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首页> 外文期刊>Journal of the Royal Society Interface >Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models
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Full observability and estimation of unknown inputs, states and parameters of nonlinear biological models

机译：非线性生物模型未知输入，状态和参数的完全可观察性和估算

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摘要

In this paper, we address the system identification problem in the context of biological modelling. We present and demonstrate a methodology for (i) assessing the possibility of inferring the unknown quantities in a dynamic model and (ii) effectively estimating them from output data. We introduce the term Full Input-State-Parameter Observability (FISPO) analysis to refer to the simultaneous assessment of state, input and parameter observability (note that parameter observability is also known as identifiability). This type of analysis has often remained elusive in the presence of unmeasured inputs. The method proposed in this paper can be applied to a general class of nonlinear ordinary differential equations models. We apply this approach to three models from the recent literature. First, we determine whether it is theoretically possible to infer the states, parameters and inputs, taking only the model equations into account. When this analysis detects deficiencies, we reformulate the model to make it fully observable. Then we move to numerical scenarios and apply an optimization-based technique to estimate the states, parameters and inputs. The results demonstrate the feasibility of an integrated strategy for (i) analysing the theoretical possibility of determining the states, parameters and inputs to a system and (ii) solving the practical problem of actually estimating their values.
机译：在本文中，我们在生物学建模背景下解决了系统识别问题。我们展示并展示（i）的方法，评估动态模型中的未知量的可能性，并有效地从输出数据估算它们。我们介绍了术语完整输入 - 状态参数可观察性（FISPO）分析，以指的是对状态，输入和参数可观察性的同时评估（注意，参数可观察性也称为可识别性）。在未测量的输入存在下，这种类型的分析通常难以实现。本文提出的方法可以应用于一般的非线性常微分方程模型。我们将这种方法应用于最近文献的三种模型。首先，我们确定理论上是否可以推断出来的状态，参数和输入，仅考虑模型方程。当此分析检测到缺陷时，我们重新格式化模型以使其完全可观察到。然后我们移动到数值方案，并应用基于优化的技术来估计状态，参数和输入。结果展示了（i）综合策略的可行性分析了确定系统，参数和输入到系统的理论可能性以及（ii）解决实际估计其值的实际问题。

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