Composite control of non-linear singularly perturbed systems: meeting a design objective

Using the integral manifold approach, a composite control—the sum of a fast control and a slow control—is derived for a particular class of non-linear singularly perturbed systems. The fast control is designed completely at the outset, thus ensuring the stability of the fast transients of the system and, furthermore, the existence of the integral manifold. A new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy. Though this approach is, by its very nature, ad hoc, the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Identification of nonlinear systems with a dynamic recurrent neural network

Two approaches are presented to calculate the weights for a Dynamic Recurrent Neural Network (DRNN) in order to identify the input-output dynamics of a class of nonlinear systems. The number of states of the identified network is constrained to be the same as the number of states of the plant.

The control of dynamical systems by neural networks

In this paper the use of neural networks for the control of dynamical systems is considered. Both identification and feedback control aspects are discussed as well as the types of system for which neural networks can provide a useful technique. Multi-layer Perceptron and Radial Basis function neural network types are looked at, with an emphasis on the latter. It is shown how basis function centre selection is a critical part of the implementation process and that multivariate clustering algorithms can be an extremely useful tool for finding centres.

Multi-satellite observed responses of precipitation and its extremes to interannual climate variability

The consistency of precipitation variability estimated from the multiple satellite-based observing systems is assessed. There is generally good agreement between TRMM TMI, SSM/I, GPCP and AMSRE datasets for the inter-annual variability of precipitation since 1997 but the HOAPS dataset appears to overestimate the magnitude of variability. Over the tropical ocean the TRMM 3B42 dataset produces unrealistic variabilitys. Based upon deseasonalised GPCP data for the period 1998-2008, the sensitivity of global mean precipitation (P) to surface temperature (T) changes (dP/dT) is about 6%/K, although a smaller sensitivity of 3.6%/K is found using monthly GPCP data over the longer period 1989-2008. Over the tropical oceans dP/dT ranges from 10-30%/K depending upon time-period and dataset while over tropical land dP/dT is -8 to -11%/K for the 1998-2008 period. Analyzing the response of the tropical ocean precipitation intensity distribution to changes in T we find the wetter area P shows a strong positive response to T of around 20%/K. The response over the drier tropical regimes is less coherent and varies with datasets, but responses over the tropical land show significant negative relationships over an interannual time-scale. The spatial and temporal resolutions of the datasets strongly influence the precipitation responses over the tropical oceans and help explain some of the discrepancy between different datasets. Consistency between datasets is found to increase on averaging from daily to 5-day time-scales and considering a 1o (or coarser) spatial resolution. Defining the wet and dry tropical ocean regime by the 60th percentile of P intensity, the 5-day average, 1o TMI data exhibits a coherent drying of the dry regime at the rate of -20%/K and the wet regime becomes wetter at a similar rate with warming.

Revealing ensemble state transition patterns in multi-electrode neuronal recordings using hidden Markov models

In order to harness the computational capacity of dissociated cultured neuronal networks, it is necessary to understand neuronal dynamics and connectivity on a mesoscopic scale. To this end, this paper uncovers dynamic spatiotemporal patterns emerging from electrically stimulated neuronal cultures using hidden Markov models (HMMs) to characterize multi-channel spike trains as a progression of patterns of underlying states of neuronal activity. However, experimentation aimed at optimal choice of parameters for such models is essential and results are reported in detail. Results derived from ensemble neuronal data revealed highly repeatable patterns of state transitions in the order of milliseconds in response to probing stimuli.

Sub-agent elements for control methods in multi-agent energy management system

Increased penetration of generation and decentralised control are considered to be feasible and effective solution for reducing cost and emissions and hence efficiency associated with power generation and distribution. Distributed generation in combination with the multi-agent technology are perfect candidates for this solution. Pro-active and autonomous nature of multi-agent systems can provide an effective platform for decentralised control whilst improving reliability and flexibility of the grid.

Strong structural controllability and the multi-link inverted pendulum

This technical note investigates the controllability of the linearized dynamics of the multilink inverted pendulum as the number of links and the number and location of actuators changes. It is demonstrated that, in some instances, there exist sets of parameter values that render the system uncontrollable and so usual methods for assessing controllability are difficult to employ. To assess the controllability, a theorem on strong structural controllability for single-input systems is extended to the multiinput case.

Exploring the construction of social class in educational discourse: the rational order of the nation state vs. global uncertainties

This article aims to create intellectual space in which issues of social inequality and education can be analyzed and discussed in relation to the multifaceted and multi-levelled complexities of the modern world. It is divided into three sections. Section One locates the concept of social class in the context of the modern nation state during the period after the Second World War. Focusing particularly on the impact of ‘Fordism’ on social organization and cultural relations, it revisits the articulation of social justice issues in the United Kingdom, and the structures put into place at the time to alleviate educational and social inequalities. Section Two problematizes the traditional concept of social class in relation to economic, technological and sociocultural changes that have taken place around the world since the mid-1980s. In particular, it charts some of the changes to the international labour market and global patterns of consumption, and their collective impact on the re-constitution of class boundaries in ‘developed countries’. This is juxtaposed with some of the major social effects of neo-classical economic policies in recent years on the sociocultural base in developing countries. It discusses some of the ways these inequalities are reflected in education. Section Three explores tensions between the educational ideals of the ‘knowledge economy’ and the discursive range of social inequalities that are emerging within and beyond the nation state. Drawing on key motifs identified throughout, the article concludes with a reassessment of the concept of social class within the global cultural economy. This is discussed in relation to some of the major equity and human rights issues in education today.

Stochastic perturbations to dynamical systems: a response theory approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Robust pole assignment in systems subject to structured perturbations

The problem of robust pole assignment by feedback in a linear, multivariable, time-invariant system which is subject to structured perturbations is investigated. A measure of robustness, or sensitivity, of the poles to a given class of perturbations is derived, and a reliable and efficient computational algorithm is presented for constructing a feedback which assigns the prescribed poles and optimizes the robustness measure.

Robust control system design for generalized state-space systems

Robustness in multi-variable control system design requires that the solution to the design problem be insensitive to perturbations in the system data. In this paper we discuss measures of robustness for generalized state-space, or descriptor, systems and describe algorithmic techniques for optimizing robustness for various applications.