Pulse shaping using state space algorithms

We discuss the use of pulse shaping for optimal excitation of samples in time-domain THz spectroscopy. Pulse shaping can be performed in a 4f optical system to specifications from state space models of the system's dynamics. Subspace algorithms may be used for the identification of the state space models.

State-space model identification of a wireless THz network

We model the large scale fading of wireless THz communications links deployed in a metropolitan area taking into account reception through direct line of sight, ground or wall reflection and diffraction. The movement of the receiver in the three dimensions is modelled by an autonomous dynamic linear system in state-space whereas the geometric relations involved in the attenuation and multi-path propagation of the electric field are described by a static non-linear mapping. A subspace algorithm in conjunction with polynomial regression is used to identify a Wiener model from time-domain measurements of the field intensity.

Self-tuning regulators—a state space approach

This paper employs a state space system description to provide a pole placement scheme via state feedback. It is shown that when a recursive least squares estimation scheme is used, the feedback employed can be expressed simply in terms of the estimated system parameters. To complement the state feedback approach, a method employing both state feedback and linear output feedback is discussed. Both methods arc then compared with the previous output polynomial type feedback schemes.

Self-tuning property of state-space self tuners

The basic assumption from implicit self-tuning theory is that, for self tuning to occur, the control input obtained from the estimated system model converges to the value whic would be obtained if the system parameters were known. As as direct result of this, only certain control strategies are acceptable. Here a general rule for the self-tuning property of pole-placement self tuners is obtained, and previous strategies are shown to be special cases of this.

On the stability radius of a generalized state-space system

The concept of “distance to instability” of a system matrix is generalized to system pencils which arise in descriptor (semistate) systems. Difficulties arise in the case of singular systems, because the pencil can be made unstable by an infinitesimal perturbation. It is necessary to measure the distance subject to restricted, or structured, perturbations. In this paper a suitable measure for the stability radius of a generalized state-space system is defined, and a computable expression for the distance to instability is derived for regular pencils of index less than or equal to one. For systems which are strongly controllable it is shown that this measure is related to the sensitivity of the poles of the system over all feedback matrices assigning the poles.

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.

Tropospheric planetary wave dynamics and mixture modeling: Two preferred regimes and a regime shift

Investigation of preferred structures of planetary wave dynamics is addressed using multivariate Gaussian mixture models. The number of components in the mixture is obtained using order statistics of the mixing proportions, hence avoiding previous difficulties related to sample sizes and independence issues. The method is first applied to a few low-order stochastic dynamical systems and data from a general circulation model. The method is next applied to winter daily 500-hPa heights from 1949 to 2003 over the Northern Hemisphere. A spatial clustering algorithm is first applied to the leading two principal components (PCs) and shows significant clustering. The clustering is particularly robust for the first half of the record and less for the second half. The mixture model is then used to identify the clusters. Two highly significant extratropical planetary-scale preferred structures are obtained within the first two to four EOF state space. The first pattern shows a Pacific-North American (PNA) pattern and a negative North Atlantic Oscillation (NAO), and the second pattern is nearly opposite to the first one. It is also observed that some subspaces show multivariate Gaussianity, compatible with linearity, whereas others show multivariate non-Gaussianity. The same analysis is also applied to two subperiods, before and after 1978, and shows a similar regime behavior, with a slight stronger support for the first subperiod. In addition a significant regime shift is also observed between the two periods as well as a change in the shape of the distribution. The patterns associated with the regime shifts reflect essentially a PNA pattern and an NAO pattern consistent with the observed global warming effect on climate and the observed shift in sea surface temperature around the mid-1970s.

