We present a novel energy-based numerical analysis of semilinear diffusion-reaction boundary value problems. Based on a suitable variational setting, the proposed computational scheme can be seen as an energy minimisation approach. More…
We study boundary regional controllability problems for a class of semilinear fractional systems. Sufficient conditions for regional boundary controllability are proved by assuming that the associated linear system is approximately…