6533b7d8fe1ef96bd126a362

RESEARCH PRODUCT

Conjugate times for smooth singular trajectories and bang-bang extremals

Ludovic FaubourgBernard BonnardEmmanuel Trélat

subject

[ MATH.MATH-OC ] Mathematics [math]/Optimization and Control [math.OC]0209 industrial biotechnologyPhysics::General Physics010102 general mathematicsMathematical analysis[MATH.MATH-OC] Mathematics [math]/Optimization and Control [math.OC]02 engineering and technology01 natural sciences020901 industrial engineering & automationExponential mappingCaustic (optics)[MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC]0101 mathematicsBang bangBang–bang controlSmoothingMathematicsConjugateSecond derivative

description

Abstract In this paper we discuss the problem of estimating conjugate times along smooth singular or bang-bang extremals. For smooth extremals conjugate times can be defined in the generic case by using the intrinsic second order derivative or the exponential mapping. An algorithm is given which was implemented in the SR-case to compute the caustic [1] or in recent applied problems [5],[9]. We investigate briefly the problem of using this algorithm in the bang-bang case by smoothing the corners of extremals

yearjournalcountryeditionlanguage
2003-04-01
https://hal.archives-ouvertes.fr/hal-00086443/file/conjugate2.pdf