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首页> 外文期刊>Fortschritt-Berichte VDI, Reihe 8. Mess-, Steuerungs- und Regelungstechnik >Uncertainty and robustness analysis of biochemical reaction networks via convex optimisation and robust control theory
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Uncertainty and robustness analysis of biochemical reaction networks via convex optimisation and robust control theory

机译：基于凸优化和鲁棒控制理论的生化反应网络不确定性和鲁棒性分析

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This thesis provides new mathematical methods to study how parametric uncertainty affects model-based predictions for biochemical reaction networks. The methods are applicable to models constructed with ordinary differential equations. Two types of predictions are considered: first, the location of steady states the network can take, and second, whether any complex dynamical behaviour such as oscillations or bistability can occur. In order to obtain guaranteed predictions under parametric uncertainty, convex optimisation is applied to construct infeasibility certificates for specific hypotheses on steady state values or types of dynamical behaviour, A feedback loop breaking approach is devised to find parameter values leading to changes in the dynamical behaviour of a biochemical network. Methods based on robust control theory are developed to detect non-robust perturbations in the network's interaction structure. As a case study, a model for a tumor necrosis factor signalling pathway is constructed and analysed with the methods developed in the thesis.
机译：本文为研究参数不确定性如何影响生化反应网络的基于模型的预测提供了新的数学方法。该方法适用于用常微分方程构造的模型。考虑了两种类型的预测：第一，网络可以采取的稳态位置，第二，是否可能发生任何复杂的动力学行为，例如振荡或双稳态。为了在参数不确定性下获得有保证的预测，采用凸优化针对稳态值或动力学行为类型的特定假设构造不可行证书，设计了一种反馈回路分解方法来寻找导致动力学行为变化的参数值。生化网络。开发了基于鲁棒控制理论的方法来检测网络交互结构中的非鲁棒扰动。作为一个案例研究，采用本文开发的方法构建并分析了肿瘤坏死因子信号通路的模型。

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