Displaying similar documents to “Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane*”

Cut locus and optimal synthesis in the sub-Riemannian problem on the group of motions of a plane

Yuri L. Sachkov (2011)

ESAIM: Control, Optimisation and Calculus of Variations

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The left-invariant sub-Riemannian problem on the group of motions (rototranslations) of a plane SE(2) is considered. In the previous works [Moiseev and Sachkov, , DOI: ; Sachkov, , DOI: ], extremal trajectories were defined, their local and global optimality were studied. In this paper the global structure of the exponential mapping is described. On this basis an explicit characterization of the cut locus and Maxwell set is obtained. The optimal synthesis is constructed.

Mean-Field Optimal Control

Massimo Fornasier, Francesco Solombrino (2014)

ESAIM: Control, Optimisation and Calculus of Variations

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We introduce the concept of which is the rigorous limit process connecting finite dimensional optimal control problems with ODE constraints modeling multi-agent interactions to an infinite dimensional optimal control problem with a constraint given by a PDE of Vlasov-type, governing the dynamics of the probability distribution of interacting agents. While in the classical mean-field theory one studies the behavior of a large number of small individuals with each other, by simplifying...

Asymptotics of accessibility sets along an abnormal trajectory

Emmanuel Trélat (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We describe precisely, under generic conditions, the contact of the accessibility set at time with an abnormal direction, first for a single-input affine control system with constraint on the control, and then as an application for a sub-Riemannian system of rank 2. As a consequence we obtain in sub-Riemannian geometry a new splitting-up of the sphere near an abnormal minimizer into two sectors, bordered by the first Pontryagin's cone along , called the L-sector and the L-sector. Moreover...

Feedback in state constrained optimal control

Francis H. Clarke, Ludovic Rifford, R. J. Stern (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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An optimal control problem is studied, in which the state is required to remain in a compact set . A control feedback law is constructed which, for given ε > 0, produces -optimal trajectories that satisfy the state constraint universally with respect to all initial conditions in . The construction relies upon a constraint removal technique which utilizes geometric properties of inner approximations of and a related trajectory tracking result. The control feedback is shown to possess...

Relaxation of optimal control problems in L-SPACES

Nadir Arada (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space ( < ∞). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.