| The Markov-Dubins problem with angular acceleration control (1997) | |||||||||||||||||
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| We study a modified version of the well known MarkovDubins problem, in which the control is angular acceleration rather than angular velocity. We show that an optimal trajectory cannot contain a junction of a bangbang and a singular piece, and use results of Zelikin and Borisov to show that there are Pontryagin extremals involving infinite chattering. 1. Introduction The Markov-Dubins problem with angular acceleration control (MDPAAC) is of interest in optimal control theory because of the challenges it poses, due to the surprisingly couterintuitive properties of its solutions. In this note, we describe the problem and prove several results on the solutions, establishing in particular the existence of extremals involving infinite chattering. The MDPAAC is the problem of describing the minimum-time trajectories for the four-dimensional control system x = cos z ; y = sin z ; (1) z = w ; w = u ; where x; y; z and w are the state variables, and the control u is required to satisf... | |||||||||||||||||
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