Controllability and Energy-Optimal Control of Time-Variant Fractional Systems
Controllability and Energy-Optimal Control of Time-Variant Fractional Systems
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DOI：
10.1109/cdc.2018.8619785
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发表时间：
2018-12
期刊：
影响因子：
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通讯作者：
Marius Eckert;K. Nagatou;Felix Rey;Oliver Stark;S. Hohmann
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文献类型：
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作者：
Marius Eckert;K. Nagatou;Felix Rey;Oliver Stark;S. Hohmann
时变分数阶模型用于描述许多应用，例如锂离子电池。对于这类模型，目前还没有分数阶伪状态方程的能控性判据和能量最优控制函数。为了克服这一局限性，本文给出了时变分数阶伪状态空间系统的能达性和能控性定义，并导出了能量最优控制问题的解析解。在这种情况下，出现了分数Gramian矩阵。分数伪态必须与规则系统的状态有不同的解释，这是本文的核心。解释上的差异的原因是分数伪状态另外取决于初始化过程。
Time-variant fractional models are used to describe many applications, e.g. lithium-ion batteries. For such models, neither a controllability criterion for fractional pseudo state space equations nor the energy-optimal control function are available so far. To overcome this limitation, in this paper a reachability and controllability definition for time-variant fractional pseudo state space systems is formulated and the analytical solution of the energy-optimal control problem is derived. In this context, a fractional Gramian-Matrix appears. The fact that the fractional pseudo state must be interpreted differently than the state of a regular system is central to this paper. The reason for the difference in the interpretation is that the fractional pseudo state additionally depends on an initialization procedure.