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Relying on the careful study of a related problem in the calculus of variations, we study a class of optimal control problems in which the control lies on the acceleration, with state constraints on the position variable. In dimension one,…
We design and analyze solution techniques for a linear-quadratic optimal control problem involving the integral fractional Laplacian. We derive existence and uniqueness results, first order optimality conditions, and regularity estimates…
In this paper, motivated by the study of optimal control problems for infinite dimensional systems with endpoint state constraints, we introduce the notion of finite codimensional (exact/approximate) controllability. Some equivalent…
The inverse conductivity problem aims at determining the unknown conductivity inside a bounded domain from boundary measurements. In practical applications, algorithms based on minimizing a regularized residual functional subject to PDE…
Traditional solvable optimal control theory predominantly focuses on quadratic costs due to their analytical tractability, yet they often fail to capture critical non-linearities inherent in real-world systems including water, energy,…
In this paper, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a…
We consider an optimal control problem governed by an elliptic variational inequality of the second kind. The problem is discretized by linear finite elements for the state and a variational discrete approach for the control. Based on a…
This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous…
In this paper a priori error estimates are derived for full discretization (in space and time) of time-optimal control problems. Various convergence results for the optimal time and the control variable are proved under different…
This paper investigates the Nash equilibrium of a bi-objective optimal control problem governed by the Stokes equations. A multi-objective Nash strategy is formulated, and fundamental theoretical results are established, including the…
Optimal control of bilinear systems has been a well-studied subject in the area of mathematical control. However, techniques for solving emerging optimal control problems involving an ensemble of structurally identical bilinear systems are…
We consider Inverse Electrical Impedance Tomography (EIT) problem on recovering electrical conductivity and potential in the body based on the measurement of the boundary voltages on the $m$ electrodes for a given electrode current. The…
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t \rho - \nu \Delta \rho - {\rm div } \big(\rho B[u]\big) = 0. \] The control variable $u$ is time-dependent and possibly…
We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…
We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…
We consider control constrained optimal control problems governed by parameterized stationary Maxwell's system with the Gauss's law. The parameters enter through dielectric, magnetic permeability, and charge density. Moreover, the parameter…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
We adopt the integral definition of the fractional Laplace operator and study an optimal control problem on Lipschitz domains that involves a fractional elliptic partial differential equation (PDE) as state equation and a control variable…
We consider optimal control problems with integer-valued controls and a total variation regularization penalty in the objective on domains of dimension two or higher. The penalty yields that the feasible set is sequentially closed in the…
This paper presents a method to approximately solve stochastic optimal control problems in which the cost function and the system dynamics are polynomial. For stochastic systems with polynomial dynamics, the moments of the state can be…