Related papers: Linear-quadratic optimal control for infinite-dime…
A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…
We consider the variational discretization of a linear-quadratic optimal control problem with pointwise control and state constraints. In order to allow for a Fr\'echet smooth norm, the problem is reformulated by means of a reflexive…
In the past couple of decades, the use of ``non-quadratic" convex cost functions has revolutionized signal processing, machine learning, and statistics, allowing one to customize solutions to have desired structures and properties. However,…
We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…
We study Hamilton Jacobi Bellman equations in an infinite dimensional Hilbert space, with Lipschitz coefficients, where the Hamiltonian has superquadratic growth with respect to the derivative of the value function, and the final condition…
The numerical analysis of a family of distributed mixed optimal control problems governed by elliptic variational inequalities (with parameter $\alpha >0$) is obtained through the finite element method when its parameter $h\rightarrow 0$.…
We revisit the linear programming approach to deterministic, continuous time, infinite horizon discounted optimal control problems. In the first part, we relax the original problem to an infinite-dimensional linear program over a measure…
In this manuscript we consider a class optimal control problem for stochastic differential delay equations. First, we rewrite the problem in a suitable infinite-dimensional Hilbert space. Then, using the dynamic programming approach, we…
Two of the main challenges in optimal control are solving problems with state-dependent running costs and developing efficient numerical solvers that are computationally tractable in high dimension. In this paper, we provide analytical…
We investigate optimal control problems governed by the elliptic partial differential equation $-\Delta u=f$ subject to Dirichlet boundary conditions on a given domain $\Omega$. The control variable in this setting is the right-hand side…
We consider a linear-quadratic elliptic optimal control problem with point evaluations of the state variable in the cost functional. The state variable is discretized by conforming linear finite elements. For control discretization, three…
Adaptive structures are equipped with sensors and actuators to actively counteract external loads such as wind. This can significantly reduce resource consumption and emissions during the life cycle compared to conventional structures. A…
We consider the optimal control of quantum systems interacting non-linearly with an electromagnetic field. We propose new monotonically convergent algorithms to solve the optimal equations. The monotonic behavior of the algorithm is ensured…
A purely state-dependent cost function can be modified by introducing a control-dependent term rewarding submaximal control utilization. A moderation incentive is identically zero on the boundary of the admissible control region and…
We consider transport processes that are modeled by first order hyperbolic partial differential equations. Our goal is to find a full state feedback that makes a given reference profile locally asymptotically stable. To accomplish this we…
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…
Feedback controllers for port-Hamiltonian systems reveal an intrinsic inverse optimality property since each passivating state feedback controller is optimal with respect to some specific performance index. Due to the nonlinear…
We analyze strict dissipativity of generalized linear quadratic optimal control problems on Hilbert spaces. Here, the term ``generalized'' refers to cost functions containing both quadratic and linear terms. We characterize strict…
In various physical implementations of quantum information processing, qubits are realized in a Lambda type system configuration as two stable lower energy levels coupled indirectly via an unstable higher energy level, that is, in…
We study a finite-dimensional continuous-time optimal control problem on finite horizon for a controlled diffusion driven by Brownian motion, in the linear-quadratic case. We admit stochastic coefficients, possibly depending on an…