Computing Guaranteed Bounds for Uncertain Cooperative and Monotone Nonlinear Systems
Computing Guaranteed Bounds for Uncertain Cooperative and Monotone Nonlinear Systems
复制标题
计算不确定合作和单调非线性系统的保证界限
DOI：
10.3182/20080706-5-kr-1001.00814
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发表时间：
2008
期刊：
影响因子：
--
通讯作者：
B. Tibken
中科院分区：
文献类型：
--
作者：
M. Gennat;B. Tibken
生物或技术应用的模型由非线性系统表示，这些系统由常微分方程定义。这些系统通常包含多个不确定或未知的参数。这些不确定性由测量误差或由建模（例如，数值建模）引起。对于某些应用，要求给定不确定系统的初值问题（IVP）的所有可能解的保证封闭性。由于IVP的解集只能在一定的情况下用代数方法求解，因此一般不能直接计算给定不确定非线性系统的保界。此外，大多数计算IVP解的数值方法不能处理具有不确定参数的系统。但对于合作系统类的IVP的所有解的紧保证界可以计算。这个类满足一定的单调性条件。此外，保上下界的计算可以应用到更大的一类常微分方程，这并不满足不确定合作系统的所有条件。对于这类单调系统，保证的封闭性可能表现出一定的高估。一些例子说明了在这方面的贡献所描述的方法。
Models of biological or technical applications are represented by nonlinear systems, which are defined by ordinary differential equations. These systems generally contain multiple uncertain or unknown parameters. These uncertainties result from measurement errors or from modeling, e.g. numerical modeling. For several applications, the guaranteed enclosure of all possible solutions of an initial value problem (IVP) of a given uncertain system is demanded. In general the calculation of guaranteed bounds of the given uncertain nonlinear system cannot be done directly, because the solution set of an IVP can be solved algebraically only in certain cases. Furthermore, most numerical methods which compute the solution of IVPs cannot handle systems with uncertain parameters. But for the class of cooperative systems tight guaranteed bounds for all solutions of the IVP can be computed. This class satisfies certain monotony conditions. Moreover the computation of guaranteed lower and upper bounds can be applied to a larger class of ordinary differential equations, which does not satisfy all conditions for uncertain cooperative systems. For this class of monotone systems the guaranteed enclosure can show some overestimation. Some examples illustrate the methods described in this contribution.