Mathematical modelling offers a variety of useful techniques to help in understanding the intrinsic behaviour of complex signal transduction networks. From the system engineering point of view, the dynamics of metabolic and signal transduction models can always be described by nonlinear ordinary differential equations (ODEs) following mass balance principles. Based on the state-space formulation, many methods from the area of automatic control can conveniently be applied to the modelling, analysis and design of cell networks. In the present study, dynamic sensitivity analysis is performed on a model of the IκB–NF-κB signal pathway system. Univariate analysis of the Euclidean-form overall sensitivities shows that only 8 out of the 64 parameters in the model have major influence on the nuclear NF-κB oscillations. The sensitivity matrix is then used to address correlation analysis, identifiability assessment and measurement set selection within the framework of least squares estimation and multivariate analysis. It is shown that certain pairs of parameters are exactly or highly correlated to each other in terms of their effects on the measured variables. The experimental design strategy provides guidance on which proteins should best be considered for measurement such that the unknown parameters can be estimated with the best statistical precision. The whole analysis scheme we describe provides efficient parameter estimation techniques for complex cell networks.

The entropy has been used to characterize the uncertainty of the tracking error for general nonlinear and non-Gaussian stochastic systems. A recursive optimization solution has been developed and the local stability condition of the closed-loop system has been established. The generality of this algorithm has been proved by the special case study of the minimum variance control for linear Gaussian systems.

Electric vehicle (EV) can be applied to discharge power back to the grid, which is called vehicle-to-grid (V2G) technology. There is a constant debate on whether V2G is an economically viable option due to the high battery degradation cost. In this work, the cost benefit of EV customers participating in V2G has been studied using different feed-in tariffs (FITs). A model is developed for minimisation of energy cost for residential users, which includes an EV, a separate energy storage system (ESS) and renewable energy supply. Key factors such as the EV driving usage, the degradation cost of EV and ESS batteries are considered. The EV driving usage is established through a designed survey, from which the probability of vehicle parking and plug in at home, the probabilities of EV under driving and parking outside can be calculated. Comprehensive case studies have been undertaken to investigate the optimisation strategies under various scenarios. Two types of electricity tariffs, time-of-use (TOU) and fixed tariffs, are considered. It is revealed that certain threshold levels of FITs are expected to allow users benefit from V2G technology. Compared with non-optimised operation, the cost saving with the optimised strategy is evident in the case studies.