Neural network enhanced generalised minimum variance self-tuning controller for nonlinear discrete-time systems

A neural network enhanced self-tuning controller is presented, which combines the attributes of neural network mapping with a generalised minimum variance self-tuning control (STC) strategy. In this way the controller can deal with nonlinear plants, which exhibit features such as uncertainties, nonminimum phase behaviour, coupling effects and may have unmodelled dynamics, and whose nonlinearities are assumed to be globally bounded. The unknown nonlinear plants to be controlled are approximated by an equivalent model composed of a simple linear submodel plus a nonlinear submodel. A generalised recursive least squares algorithm is used to identify the linear submodel and a layered neural network is used to detect the unknown nonlinear submodel in which the weights are updated based on the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model therefore the nonlinear submodel is naturally accommodated within the control law. Two simulation studies are provided to demonstrate the effectiveness of the control algorithm.

Stable reduced-order models for discrete-time systems

The Routh-stability method is employed to reduce the order of discrete-time system transfer functions. It is shown that the Routh approximant is well suited to reduce both the denominator and the numerator polynomials, although alternative methods, such as PadÃ�Â(c)-Markov approximation, are also used to fit the model numerator coefficients.

Numerical convergence of the Block-Maxima approach to the generalized extreme value distribution

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems. In this setting, recent works have shown how to get a statistics of extremes in agreement with the classical Extreme Value Theory. We pursue these investigations by giving analytical expressions of Extreme Value distribution parameters for maps that have an absolutely continuous invariant measure. We compare these analytical results with numerical experiments in which we study the convergence to limiting distributions using the so called block-maxima approach, pointing out in which cases we obtain robust estimation of parameters. In regular maps for which mixing properties do not hold, we show that the fitting procedure to the classical Extreme Value Distribution fails, as expected. However, we obtain an empirical distribution that can be explained starting from a different observable function for which Nicolis et al. (Phys. Rev. Lett. 97(21): 210602, 2006) have found analytical results.

Extreme value distribution for singular measures

In this paper we perform an analytical and numerical study of Extreme Value distributions in discrete dynamical systems that have a singular measure. Using the block maxima approach described in Faranda et al. [2011] we show that, numerically, the Extreme Value distribution for these maps can be associated to the Generalised Extreme Value family where the parameters scale with the information dimension. The numerical analysis are performed on a few low dimensional maps. For the middle third Cantor set and the Sierpinskij triangle obtained using Iterated Function Systems, experimental parameters show a very good agreement with the theoretical values. For strange attractors like Lozi and H\`enon maps a slower convergence to the Generalised Extreme Value distribution is observed. Even in presence of large statistics the observed convergence is slower if compared with the maps which have an absolute continuous invariant measure. Nevertheless and within the uncertainty computed range, the results are in good agreement with the theoretical estimates.

Dynamic integrated system optimization and parameter estimation for discrete time optimal control of nonlinear systems

An algorithm for solving nonlinear discrete time optimal control problems with model-reality differences is presented. The technique uses Dynamic Integrated System Optimization and Parameter Estimation (DISOPE), which achieves the correct optimal solution in spite of deficiencies in the mathematical model employed in the optimization procedure. A version of the algorithm with a linear-quadratic model-based problem, implemented in the C+ + programming language, is developed and applied to illustrative simulation examples. An analysis of the optimality and convergence properties of the algorithm is also presented.

An event-based approach to validating solar wind speed predictions: high-speed enhancements in the Wang-Sheeley-Arge model

