Related papers: Excess-continuous prox-regular sweeping processes
The aim of this paper is twofold. On one hand we prove that the Moreau's sweeping process driven by a uniformly prox-regular moving set with local bounded retraction has a unique solution provided that the coefficient of prox-regularity is…
In this paper, we study the existence of solutions to sweeping processes in the presence of stochastic perturbations, where the moving set takes uniformly prox-regular values and varies continuously with respect to the Hausdorff distance,…
We consider the free endpoint Mayer problem for a controlled Moreau process, the control acting as a perturbation of the dynamics driven by the normal cone, and derive necessary optimality conditions of Pontryagin's Maximum Principle type.…
In this paper, we deal with sweeping processes on (possibly infinite-dimensional) Riemannian Hilbert manifolds. We extend the useful notions (proximal normal cone, prox-regularity) already defined in the setting of a Hilbert space to the…
Let $C(t)$, $t\geq0$ be a Lipschitz set-valued map with closed and (mildly non-)convex values and $f(t, x,u)$ be a map, Lipschitz continuous w.r.t. $x$. We consider the problem of reaching a target $S$ within the graph of $C$ subject to the…
In this paper we provide a formulation for sweeping processes with arbitrary locally bounded retraction, not necessarily left or right continuous. Moreover we provide a proof of the existence and uniqueness of solutions for this formulation…
The paper concerns optimal control of discontinuous differential inclusions of the normal cone type governed by a generalized version of the Moreau sweeping process with control functions acting in both nonconvex moving sets and additive…
A controlled sweeping process with prox-regular set, $W^{1,2}$-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived via strong…
This paper deals with optimal control problems described by a controlled version of Moreau's sweeping process governed by convex polyhedra, where measurable control actions enter additive perturbations. This class of problems, which…
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and…
This paper concerns optimal control problems for a class of sweeping processes governed by discontinuous unbounded differential inclusions that are described via normal cone mappings to controlled moving sets. Largely motivated by…
We consider a class of time-dependent inclusions in Hilbert spaces for which we state and prove an existence and uniqueness result. The proof is based on arguments of variational inequalities, convex analysis and fixed point theory. Then we…
The aim of this paper is to study a wide class of non-convex sweeping processes with moving constraint whose translation and deformation are represented by regulated functions, i.e., functions of not necessarily bounded variation admitting…
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 paper, we introduce and study degenerate state-dependent sweeping processes with nonregular moving sets (subsmooth and positively $\alpha$-far). Based on the Moreau-Yosida regularization, we prove the existence of solutions under…
The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in…
In this paper, we analyze and discuss the well-posedness of a new variant of the so-called sweeping process, introduced by J.J. Moreau in the early 70's \cite{More71} with motivation in plasticity theory. In this variant, the normal cone to…
We use the ideas of Adly-Attoych-Cabot [Adv. Mech. Math., 12, Springer, 2006] on finite-time stabilization of dry friction oscillators to establish a theorem on finite-time stabilization of differential inclusions with a moving polyhedral…
In the setting adopted by Edmond and Thibault [Mathematical Programming 104 (2005), 347--373], we study a class of perturbed sweeping processes. Under suitable assumptions, we obtain two solution existence theorems for perturbed sweeping…
This paper addresses, for the first time in the literature, optimal control problems for dynamic systems governed by a novel class of sweeping processes with time delay. We establish well-posedness of such processes, in the sense of the…