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Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints

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...

Second-order sufficient optimality conditions for control problems with linearly independent gradients of control constraints

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...

Semi-Smooth Newton Methods for the Time Optimal Control of Nonautonomous Ordinary Differential Equations

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...

Singularly perturbed set of periodic functional-differential equations arising in optimal control theory

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.

Stabilisation polynomiale et analytique de l’équation des ondes sur un rectangle

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.

Stability and boundedness of controllable continuous flows

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.

Stabilization of wave systems with input delay in the boundary control

Gen Qi Xu, Siu Pang Yung, Leong Kwan Li (2006)

ESAIM: Control, Optimisation and Calculus of Variations

In the present paper, we consider a wave system that is fixed at one end and a boundary control input possessing a partial time delay of weight ( 1 - μ ) is applied over the other end. Using a simple boundary velocity feedback law, we show that the closed loop system generates a C0 group of linear operators. After a spectral analysis, we show that the closed loop system is a Riesz one, that is, there is a sequence of eigenvectors and generalized eigenvectors that forms a Riesz basis for the state Hilbert...

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