Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations
Optimal Experimental Design for Uncertain Systems Based on Coupled Differential Equations
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DOI：
10.1109/access.2021.3071038
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发表时间：
2021-01-01
期刊：
影响因子：
3.9
通讯作者：
Yoon, Byung-Jun
中科院分区：
文献类型：
--
作者：
Hong, Youngjoon;Kwon, Bongsuk;Yoon, Byung-Jun
研究了参数不完全已知的耦合常微分方程描述的不确定系统的最优试验设计问题。这项工作的主要目标是开发一个通用的实验设计策略，适用于任何常微分方程为基础的模型中存在的不确定性。为了这个目的，我们专注于非同质仓本模型在这项研究中作为一种工具，开发的OED战略。仓本模型由N个相互作用的振子组成，它们由耦合常微分方程描述，在生物和化学振子的同步现象研究中得到了广泛的应用。这里我们假设振子之间的成对耦合强度是不均匀的和未知的。这就产生了可能的仓本模型的不确定性类，其中包括真正的未知模型。针对一类不确定的Kuramoto模型，研究了通过外部控制实现不确定模型的鲁棒同步问题。如果实验预算可用于执行实验，以减少模型的不确定性，一个重要的实际问题是如何实验可以优先级，以便可以选择的预算内，可以最有效地减少不确定性的实验序列。在本文中，我们提出了一个OED策略，通过平均客观不确定性成本（MOCU）量化模型的客观不确定性，在此基础上，我们确定的最佳实验，预计将最大限度地减少MOCU。我们证明了量化的潜在实验在设计最优实验的操作影响的重要性，并表明基于MOCU的OED计划使我们能够最大限度地减少不确定的仓本模型的鲁棒控制的成本与最少的实验相比，其他替代品。该方案具有较强的通用性，可应用于任何由耦合常微分方程表示的不确定复杂系统。
We consider the optimal experimental design (OED) problem for an uncertain system described by coupled ordinary differential equations (ODEs), whose parameters are not completely known. The primary objective of this work is to develop a general experimental design strategy that is applicable to any ODE-based model in the presence of uncertainty. For this purpose, we focus on non-homogeneous Kuramoto models in this study as a vehicle to develop the OED strategy. A Kuramoto model consists of N interacting oscillators described by coupled ODEs, and they have been widely studied in various domains to investigate the synchronization phenomena in biological and chemical oscillators. Here we assume that the pairwise coupling strengths between the oscillators are non-uniform and unknown. This gives rise to an uncertainty class of possible Kuramoto models, which includes the true unknown model. Given an uncertainty class of Kuramoto models, we focus on the problem of achieving robust synchronization of the uncertain model through external control. Should experimental budget be available for performing experiments to reduce model uncertainty, an important practical question is how the experiments can be prioritized so that one can select the sequence of experiments within the budget that can most effectively reduce the uncertainty. In this paper, we present an OED strategy that quantifies the objective uncertainty of the model via the mean objective cost of uncertainty (MOCU), based on which we identify the optimal experiment that is expected to maximally reduce the MOCU. We demonstrate the importance of quantifying the operational impact of the potential experiments in designing optimal experiments and show that the MOCU-based OED scheme enables us to minimize the cost of robust control of the uncertain Kuramoto model with the fewest experiments compared to other alternatives. The proposed scheme is fairly general and can be applied to any uncertain complex system represented by coupled ODEs.