Fractional order modeling of large three-dimensional RC networks

An incidence matrix analysis is used to model a three-dimensional network consisting of resistive and capacitive elements distributed across several interconnected layers. A systematic methodology for deriving a descriptor representation of the network with random allocation of the resistors and capacitors is proposed. Using a transformation of the descriptor representation into standard state-space form, amplitude and phase admittance responses of three-dimensional random RC networks are obtained. Such networks display an emergent behavior with a characteristic Jonscher-like response over a wide range of frequencies. A model approximation study of these networks is performed to infer the admittance response using integral and fractional order models. It was found that a fractional order model with only seven parameters can accurately describe the responses of networks composed of more than 70 nodes and 200 branches with 100 resistors and 100 capacitors. The proposed analysis can be used to model charge migration in amorphous materials, which may be associated to specific macroscopic or microscopic scale fractal geometrical structures in composites displaying a viscoelastic electromechanical response, as well as to model the collective responses of processes governed by random events described using statistical mechanics.

Neurofuzzy control using Kalman filtering state feedback with coloured noise for unknown non-linear processes

This paper presents a controller design scheme for a priori unknown non-linear dynamical processes that are identified via an operating point neurofuzzy system from process data. Based on a neurofuzzy design and model construction algorithm (NeuDec) for a non-linear dynamical process, a neurofuzzy state-space model of controllable form is initially constructed. The control scheme based on closed-loop pole assignment is then utilized to ensure the time invariance and linearization of the state equations so that the system stability can be guaranteed under some mild assumptions, even in the presence of modelling error. The proposed approach requires a known state vector for the application of pole assignment state feedback. For this purpose, a generalized Kalman filtering algorithm with coloured noise is developed on the basis of the neurofuzzy state-space model to obtain an optimal state vector estimation. The derived controller is applied in typical output tracking problems by minimizing the tracking error. Simulation examples are included to demonstrate the operation and effectiveness of the new approach.

Neurofuzzy state identification using prefiltering

A new state estimator algorithm is based on a neurofuzzy network and the Kalman filter algorithm. The major contribution of the paper is recognition of a bias problem in the parameter estimation of the state-space model and the introduction of a simple, effective prefiltering method to achieve unbiased parameter estimates in the state-space model, which will then be applied for state estimation using the Kalman filtering algorithm. Fundamental to this method is a simple prefiltering procedure using a nonlinear principal component analysis method based on the neurofuzzy basis set. This prefiltering can be performed without prior system structure knowledge. Numerical examples demonstrate the effectiveness of the new approach.

Development and application of a novel algorithm for steady-state optimising control using dynamic information

A novel optimising controller is designed that leads a slow process from a sub-optimal operational condition to the steady-state optimum in a continuous way based on dynamic information. Using standard results from optimisation theory and discrete optimal control, the solution of a steady-state optimisation problem is achieved by solving a receding-horizon optimal control problem which uses derivative and state information from the plant via a shadow model and a state-space identifier. The paper analyzes the steady-state optimality of the procedure, develops algorithms with and without control rate constraints and applies the procedure to a high fidelity simulation study of a distillation column optimisation.

Multivariate analysis of the dielectric response of materials modeled using networks of resistors and capacitors

We discuss the modeling of dielectric responses of electromagnetically excited networks which are composed of a mixture of capacitors and resistors. Such networks can be employed as lumped-parameter circuits to model the response of composite materials containing conductive and insulating grains. The dynamics of the excited network systems are studied using a state space model derived from a randomized incidence matrix. Time and frequency domain responses from synthetic data sets generated from state space models are analyzed for the purpose of estimating the fraction of capacitors in the network. Good results were obtained by using either the time-domain response to a pulse excitation or impedance data at selected frequencies. A chemometric framework based on a Successive Projections Algorithm (SPA) enables the construction of multiple linear regression (MLR) models which can efficiently determine the ratio of conductive to insulating components in composite material samples. The proposed method avoids restrictions commonly associated with Archie’s law, the application of percolation theory or Kohlrausch-Williams-Watts models and is applicable to experimental results generated by either time domain transient spectrometers or continuous-wave instruments. Furthermore, it is quite generic and applicable to tomography, acoustics as well as other spectroscopies such as nuclear magnetic resonance, electron paramagnetic resonance and, therefore, should be of general interest across the dielectrics community.