N.U. Ahmed (2002)
Discussiones Mathematicae, Differential Inclusions, Control and Optimization
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
Ahmed, N.U., Kerbal, Sebti (1993)
Journal of Applied Mathematics and Stochastic Analysis
Hana Svobodová, Jiří Vaníček (1960)
Časopis pro pěstování matematiky
Fabio Ancona, Alberto Bressan (1999)
ESAIM: Control, Optimisation and Calculus of Variations
Fabio Ancona, Alberto Bressan (2010)
ESAIM: Control, Optimisation and Calculus of Variations
This paper is concerned with the structure of asymptotically stabilizing feedbacks for a nonlinear control system on . We first introduce a family of discontinuous, piecewise smooth vector fields and derive a number of properties enjoyed by solutions of the corresponding O.D.E's. We then define a class of “patchy feedbacks” which are obtained by patching together a locally finite family of smooth controls. Our main result shows that, if a system is asymptotically controllable at the origin,...
Tolstonogov, A.A. (2004)
Sibirskij Matematicheskij Zhurnal
Alessia Marigo, Benedetto Piccoli (2002)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii–Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.
Alessia Marigo, Benedetto Piccoli (2010)
ESAIM: Control, Optimisation and Calculus of Variations
In this paper we analyze several concepts of solution to discontinuous ODEs in relation to feedbacks generated by optimal syntheses. Optimal trajectories are called Stratified Solutions in case of regular synthesis in the sense of Boltyanskii-Brunovsky. We introduce a concept of solution called Krasowskii Cone Robust that characterizes optimal trajectories for minimum time on the plane and for general problems under suitable assumptions.
Caiado, M.I., Sarychev, A.V. (2005)
Rendiconti del Seminario Matematico
K. Maciej Przyłuski, Andrzej M. Sosnowski (1994)
Kybernetika
J. Bonnans, Audrey Hermant (2009)
Control and Cybernetics
M. Serhani, N. Raissi, P. Cartigny (2009)
Mathematical Modelling of Natural Phenomena
In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium μ is not well known. On the other hand, when also the substrate concentration in the feed stream sin is unknown, we provide an observer of system and propose a design of robust feedback control in...
Nikolai P. Osmolovskii (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints they guarantee the bounded strong quadratic growth...
Nikolai P. Osmolovskii (2012)
ESAIM: Control, Optimisation and Calculus of Variations
Second-order sufficient conditions of a bounded strong minimum are derived for optimal control problems of ordinary differential equations with initial-final state constraints of equality and inequality type and control constraints of inequality type. The conditions are stated in terms of quadratic forms associated with certain tuples of Lagrange multipliers. Under the assumption of linear independence of gradients of active control constraints they...
Rubeša, Jelena, Kunisch, Karl (2010)
Mathematica Balkanica New Series
AMS Subj. Classification: 49J15, 49M15The control problem of minimal time transition between two stationary points are formulated in a framework of an indirect numerical method. The problem is regularized and the monotone behavior of the regularisation procedure is investigated. Semi-smooth Newton method applied on the regularized problems converge superlinearly and usually produce a very accurate solution. Differently from other methods, this one does not need a-priory knowledge of the control switching...
Glizer, Valery Y. (2017)
Proceedings of Equadiff 14
We consider the singularly perturbed set of periodic functional-differential matrix Riccati equations, associated with a periodic linear-quadratic optimal control problem for a singularly perturbed delay system. The delay is small of order of a small positive multiplier for a part of the derivatives in the system. A zero-order asymptotic solution to this set of Riccati equations is constructed and justified.
Phu, Nguyen Dinh, Tung, Tran Thanh (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
Ammar Moulahi, Salsabil Nouira (2010)
Annales mathématiques Blaise Pascal
On considère l’équation des ondes sur un rectangle avec un feedback de type Dirichlet. On se place dans le cas où la condition de contrôle géométrique n’est pas satisfaite (BLR Condition), ce qui implique qu’on n’a pas stabilité exponentielle dans l’espace d’énérgie. On prouve qu’on peut trouver un sous espace de l’espace d’énergie tel qu’on a stabilité exponentielle. De plus, on montre un résultat de décroissance polynomiale pour toute donnée initiale régulière.
František Tumajer (1988)
Aplikace matematiky
In the paper the concept of a controllable continuous flow in a metric space is introduced as a generalization of a controllable system of differential equations in a Banach space, and various kinds of stability and of boundedness of this flow are defined. Theorems stating necessary and sufficient conditions for particular kinds of stability and boundedness are formulated in terms of Ljapunov functions.
Kazimierz Malanowski (2001)