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Optimal impulsive control of delay systems

Florent Delmotte, Erik I. Verriest, Magnus Egerstedt (2008)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we solve an optimal control problem using the calculus of variation. The system under consideration is a switched autonomous delay system that undergoes jumps at the switching times. The control variables are the instants when the switches occur, and a set of scalars which determine the jump amplitudes. Optimality conditions involving analytic expressions for the partial derivatives of a given cost function with respect to the control variables are derived using the calculus of variation....

Optimality Conditions for a Nonlinear Boundary Value Problem Using Nonsmooth Analysis

Mohamed Akkouchi, Abdellah Bounabat, Manfred Goebel (2003)

Annales mathématiques Blaise Pascal

We study in this paper a Lipschitz control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. The nonlinear part of the equation is governed by a Nemytskij operator defined by a Lipschitzian but possibly nonsmooth function. We prove the existence of optimal controls and obtain a necessary optimality conditions looking somehow to the Pontryagin’s maximum principle. These conditions...

Patchy Vector Fields and Asymptotic Stabilization

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 ℝ n . 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,...

Pointwise minimization of supplemented variational problems

Peter Kosmol, Dieter Müller-Wichards (2004)

Colloquium Mathematicae

We describe an approach to variational problems, where the solutions appear as pointwise (finite-dimensional) minima for fixed t of the supplemented Lagrangian. The minimization is performed simultaneously with respect to the state variable x and ẋ, as opposed to Pontryagin's maximum principle, where optimization is done only with respect to the ẋ-variable. We use the idea of the equivalent problems of Carathéodory employing suitable (and simple) supplements to the original minimization problem....

P-order necessary and sufficient conditions for optimality in singular calculus of variations

Agnieszka Prusińska, Alexey Tret'yakov (2010)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

This paper is devoted to singular calculus of variations problems with constraint functional not regular at the solution point in the sense that the first derivative is not surjective. In the first part of the paper we pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we formulate and prove necessary and sufficient conditions for optimality in singular case and illustrate our results by classical example of calculus of variations...

Quadratic functionals with a variable singular end point

Zuzana Došlá, PierLuigi Zezza (1992)

Commentationes Mathematicae Universitatis Carolinae

In this paper we introduce the definition of coupled point with respect to a (scalar) quadratic functional on a noncompact interval. In terms of coupled points we prove necessary (and sufficient) conditions for the nonnegativity of these functionals.

Regular syntheses and solutions to discontinuous ODEs

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.

Regular syntheses and solutions to discontinuous ODEs

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.

Regularity along optimal trajectories of the value function of a Mayer problem

Carlo Sinestrari (2004)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.

Regularity along optimal trajectories of the value function of a Mayer problem

Carlo Sinestrari (2010)

ESAIM: Control, Optimisation and Calculus of Variations

We consider an optimal control problem of Mayer type and prove that, under suitable conditions on the system, the value function is differentiable along optimal trajectories, except possibly at the endpoints. We provide counterexamples to show that this property may fail to hold if some of our conditions are violated. We then apply our regularity result to derive optimality conditions for the trajectories of the system.

Currently displaying 101 – 120 of 189