Modeling of complex-valued Wiener systems using B-spline neural network

In this brief, a new complex-valued B-spline neural network is introduced in order to model the complex-valued Wiener system using observational input/output data. The complex-valued nonlinear static function in the Wiener system is represented using the tensor product from two univariate B-spline neural networks, using the real and imaginary parts of the system input. Following the use of a simple least squares parameter initialization scheme, the Gauss-Newton algorithm is applied for the parameter estimation, which incorporates the De Boor algorithm, including both the B-spline curve and the first-order derivatives recursion. Numerical examples, including a nonlinear high-power amplifier model in communication systems, are used to demonstrate the efficacy of the proposed approaches.

Inverting recurrent neural networks for internal model control of nonlinear systems

In this paper, we show how a set of recently derived theoretical results for recurrent neural networks can be applied to the production of an internal model control system for a nonlinear plant. The results include determination of the relative order of a recurrent neural network and invertibility of such a network. A closed loop controller is produced without the need to retrain the neural network plant model. Stability of the closed-loop controller is also demonstrated.

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.

A normative approach to multi-agent systems for intelligent buildings

Building Management Systems (BMS) are widely adopted in modern buildings around the world in order to provide high-quality building services, and reduce the running cost of the building. However, most BMS are functionality-oriented and do not consider user personalization. The aim of this research is to capture and represent building management rules using organizational semiotics methods. We implement Semantic Analysis, which determines semantic units in building management and their relationship patterns of behaviour, and Norm Analysis, which extracts and specifies the norms that establish how and when these management actions occur. Finally, we propose a multi-agent framework for norm based building management. This framework contributes to the design domain of intelligent building management system by defining a set of behaviour patterns, and the norms that govern the real-time behaviour in a building.

Disentangling multi-level systems: averaging, correlations and memory

We consider two weakly coupled systems and adopt a perturbative approach based on the Ruelle response theory to study their interaction. We propose a systematic way of parameterizing the effect of the coupling as a function of only the variables of a system of interest. Our focus is on describing the impacts of the coupling on the long term statistics rather than on the finite-time behavior. By direct calculation, we find that, at first order, the coupling can be surrogated by adding a deterministic perturbation to the autonomous dynamics of the system of interest. At second order, there are additionally two separate and very different contributions. One is a term taking into account the second-order contributions of the fluctuations in the coupling, which can be parameterized as a stochastic forcing with given spectral properties. The other one is a memory term, coupling the system of interest to its previous history, through the correlations of the second system. If these correlations are known, this effect can be implemented as a perturbation with memory on the single system. In order to treat this case, we present an extension to Ruelle's response theory able to deal with integral operators. We discuss our results in the context of other methods previously proposed for disentangling the dynamics of two coupled systems. We emphasize that our results do not rely on assuming a time scale separation, and, if such a separation exists, can be used equally well to study the statistics of the slow variables and that of the fast variables. By recursively applying the technique proposed here, we can treat the general case of multi-level systems.

Bistable systems with stochastic noise: virtues and limits of effective one-dimensional Langevin equations

The understanding of the statistical properties and of the dynamics of multistable systems is gaining more and more importance in a vast variety of scientific fields. This is especially relevant for the investigation of the tipping points of complex systems. Sometimes, in order to understand the time series of given observables exhibiting bimodal distributions, simple one-dimensional Langevin models are fitted to reproduce the observed statistical properties, and used to investing-ate the projected dynamics of the observable. This is of great relevance for studying potential catastrophic changes in the properties of the underlying system or resonant behaviours like those related to stochastic resonance-like mechanisms. In this paper, we propose a framework for encasing this kind of studies, using simple box models of the oceanic circulation and choosing as observable the strength of the thermohaline circulation. We study the statistical properties of the transitions between the two modes of operation of the thermohaline circulation under symmetric boundary forcings and test their agreement with simplified one-dimensional phenomenological theories. We extend our analysis to include stochastic resonance-like amplification processes. We conclude that fitted one-dimensional Langevin models, when closely scrutinised, may result to be more ad-hoc than they seem, lacking robustness and/or well-posedness. They should be treated with care, more as an empiric descriptive tool than as methodology with predictive power.

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.

Holocene settlement shifts and paleoenvironments on the Central Iranian Plateau: investigating linked systems

For thousands of years, humans have inhabited locations that are highly vulnerable to the impacts of climate change, earthquakes, and floods. In order to investigate the extent to which Holocene environmental changes may have impacted on cultural evolution, we present new geologic, geomorphic, and chronologic data from the Qazvin Plain in northwest Iran that provides a backdrop of natural environmental changes for the simultaneous cultural dynamics observed on the Central Iranian Plateau. Well-resolved archaeological data from the neighbouring settlements of Zagheh (7170—6300 yr BP), Ghabristan (6215—4950 yr BP) and Sagzabad (4050—2350 yr BP) indicate that Holocene occupation of the Hajiarab alluvial fan was interrupted by a 900 year settlement hiatus. Multiproxy climate data from nearby lakes in northwest Iran suggest a transition from arid early-Holocene conditions to more humid middle-Holocene conditions from c. 7550 to 6750 yr BP, coinciding with the settlement of Zagheh, and a peak in aridity at c. 4550 yr BP during the settlement hiatus. Palaeoseismic investigations indicate that large active fault systems in close proximity to the tell sites incurred a series of large (MW ~7.1) earthquakes with return periods of ~500—1000 years during human occupation of the tells. Mapping and optically stimulated luminescence (OSL) chronology of the alluvial sequences reveals changes in depositional style from coarse-grained unconfined sheet flow deposits to proximal channel flow and distally prograding alluvial deposits sometime after c. 8830 yr BP, possibly reflecting an increase in moisture following the early-Holocene arid phase. The coincidence of major climate changes, earthquake activity, and varying sedimentation styles with changing patterns of human occupation on the Hajiarab fan indicate links between environmental and anthropogenic systems. However, temporal coincidence does not necessitate a fundamental causative dependency.

