Relationship between åström control and the kalman linear regulator — Caines revisited

The relationship between minimum variance and minimum expected quadratic loss feedback controllers for linear univariate discrete-time stochastic systems is reviewed by taking the approach used by Caines. It is shown how the two methods can be regarded as providing identical control actions as long as a noise-free measurement state-space model is employed.

Optimal observers for ARMA models

A polynomial-based ARMA model, when posed in a state-space framework can be regarded in many different ways. In this paper two particular state-space forms of the ARMA model are considered, and although both are canonical in structure they differ in respect of the mode in which disturbances are fed into the state and output equations. For both forms a solution is found to the optimal discrete-time observer problem and algebraic connections between the two optimal observers are shown. The purpose of the paper is to highlight the fact that the optimal observer obtained from the first state-space form, commonly known as the innovations form, is not that employed in an optimal controller, in the minimum-output variance sense, whereas the optimal observer obtained from the second form is. Hence the second form is a much more appropriate state-space description to use for controller design, particularly when employed in self-tuning control schemes.

Using self-organising feature maps for the control of artificial organisms

Variations on the standard Kohonen feature map can enable an ordering of the map state space by using only a limited subset of the complete input vector. Also it is possible to employ merely a local adaptation procedure to order the map, rather than having to rely on global variables and objectives. Such variations have been included as part of a hybrid learning system (HLS) which has arisen out of a genetic-based classifier system. In the paper a description of the modified feature map is given, which constitutes the HLSs long term memory, and results in the control of a simple maze running task are presented, thereby demonstrating the value of goal related feedback within the overall network.

Control strategy for Boolean input systems

The purpose of this paper is to design a control law for continuous systems with Boolean inputs allowing the output to track a desired trajectory. Such systems are controlled by items of commutation. This type of systems, with Boolean inputs, has found increasing use in the electric industry. Power supplies include such systems and a power converter represents one of theses systems. For instance, in power electronics the control variable is the switching OFF and ON of components such as thyristors or transistors. In this paper, a method is proposed for the designing of a control law in state space for such systems. This approach is implemented in simulation for the control of an electronic circuit.

Wavelet filtered modelling applied to measurements of a waveguide's THz time domain response

A quasi-optical de-embedding technique for characterizing waveguides is demonstrated using wideband time-resolved terahertz spectroscopy. A transfer function representation is adopted for the description of the signal in the input and output port of the waveguides. The time domain responses were discretised and the waveguide transfer function was obtained through a parametric approach in the z-domain after describing the system with an ARX as well as with a state space model. Prior to the identification procedure, filtering was performed in the wavelet domain to minimize signal distortion and the noise propagating in the ARX and subspace models. The model identification procedure requires isolation of the phase delay in the structure and therefore the time-domain signatures must be firstly aligned with respect to each other before they are compared. An initial estimate of the number of propagating modes was provided by comparing the measured phase delay in the structure with theoretical calculations that take into account the physical dimensions of the waveguide. Models derived from measurements of THz transients in a precision WR-8 waveguide adjustable short will be presented.

Novel developments in process optimisation using predictive control

In industrial practice, constrained steady state optimisation and predictive control are separate, albeit closely related functions within the control hierarchy. This paper presents a method which integrates predictive control with on-line optimisation with economic objectives. A receding horizon optimal control problem is formulated using linear state space models. This optimal control problem is very similar to the one presented in many predictive control formulations, but the main difference is that it includes in its formulation a general steady state objective depending on the magnitudes of manipulated and measured output variables. This steady state objective may include the standard quadratic regulatory objective, together with economic objectives which are often linear. Assuming that the system settles to a steady state operating point under receding horizon control, conditions are given for the satisfaction of the necessary optimality conditions of the steady-state optimisation problem. The method is based on adaptive linear state space models, which are obtained by using on-line identification techniques. The use of model adaptation is justified from a theoretical standpoint and its beneficial effects are shown in simulations. The method is tested with simulations of an industrial distillation column and a system of chemical reactors.

A practical approach for training dynamic recurrent neural networks: use of Apriori information

Presents a technique for incorporating a priori knowledge from a state space system into a neural network training algorithm. The training algorithm considered is that of chemotaxis and the networks being trained are recurrent neural networks. Incorporation of the a priori knowledge ensures that the resultant network has behaviour similar to the system which it is modelling.

Reduced complexity set-point following in self-tuning control

An external input signal is incorporated into a self-tuning controller which, although it is based on a CARMA system model, employs a state-space framework for control law calculations. Steady-state set point following can then be accomplished even when only a recursive least squares parameter estimation scheme is used, despite the fact that the disturbance affecting the system may well be coloured.

Implementation of microprocessor based self-tuning control on a heating system

This paper describes the implementation, using a microprocessor, of a self-tuning control algorithm on a heating system. The algorithm is based on recursive least squares parameter estimation with a state-space, pole placement design criterion and shows how the controller behaves when applied to an actual system.