One of the primary goals of the Center for Integrated Space Weather Modeling (CISM) effort is to assess and improve prediction of the solar wind conditions in near‐Earth space, arising from both quasi‐steady and transient structures. We compare 8 years of L1 in situ observations to predictions of the solar wind speed made by the Wang‐Sheeley‐Arge (WSA) empirical model. The mean‐square error (MSE) between the observed and model predictions is used to reach a number of useful conclusions: there is no systematic lag in the WSA predictions, the MSE is found to be highest at solar minimum and lowest during the rise to solar maximum, and the optimal lead time for 1 AU solar wind speed predictions is found to be 3 days. However, MSE is shown to frequently be an inadequate “figure of merit” for assessing solar wind speed predictions. A complementary, event‐based analysis technique is developed in which high‐speed enhancements (HSEs) are systematically selected and associated from observed and model time series. WSA model is validated using comparisons of the number of hit, missed, and false HSEs, along with the timing and speed magnitude errors between the forecasted and observed events. Morphological differences between the different HSE populations are investigated to aid interpretation of the results and improvements to the model. Finally, by defining discrete events in the time series, model predictions from above and below the ecliptic plane can be used to estimate an uncertainty in the predicted HSE arrival times.

Single-trial event-related potential analysis for brain-computer interfaces

Abstract. Different types of mental activity are utilised as an input in Brain-Computer Interface (BCI) systems. One such activity type is based on Event-Related Potentials (ERPs). The characteristics of ERPs are not visible in single-trials, thus averaging over a number of trials is necessary before the signals become usable. An improvement in ERP-based BCI operation and system usability could be obtained if the use of single-trial ERP data was possible. The method of Independent Component Analysis (ICA) can be utilised to separate single-trial recordings of ERP data into components that correspond to ERP characteristics, background electroencephalogram (EEG) activity and other components with non- cerebral origin. Choice of specific components and their use to reconstruct “denoised” single-trial data could improve the signal quality, thus allowing the successful use of single-trial data without the need for averaging. This paper assesses single-trial ERP signals reconstructed using a selection of estimated components from the application of ICA on the raw ERP data. Signal improvement is measured using Contrast-To-Noise measures. It was found that such analysis improves the signal quality in all single-trials.

Automatic artefact removal from event-related potentials via clustering

This paper outlines a method for automatic artefact removal from multichannel recordings of event-related potentials (ERPs). The proposed method is based on, firstly, separation of the ERP recordings into independent components using the method of temporal decorrelation source separation (TDSEP). Secondly, the novel lagged auto-mutual information clustering (LAMIC) algorithm is used to cluster the estimated components, together with ocular reference signals, into clusters corresponding to cerebral and non-cerebral activity. Thirdly, the components in the cluster which contains the ocular reference signals are discarded. The remaining components are then recombined to reconstruct the clean ERPs.

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform

A novel radix-3/9 algorithm for type-III generalized discrete Hartley transform (GDHT) is proposed, which applies to length-3(P) sequences. This algorithm is especially efficient in the case that multiplication is much more time-consuming than addition. A comparison analysis shows that the proposed algorithm outperforms a known algorithm when one multiplication is more time-consuming than five additions. When combined with any known radix-2 type-III GDHT algorithm, the new algorithm also applies to length-2(q)3(P) sequences.

Adaptive deadbeat control of stochastic systems

This paper considers the use of a discrete-time deadbeat control action on systems affected by noise. Variations on the standard controller form are discussed and comparisons are made with controllers in which noise rejection is a higher priority objective. Both load and random disturbances are considered in the system description, although the aim of the deadbeat design remains as a tailoring of reference input variations. Finally, the use of such a deadbeat action within a self-tuning control framework is shown to satisfy, under certain conditions, the self-tuning property, generally though only when an extended form of least-squares estimation is incorporated.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

A new approach for the solution of the optimal set-point tracking problem for nonlinear systems

In this paper, a discrete time dynamic integrated system optimisation and parameter estimation algorithm is applied to the solution of the nonlinear tracking optimal control problem. A version of the algorithm with a linear-quadratic model-based problem is developed and implemented in software. The algorithm implemented is tested with simulation examples.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Generalised prime systems with periodic integer counting function

We study generalised prime systems (both discrete and continuous) for which the `integer counting function' N(x) has the property that N(x) ¡ cx is periodic for some c > 0. We show that this is extremely rare. In particular, we show that the only such system for which N is continuous is the trivial system with N(x) ¡ cx constant, while if N has finitely many discontinuities per bounded interval, then N must be the counting function of the g-prime system containing the usual primes except for finitely many. Keywords and phrases: Generalised prime systems. I