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Communication Dans Un Congrès Année : 2013

Generic fractal structure of the optimal synthesis in problems with affine multi-dimensional control

Résumé

We consider a linear-quadratic deterministic optimal control problem where the control takes values in a two-dimensional simplex. The phase portrait of the optimal synthesis contains second-order singular extremals and exhibits modes of infinite accumulations of switchings in finite time, so-called chattering. We prove the presence of an entirely new phenomenon, namely a chaotic behaviour of the set of optimal trajectories. The set of optimal non-wandering trajectories has the structure of a Cantor set, and the dynamics of the system is described by a topological Markov chain. We compute the entropy and the Hausdorff dimension of the non-wandering set. This behaviour is generic for piece-wise smooth Hamiltonian systems in the vicinity of a junction of three discontinuity hypersurface strata.
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Dates et versions

hal-00945426 , version 1 (12-02-2014)

Identifiants

  • HAL Id : hal-00945426 , version 1

Citer

Roland Hildebrand, Lev V. Lokutsievskiy, Mikhail I. Zelikin. Generic fractal structure of the optimal synthesis in problems with affine multi-dimensional control. ECC 2013 - European Control Conference, Jul 2013, Zurich, Switzerland. pp.3197-3202. ⟨hal-00945426⟩
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