A design method and applications of periodic solutions in hybrid systems by variations of threshold values

2015 Fiscal Year Final Research Report

• Project/Area Number: 25420373
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Communication/Network engineering
• Research Institution: The University of Tokushima
• Principal Investigator: UETA TETSUSHI 徳島大学, 情報センター, 教授 (00243733)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: ハイブリッドシステム / リミットサイクル / ポアンカレ写像 / 安定性

Outline of Final Research Achievements

We investigate a schematic approach for producing a desired-shape limit cycle by providing several different vector fields and threshold values. In a partial state space sectioned by the threshold values, a differential equation with fixed parameter values gives a family of flows for
initial values sets. By combining these partial state spaces, a limit cycle can be obtained. This can be regarded as a hybrid system. If one provide threshold values and corresponding partial spaces initially, our procedure may compute suitable position of threshold values to fit the desired-shape limit cycle. We study required technologies about computations of variational equation for threshold values, optimization methods. As an application, we propose an open loop control system realizing a limit cycle holding a desired stability for the a hybrid system. We also propose a framework as finite-state automata describing dynamics of the hybrid system.

Free Research Field

非線形工学，分岐理論