Pyrene-Modified quartz crystal microbalance for the detection of polynitroaromatic compounds

The synthesis of a dithiol-functionalized pyrene derivative is reported, together with studies of interactions between this receptor (and other related pyrenes) and nitroaromatic compounds (NACs), in both solution and in the solid state. Spectroscopic analysis in solution and X-ray crystallographic analysis of cocrystals of pyrene and NACs in the solid state indicate that supramolecular interactions lead to the formation of defined pi-pi stacked complexes. The dithiolfunctionalized pyrene derivative can be used to modify the surface of a gold quartz crystal microbalance (QCM) to create a unique π-electron rich surface, which is able to interact with electron poor aromatic compounds. For example, exposure of the modified QCM surface to the nitroaromatic compound 2,4-dinitrotoluene (DNT) in solution results in a reduction in the resonant frequency of the QCM as a result of supramolecular interactions between the electron-rich pyrenyl surface layer and the electron-poor DNT molecules. These results suggest the potential use of such modified QCM surfaces for the detection of explosive NACs.

Efficient non-linear data assimilation in geophysical fluid dynamics

New ways of combining observations with numerical models are discussed in which the size of the state space can be very large, and the model can be highly nonlinear. Also the observations of the system can be related to the model variables in highly nonlinear ways, making this data-assimilation (or inverse) problem highly nonlinear. First we discuss the connection between data assimilation and inverse problems, including regularization. We explore the choice of proposal density in a Particle Filter and show how the ’curse of dimensionality’ might be beaten. In the standard Particle Filter ensembles of model runs are propagated forward in time until observations are encountered, rendering it a pure Monte-Carlo method. In large-dimensional systems this is very inefficient and very large numbers of model runs are needed to solve the data-assimilation problem realistically. In our approach we steer all model runs towards the observations resulting in a much more efficient method. By further ’ensuring almost equal weight’ we avoid performing model runs that are useless in the end. Results are shown for the 40 and 1000 dimensional Lorenz 1995 model.

On the equivalence between radiance and retrieval assimilation

The need for consistent assimilation of satellite measurements for numerical weather prediction led operational meteorological centers to assimilate satellite radiances directly using variational data assimilation systems. More recently there has been a renewed interest in assimilating satellite retrievals (e.g., to avoid the use of relatively complicated radiative transfer models as observation operators for data assimilation). The aim of this paper is to provide a rigorous and comprehensive discussion of the conditions for the equivalence between radiance and retrieval assimilation. It is shown that two requirements need to be satisfied for the equivalence: (i) the radiance observation operator needs to be approximately linear in a region of the state space centered at the retrieval and with a radius of the order of the retrieval error; and (ii) any prior information used to constrain the retrieval should not underrepresent the variability of the state, so as to retain the information content of the measurements. Both these requirements can be tested in practice. When these requirements are met, retrievals can be transformed so as to represent only the portion of the state that is well constrained by the original radiance measurements and can be assimilated in a consistent and optimal way, by means of an appropriate observation operator and a unit matrix as error covariance. Finally, specific cases when retrieval assimilation can be more advantageous (e.g., when the estimate sought by the operational assimilation system depends on the first guess) are discussed.

Predictive computed-torque control of a PUMA 560 manipulator robot

This paper describes the integration of constrained predictive control and computed-torque control, and its application on a six degree-of-freedom PUMA 560 manipulator arm. The real-time implementation was based on SIMULINK, with the predictive controller and the computed-torque control law implemented in the C programming language. The constrained predictive controller solved a quadratic programming problem at every sampling interval, which was as short as 10 ms, using a prediction horizon of 150 steps and an 18th order state space model.

The North Atlantic jet stream under climate change and its relation to the NAO and EA patterns

This paper describes recent variations of the North Atlantic eddy-driven jet stream and analyzes the mean response of the jet to anthropogenic forcing in climate models. Jet stream changes are analyzed both using a direct measure of the near-surface westerly wind maximum and using an EOF-based approach. This allows jet stream changes to be related to the widely used leading patterns of variability: the North Atlantic Oscillation (NAO) and East Atlantic (EA) pattern. Viewed in NAO–EA state space, isolines of jet latitude and speed resemble a distorted polar coordinate system, highlighting the dependence of the jet stream quantities on both spatial patterns. Some differences in the results of the two methods are discussed, but both approaches agree on the general characteristics of the climate models. While there is some agreement between models on a poleward shift of the jet stream in response to anthropogenic forcing, there is still considerable spread between different model projections, especially in winter. Furthermore, the model responses to forcing are often weaker than their biases when compared to a reanalysis. Diagnoses of jet stream changes can be sensitive to the methodologies used, and several aspects of this are also discussed.

Feedback design for regularizing descriptor systems

This paper surveys numerical techniques for the regularization of descriptor (generalized state-space) systems by proportional and derivative feedback. We review generalizations of controllability and observability to descriptor systems along with definitions of regularity and index in terms of the Weierstraß canonical form. Three condensed forms display the controllability and observability properties of a descriptor system. The condensed forms are obtained through orthogonal equivalence transformations and rank decisions, so they may be computed by numerically stable algorithms. In addition, the condensed forms display whether a descriptor system is regularizable, i.e., when the system pencil can be made to be regular by derivative and/or proportional output feedback, and, if so, what index can be achieved. Also included is a a new characterization of descriptor systems that can be made to be regular with index 1 by proportional and derivative output feedback.