Related papers: Subdifferential analysis of differential inclusion…
The Euler scheme is up to date the most important numerical method for ordinary differential inclusions, because the use of the available higher-order methods is prohibited by their enormous complexity after spatial discretization.…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…
This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in the modeling of certain physical systems. The differential inclusion is described by a time-dependent set-valued mapping…
The paper explores the differential inclusion of a special form. It is supposed that the support function of the set in the right-hand side of an inclusion may contain the sum of the maximum and the minimum of the finite number of…
We explore the possibility to derive basic calculus rules for some subdifferential constructions associated to set-valued maps between normed vector spaces. Then, we use these results in order to write optimality conditions for a special…
The main goal of this paper is developing the method of discrete approximations to derive necessary optimality conditions for a class of constrained sweeping processes with nonsmooth perturbations. Optimal control problems for sweeping…
The article discusses the gradient discretisation method (GDM) for distributed optimal control problems governed by diffusion equation with pure Neumann boundary condition. Using the GDM framework enables to develop an analysis that…
We consider a nonlinear Neumann elliptic inclusion with a source (reaction term) consisting of a convex subdifferential plus a multivalued term depending on the gradient. The convex subdifferential incorporates in our framework problems…
The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…
This paper is concerned with the derivation of necessary conditions for the optimal shape of a design problem governed by a non-smooth PDE. The main particularity thereof is the lack of differentiability of the nonlinearity in the state…
The paper deals with the optimal control problem described by second order evolution differential inclusions; to this end first we use an auxiliary problem with second order discrete and discrete-approximate inclusions. Then applying…
In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…
In recent years, deep learning has been connected with optimal control as a way to define a notion of a continuous underlying learning problem. In this view, neural networks can be interpreted as a discretization of a parametric Ordinary…
The existence of solutions of some nonlocal initial value problems for differential inclusions is established. The guiding potential method is used and the topological degree theory for admissible multivalued vector fields is applied. Some…
We obtain Euler-Lagrange and transversality optimality conditions for higher-order infinite horizon variational problems on a time scale. The new necessary optimality conditions improve the classical results both in the continuous and…
Necessary optimality conditions in Lagrangian form and the sequential minimization framework are extended to mixed-integer nonlinear optimization, without any convexity assumptions. Building upon a recently developed notion of local…
The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…
We develop adaptive discretization algorithms for locally optimal experimental design of nonlinear prediction models. With these algorithms, we refine and improve a pertinent state-of-the-art algorithm in various respects. We establish…
The directional subdifferential of the value function gives an estimate on how much the optimal value changes under a perturbation in a certain direction. In this paper we derive upper estimates for the directional limiting and singular…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…