Related papers: A Control Space Ensuring the Strong Convergence of…
We consider a stochastic control problem where the set of controls is not necessarily convex and the system is governed by a nonlinear backward stochastic differential equation. We establish necessary as well as sufficient conditions of…
In this article, we investigate a time-optimal state-constrained bilevel optimal control problem whose lower-level dynamics feature a sweeping control process involving a {\it truncated normal cone}. By bilevel, it is meant that the…
The paper puts forward sufficient conditions for local controllability of a control dynamical system. The results obtained are meaningful in the case when the linear approximation to this system is not completely controllable. As a…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex and the the variable control has two components, the first being absolutely continuous and the second singular. The system is…
An optimal control problem for the continuity equation is considered. The aim of a "controller" is to maximize the total mass within a target set at a given time moment. The existence of optimal controls is established. For a particular…
This paper describes the reachable set and resolves an optimal control problem for the scalar conservation laws with discontinuous flux. We give a necessary and sufficient criteria for the reachable set. A new backward resolution has been…
We consider an optimal control problem governed by a rate-inde\-pendent system with non-convex energy. The state equation is approximated by means of viscous regularization w.r.t.\ to hierarchy of two different Hilbert spaces. The…
In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…
We consider the problem of approximating the reachable set of a discrete-time polynomial system from a semialgebraic set of initial conditions under general semialgebraic set constraints. Assuming inclusion in a given simple set like a box…
The paper is concerned with an optimal control problem governed by the rate-independent system of quasi-static perfect elasto-plasticity. The objective is optimize the displacement field in the domain occupied by the body by means of…
In this paper, we develop an inexact version of the catching-up algorithm for sweeping processes. We define a new notion of approximate projection, which is compatible with any numerical method for approximating exact projections, as this…
For affine control systems with bounded control range the control sets, i.e., the maximal subsets of complete approximate controllability, are studied using spectral properties. For hyperbolic systems there is a unique control set with…
Constrained dynamical systems are systems such that, by some means, the state stays within a given set. Two such systems are the (perturbed) Moreau sweeping process and the recently proposed extended Projected Dynamical System (ePDS). We…
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…
Optimal Dirichlet boundary control for a fractional/normal evolution with a final observation is considered. The unique existence of the solution and the first-order optimality condition of the optimal control problem are derived. The…
This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods…
Li, Chen, Tai & E. (J. Machine Learning Research, 2018) have proposed a regularization of the forward-backward sweep iteration for solving the Pontryagin maximum principle in optimal control problems. The authors prove the global…
We analyze the Ericksen--Leslie system equipped with the Oseen--Frank energy in three space dimensions. Recently, the author introduced the concept of dissipative solutions. These solutions show several advantages in comparison to the…
We consider a stochastic control problem where the set of strict (classical) controls is not necessarily convex, and the system is governed by a nonlinear backward stochastic differential equation. By introducing a new approach, we…
The Method of Successive Approximations (MSA) is a fixed-point iterative method used to solve stochastic optimal control problems. It is an indirect method based on the conditions derived from the Stochastic Maximum Principle (SMP), an…