Page 1

Displaying 1 – 9 of 9

Showing per page

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.

Riemannian metrics on 2D-manifolds related to the Euler−Poinsot rigid body motion

Bernard Bonnard, Olivier Cots, Jean-Baptiste Pomet, Nataliya Shcherbakova (2014)

ESAIM: Control, Optimisation and Calculus of Variations

The Euler−Poinsot rigid body motion is a standard mechanical system and it is a model for left-invariant Riemannian metrics on SO(3). In this article using the Serret−Andoyer variables we parameterize the solutions and compute the Jacobi fields in relation with the conjugate locus evaluation. Moreover, the metric can be restricted to a 2D-surface, and the conjugate points of this metric are evaluated using recent works on surfaces of revolution. Another related 2D-metric on S2 associated to the...

Currently displaying 1 – 9 of 9

Page 1