Displaying similar documents to “On the perturbations in a time-optimal closed-loop system”

Infinite time regular synthesis

B. Piccoli (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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In this paper we provide a new sufficiency theorem for regular syntheses. The concept of regular synthesis is discussed in [12], where a sufficiency theorem for finite time syntheses is proved. There are interesting examples of optimal syntheses that are very regular, but whose trajectories have time domains not necessarily bounded. The regularity assumptions of the main theorem in [12] are verified by every piecewise smooth feedback control generating extremal trajectories that reach...

Regular syntheses and solutions to discontinuous ODEs

Alessia Marigo, Benedetto Piccoli (2010)

ESAIM: Control, Optimisation and Calculus of Variations

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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.

Holomorph of generalized Bol loops II

Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéiọlá, Bolaji Ajibola Popoola (2015)

Discussiones Mathematicae - General Algebra and Applications

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The notion of the holomorph of a generalized Bol loop (GBL) is characterized afresh. The holomorph of a right inverse property loop (RIPL) is shown to be a GBL if and only if the loop is a GBL and some bijections of the loop are right (middle) regular. The holomorph of a RIPL is shown to be a GBL if and only if the loop is a GBL and some elements of the loop are right (middle) nuclear. Necessary and sufficient conditions for the holomorph of a RIPL to be a Bol loop are deduced. Some...

Regular permutation sets and loops

Rita Capodaglio (2003)

Bollettino dell'Unione Matematica Italiana

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Two suitable composition laws are defined in a regular permutation set in order to find new characterizations of some important classes of loops.