Time-optimal hands-off control for linear time-invariant systems

• Autores: Takuya Ikeda, Masaaki Nagahara
• Localización: Automatica: A journal of IFAC the International Federation of Automatic Control, ISSN 0005-1098, Nº. 99, 2019, págs. 54-58
• Idioma: inglés
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• Resumen

  • In this article, we investigate theoretical properties of the time-optimal hands-off control for linear time-invariant systems. The purpose of the control is to maximize the time duration on which the control value is exactly zero (maximum hands-off control) and also to minimize the response time to achieve a given state transition (time-optimal control). For this, we introduce a cost function described by a linear combination of the L0 measure and the response time of the control. Since the L0 measure is non-convex and discontinuous, we adopt the L1 relaxation technique for the analysis of the optimal control. By using this relaxation, we show the existence of the time-optimal hands-off control, and the equivalence between L0 andL1 optimal controls under the normality assumption.