High-order variations and small-time local attainability

We study the problem of small-time local attainability (STLA) of a closed set. For doing this, we introduce a new concept of variations of the reachable set, well adapted to a given closed set and prove a new attainability result

Lokalna sterowalność układów liniowych z ograniczeniem na stan

W pracy rozważa się problem momentalnej lokalnej sterowalności liniowego układu z ograniczeniem na współrzędne stanu.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej naukę

Viability and an Olech Type Result

[Krastanov M. I.; Кръстанов М. И.]; [Ribarska N. K.; Рибарска Н. К.]2010 Mathematics Subject Classification: 34A36, 34A60

On the Existence of Lipschitz Continuous Optimal Feedback Control

We consider an optimal control problem involving a nonlinear ODE with control, an integral cost functional, and a control constraint. Our main assumptions include a coercivity condition and the condition that the optimal control is an isolated solution of the variational inequality appearing in the first-order optimality condition. We show that the optimal open-loop control is Lipschitz continuous in time; moreover, we identify the dependence of the Lipschitz constant of the optimal control on the data of the problem. Then, we establish the existence of a Lipschitz continuous optimal feedback control. As an application, we study regularity properties of the optimal value function. A main tool for obtaining these results is the property of uniform strong metric regularity.National Science FoundationAustralian Research Council (ARC)Austrian Science Foundation (FWF

Metrická regularita pro zobecněné diferenciálně- algebraická rovnice

V článku jsou studovány zobecněné diferenciálně- algebraická rovnice, což je systém skládající se z obyčejné diferenciální rovnice a algebraické vazby reprezentované např. variační nerovnicí nebo zobecněnou rovnicí. Tento model pokrývá široké spektrum problémů. např. diferenciálně-variační nerovnice, systémy z teorie řízení s omezeními, nebo systémy dané jakožto nutné podmínky optimality v teorii optimálního řízení.In this paper we consider a control system coupled with a generalized equation, which we call a differential generalized equation (DGE). This model covers a large territory in control and optimization, such as differential variational inequalities, control systems with constraints, as well as necessary optimality conditions in optimal control

AN EULER–NEWTON CONTINUATION METHOD FOR TRACKING SOLUTION TRAJECTORIES OF PARAMETRIC VARIATIONAL INEQUALITIES ∗

Abstract. A finite-dimensional variational inequality parameterized by t ∈ [0, 1] is studied under the assumption that each point of the graph of its generally set-valued solution mapping is a point of strongly regularity. It is shown that there are finitely many Lipschitz continuous functions on [0, 1] whose graphs do not intersect each other such that for each value of the parameter the set of values of the solution mapping is the union of the values of these functions. Moreover, the property of strong regularity is uniform with respect to the parameter along any such function graph. An Euler–Newton continuation method for tracking a solution trajectory is introduced and demonstrated to have l ∞ accuracy of order O(h4), thus generalizing a known error estimate for equations. Two examples of tracking economic equilibrium parametrically illustrate the theoretical results

Generic progressive heterogeneous processes in nucleation

10.1021/la991333gLangmuir16187337-7345LANG