About the continuity of reachable sets of restricted affine control systems

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• 作者：Ví ; ctor Ayala¹ ; ^a ; ^{vayala@ucn.cl} ; Heriberto Romá ; n-Flores² ; ^a ; Adriano Da Silva³ ; ^b
• 关键词：Affine system ; Accessible sets ; Lower semi-continuity ; Hausdorff metric
• 刊名：Chaos, Solitons & Fractals
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：94
• 期：Complete
• 页码：37-43
• 全文大小：443 K
• 卷排序：94

文摘

In this paper we prove that for a restricted affine control system on a connected manifold M, the associated reachable sets up to the time t varies continuously in each independent variable: time, state and the range of the admissible control functions. However, as a global map it is just lower semi-continuous. We show a bilinear control system on the plane where the global map has a discontinuity point. According to the Pontryagin Maximum Principal, in order to synthesizes the optimal control the Hausdorff metric continuity is crucial. We mention some references with concrete applications. Finally, we apply the result to the class of Linear control systems on Lie groups.