Related papers: Vector-valued multibang control of differential eq…
We consider a class of infinite-dimensional optimization problems in which a distributed vector-valued variable should pointwise almost everywhere take values from a given finite set $\mathcal{M}\subset\mathbb{R}^m$. Such hybrid…
We consider a nonlinear control system with vector-valued measures as controls and with dynamics depending on time delayed states. First, we introduce a notion of discontinuous, bounded variation solution associated with this system and…
Motivated by the problem of designing robust composite pulses for Bloch equations in the presence of natural perturbations, we study an abstract optimal ensemble control problem in a probabilistic setting with a general nonlinear…
We study a dynamic stochastic control problem subject to Knightian uncertainty with multi-objective (vector-valued) criteria. Assuming the preferences across expected multi-loss vectors are represented by a given, yet general, preorder, we…
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…
An optimal control problem for the linear wave equation with control cost chosen as the BV semi-norm in time is analyzed. This formulation enhances piecewise constant optimal controls and penalizes the number of jumps. Existence of optimal…
We consider control-constrained linear-quadratic optimal control problems on evolving surfaces. In order to formulate well-posed problems, we prove existence and uniqueness of weak solutions for the state equation, in the sense of…
We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators,…
Optimal control problems for semilinear elliptic equations with control costs in the space of bounded variations are analysed. BV-based optimal controls favor piecewise constant, and hence 'simple' controls, with few jumps. Existence of…
This work is concerned with optimal control of partial differential equations where the control enters the state equation as a coefficient and should take on values only from a given discrete set of values corresponding to available…
In this paper, we investigate optimal control problems governed by semilinear elliptic variational inequalities involving constraints on the state, and more precisely the obstacle problem. Since we adopt a numerical point of view, we first…
We study the existence and uniqueness of a solution for the multivalued stochastic differential equation with delay (the multivalued term is of subdifferential type): \[ \left\{\begin{array} [c]{r} dX(t)+\partial\varphi\left(X(t)\right)…
We study a stochastic control problem for a Volterra-type controlled forward equation with past dependence obtained via convolution with a deterministic kernel. To be able to apply dynamic programming to solve the problem, we lift it to…
A parametric constrained convex optimal control problem, where the initial state is perturbed and the linear state equation contains a noise, is considered in this paper. Formulas for computing the subdifferential and the singular…
This paper presents sufficient conditions for optimal control of systems with dynamics given by a linear operator, in order to obtain an explicit solution to the Bellman equation that can be calculated in a distributed fashion. Further, 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…
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…
We consider the Chance Constrained Model Predictive Control problem for polynomial systems subject to disturbances. In this problem, we aim at finding optimal control input for given disturbed dynamical system to minimize a given cost…
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain…
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…