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.

Regularization of Descriptor Systems by Derivative and Proportional State Feedback

For linear multivariable time-invariant continuous or discrete-time singular systems it is customary to use a proportional feedback control in order to achieve a desired closed loop behaviour. Derivative feedback is rarely considered. This paper examines how derivative feedback in descriptor systems can be used to alter the structure of the system pencil under various controllability conditions. It is shown that derivative and proportional feedback controls can be constructed such that the closed loop system has a given form and is also regular and has index at most 1. This property ensures the solvability of the resulting system of dynamic-algebraic equations. The construction procedures used to establish the theory are based only on orthogonal matrix decompositions and can therefore be implemented in a numerically stable way. The problem of pole placement with derivative feedback alone and in combination with proportional state feedback is also investigated. A computational algorithm for improving the “conditioning” of the regularized closed loop system is derived.

System identification of Wiener systems with B-spline functions using De Boor recursion

In this article a simple and effective algorithm is introduced for the system identification of the Wiener system using observational input/output data. The nonlinear static function in the Wiener system is modelled using a B-spline neural network. The Gauss–Newton algorithm is combined with De Boor algorithm (both curve and the first order derivatives) for the parameter estimation of the Wiener model, together with the use of a parameter initialisation scheme. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

A model-based PID controller for Hammerstein systems using B-spline neural networks

In this paper, a new model-based proportional–integral–derivative (PID) tuning and controller approach is introduced for Hammerstein systems that are identified on the basis of the observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The control signal is composed of a PID controller, together with a correction term. Both the parameters in the PID controller and the correction term are optimized on the basis of minimizing the multistep ahead prediction errors. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on B-spline neural networks and the associated Jacobian matrix are calculated using the de Boor algorithms, including both the functional and derivative recursions. Numerical examples are utilized to demonstrate the efficacy of the proposed approaches.

Modelling and inverting complex-valued Wiener systems

We develop a complex-valued (CV) B-spline neural network approach for efficient identification and inversion of CV Wiener systems. The CV nonlinear static function in the Wiener system is represented using the tensor product of two univariate B-spline neural networks. With the aid of a least squares parameter initialisation, the Gauss-Newton algorithm effectively estimates the model parameters that include the CV linear dynamic model coefficients and B-spline neural network weights. The identification algorithm naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. An accurate inverse of the CV Wiener system is then obtained, in which the inverse of the CV nonlinear static function of the Wiener system is calculated efficiently using the Gaussian-Newton algorithm based on the estimated B-spline neural network model, with the aid of the De Boor recursions. The effectiveness of our approach for identification and inversion of CV Wiener systems is demonstrated using the application of digital predistorter design for high power amplifiers with memory

B-spline neural networks based PID controller for Hammerstein systems

A new PID tuning and controller approach is introduced for Hammerstein systems based on input/output data. A B-spline neural network is used to model the nonlinear static function in the Hammerstein system. The control signal is composed of a PID controller together with a correction term. In order to update the control signal, the multistep ahead predictions of the Hammerstein system based on the B-spline neural networks and the associated Jacobians matrix are calculated using the De Boor algorithms including both the functional and derivative recursions. A numerical example is utilized to demonstrate the efficacy of the proposed approaches.

Bis(azidophenyl)phosphole building block for extended π-conjugated systems

Novel bis(azidophenyl)phosphole sulfide building block 8 has been developed to give access to a plethora of phosphole-containing π-conjugated systems in a simple synthetic step. This was explored for the reaction of the two azido moieties with phenyl-, pyridyl- and thienylacetylenes, to give bis(aryltriazolyl)-extended π-systems, having either the phosphole sulfide (9) or the phosphole (10) group as central ring. These conjugated frameworks exhibit intriguing photophysical and electrochemical properties that vary with the nature of the aromatic end-group. The λ3-phospholes 10 display blue fluorescence (λem = 460–469 nm) with high quan-tum yield (ΦF = 0.134–0.309). The radical anion of pyridylsubstituted phosphole sulfide 9b was observed with UV/Vis spectroscopy. TDDFT calculations on the extended π-systems showed some variation in the shape of the HOMOs, which was found to have an effect on the extent of charge transfer, depending on the aromatic end-group. Some fine-tuning of the emission maxima was observed, albeit subtle, showing a decrease in conjugation in the order thienyl � phenyl � pyridyl. These results show that variations in the distal ends of such π-systems have a subtle but significant effect on photophysical properties.