Related papers: Optimal Control on Positive Cones
We consider optimal control problems for partial differential equations where the controls take binary values but vary over the time horizon, they can thus be seen as dynamic switches. The switching patterns may be subject to combinatorial…
This paper aims to study a family of deterministic optimal control problems in infinite dimensional spaces. The peculiar feature of such problems is the presence of a positivity state constraint, which often arises in economic applications.…
In this paper, we study a stochastic optimal control problem under a type of consistent convex expectation dominated by G-expectation. By the separation theorem for convex sets, we get the representation theorems for this convex expectation…
We focus on optimal control problems governed by elliptic, quasilinear PDEs. Though there are various examples of such problems in the literature, we make an attempt at describing some general principles by dealing with three basic…
This paper is dedicated to the stability analysis of the optimal solutions of a control problem associated with a semilinear elliptic equation. The linear differential operator of the equation is neither monotone nor coercive due to the…
Quantum optimal control theory is a powerful tool for engineering quantum systems subject to external fields such as the ones created by intense lasers. The formulation relies on a suitable definition for a target functional, that…
A method of optimal control computation is proposed for problems with control and state constraints. It uses a sequence of control structure adjustments in the form of generations and reductions of nodes and arcs, which do not change the…
The problems of optimizing the value of an arbitrary observable of the two-level system at both a fixed time and the shortest possible time is theoretically explored. Complete identification and classification along with comprehensive…
Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…
A convex optimization problem in conic form involves minimizing a linear functional over the intersection of a convex cone and an affine subspace. In some cases, it is possible to replace a conic formulation using a certain cone, with a…
An optimal control problem for a model of tumor growth is studied. In a given subdomain, it is required to minimize the density of tumor cells, while the drug concentration in tissue is limited by given minimal and maximal values. Based on…
In this paper we derive a necessary optimality condition for a local optimal solution of some control problems. These optimal control problems are governed by a semi-linear Vettsel boundary value problem of a linear elliptic equation. The…
In this paper we study a problem of looking for an optimal solution of a system of the differential equations with a control and an optimized function. The system of differential equations is changed for two systems with the upper and lower…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…
This paper is concerned with a stochastic linear-quadratic optimal control problem in a finite time horizon, where the coefficients of the control system are allowed to be random, and the weighting matrices in the cost functional are…
We consider the problem of computing optimal linear control policies for linear systems in finite-horizon. The states and the inputs are required to remain inside pre-specified safety sets at all times despite unknown disturbances. In this…
We consider a system that is exactly controllable. For given initial state, terminal state and objective function, an optimal control is often well-defined. Such an optimal control has the disadvantage that although it works perfectly well…
Positive systems naturally arise in situations where the model tracks physical quantities. Although the linear case is well understood, analysis and controller design for nonlinear positive systems remain challenging. Model reduction…
We consider optimal control of the scalar wave equation where the control enters as a coefficient in the principal part. Adding a total variation penalty allows showing existence of optimal controls, which requires continuity results for…
In this paper, a convex optimization-based method is proposed for numerically solving dynamic programs in continuous state and action spaces. The key idea is to approximate the output of the Bellman operator at a particular state by the…