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•An observer for the nonlinear DFN Li-ion battery model is introduced.•The observer exploits the monotonicity of the Butler–Volmer kinetics and the inclusion of double layer dynamics.•Accurate estimates of the state-of-charge and the overpotential distribution across the battery are obtained.

•A method to synthesize circuits from physical supercapacitor models is introduced.•The method uses discretisation, model order reduction and passive circuit synthesis.•A wide class of circuits are synthesized from a wide class of physical models.•A physical interpretation is given to the synthesized circuits.•Online synthesis is studied and related to parameter estimation of the circuit.

Annual deaths from scarlet fever in Liverpool, UK during 1848–1900 have been used as a model system for studying the historical dynamics of the epidemics. Mathematical models are developed which include the growth of the population and the death rate from scarlet fever. Time-series analysis of the results shows that there were two distinct phases to the disease (i) 1848–1880: regular epidemics (wavelength = 3.7 years) consistent with the system being driven by an oscillation in the transmission coefficient (δβ) at its resonant frequency, probably associated with dry conditions in winter (ii) 1880–1900: an undriven SEIR system with a falling endemic level and decaying epidemics. This period was associated with improved nutritive levels. There is also evidence from time-series analysis that raised wheat prices in pregnancy caused increased susceptibility in the subsequent children. The pattern of epidemics and the demographic characteristics of the population can be replicated in the modelling which provides insights into the detailed epidemiology of scarlet fever in this community in the 19th century.

Liverpool, U.K., 1863--1900, has been used as a model to explore the interaction between measles epidemics and the population dynamics in an overcrowded community with inadequate nutrition using a non-linear model which allows the estimation of certain underlying demographic parameters. The results are consistent with a system that is driven by an oscillation in the transmission parameter that is compounded of an oscillation in autumn temperatures (at the resonant frequency of the system, 2.4 years) and, secondarily, by an oscillation in wheat prices (wavelength = 5.3 years, twice that of the epidemics).

The control strategy is based on minimising the expected range of variations observed within a single scan across the width of the sheet. This can be considered as an ℓ∞ minimisation problem and implemented using efficient algorithms based on the simplex method of linear programming. The BIBO stability of the controlled system is analysed and it is shown that the stability of the full multivariable system is determined by the stability of a scalar dynamic term. In general, the controller is suboptimal in the sense that it minimises an upper bound on the expected range of variations across the sheet, but for a certain class of disturbance models the expected value of the range can be minimised optimally by using the minimum variance solution.

The paper addresses the problem of estimating the ‘effective’ actuator centre locations in a plastics extrusion process while the process is operating in closed loop. It shows that it is possible to use a lower-order model estimator and hence considerably reduce the complexity of the procedure. The estimator is described as a radial basis function network, where the basis functions in the hidden layer are defined using discrete Chebyshev polynomials. The problem is considered as a nonlinear optimisation problem and solved online using a recursive prediction error method.

The evolution of smallpox outbreaks in London. 1647-1893, was studied using data fronl the Bills of Mortalit.y. Strong coherence was observed between the epidemics of smallpox and seasonal effects such as rainfall and Winter temperatures. An SIR model is used to suggest an explanation for these observations in terms of periodic variations in the force of the infection. It is suggested that the progressive change in the interepidemic period is due to the growing population and to an increase in the force of the infection. After 1800, the effects of vaccination and variolation cause the endemic level of the disease to fall and the interepidemic period to increase and the dynamics of the disease are described by an unforced SIR model exhibiting severe outbreaks of smallpox followed by decaying oscillations

The interepidemic interval (T) of measles in London from 1647 to 1837 evolved progressively from 5-yearly to 2-yearly by 1800. Measles mortality was significantly (p<0.001) cross-correlated with the annual wheat prices, a good index of nutrition although at a 2-year lag. Epidemics correlated with low autumn temperatures (p<0.001). A linearised model of the dynamics of epidemics shows thatTis determined by the product of population (N) and susceptibility (β) and that the system will settle at its steady state unless the epidemics are driven. It is suggested that (i) the progressive change inTwas caused by a rise in population size (N) and an increased susceptibility (β) related to malnutrition and (ii) epidemics were driven by oscillations in low autumn temperature (p<0.001) and by cycles of susceptible young children produced by malnutrition during pregnancy.

A computationally efficient reduced model estimator is described for determining the effective position of actuators used for cross-directional control in web processes. The estimator is represented as a Radial Basis Function Network, where the basis functions in the hidden layer are defined using discrete Chebyshev polynomials. The problem is considered as a nonlinear optimization problem and solved online using a recursive prediction error method. Convergence analysis is used to compare the performance of both full and reduced model estimators, with the advantages of the reduced model being demonstrated using results obtained from an industrial plastic film extrusion test bed.

This paper addresses the problem of estimating the effective actuator centre locations in a paper machine whilst the process is operating in closed loop. A reduced order estimator employing a Radial Basis Function Network is described, where the basis functions in the hidden layer are defined using Discrete Chebyshev Polynomials. The problem is considered as a nonlinear optimisation problem and solved online using a recursive prediction error method.

Industrial web processes are usually treated by control engineers as special forms of multivariable system. However, based upon fundamental modelling arguments, more natural paradigms emerge two dimensional (2D) dynamical systems and orthogonal transform processes. This approach is followed here, along with the associated estimation and control algorithms. The important issue of dimensionality is also addressed and control specific data compression methods are discussed as are the data collection and sensing issues which are specific to web forming processes. All the methods discussed use synthesis procedures and thus have a natural adaptive interpretation.