An obstruction to solvability of the reach control problem using affine feedback

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• 作者：Miad Moarref ^{miad.moarref@utoronto.ca" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Melkior Ornik ^{melkior.ornik@scg.utoronto.ca" class="auth_mail" title="E-mail the corresponding author}Author Vitae ; Mireille E. Broucke¹ ; ^{broucke@control.utoronto.ca" class="auth_mail" title="E-mail the corresponding author}Author Vitae
• 关键词：Reach control problem ; Affine feedback ; Dual cones ; Cone conditions
• 刊名：Automatica
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：71
• 期：Complete
• 页码：229-236
• 全文大小：714 K

文摘

This paper studies the reach control problem (RCP) using affine feedback on simplices. The contributions of this paper are threefold. First, we identify a new obstruction to solvability of the RCP using affine feedback and provide necessary and sufficient conditions for occurrence of such an obstruction. Second, for two-input systems, these conditions are formulated in terms of scalar linear inequalities. Third, computationally efficient necessary conditions are proposed for checking the obstruction for multi-input systems as feasibility programs in terms of linear inequalities. In contrast to the previous work in the literature, no assumption is imposed on the set of possible equilibria, so the results are applicable to the general RCP.