Modelling and identification of non-linear deterministic systems in the delta-domain

This paper provides a formulation for using the delta-operator in the modelling of non-linear systems. It is shown that a unique representation of a deterministic non-linear auto-regressive with exogenous input (NARX) model can be obtained for polynomial basis functions using the delta-operator and expressions are derived to convert between the shift- and delta- domain. A delta-NARX model is applied to the identification of a test problem (a Van-der-Pol oscillator): a comparison is made with the standard shift operator non-linear model and it is demonstrated that the delta-domain approach improves the numerical properties of structure detection, leads to a parsimonious description and provides a model that is closely linked to the continuous-time non-linear system in terms of both parameters and structure

Maximum-likelihood estimation of delta-domain model parameters from noisy output signals

Fast sampling is desirable to describe signal transmission through wide-bandwidth systems. The delta-operator provides an ideal discrete-time modeling description for such fast-sampled systems. However, the estimation of delta-domain model parameters is usually biased by directly applying the delta-transformations to a sampled signal corrupted by additive measurement noise. This problem is solved here by expectation-maximization, where the delta-transformations of the true signal are estimated and then used to obtain the model parameters. The method is demonstrated on a numerical example to improve on the accuracy of using a shift operator approach when the sample rate is fast

Variable neural networks for adaptive control of nonlinear systems

This paper is concerned with the adaptive control of continuous-time nonlinear dynamical systems using neural networks. A novel neural network architecture, referred to as a variable neural network, is proposed and shown to be useful in approximating the unknown nonlinearities of dynamical systems. In the variable neural networks, the number of basis functions can be either increased or decreased with time, according to specified design strategies, so that the network will not overfit or underfit the data set. Based on the Gaussian radial basis function (GRBF) variable neural network, an adaptive control scheme is presented. The location of the centers and the determination of the widths of the GRBFs in the variable neural network are analyzed to make a compromise between orthogonality and smoothness. The weight-adaptive laws developed using the Lyapunov synthesis approach guarantee the stability of the overall control scheme, even in the presence of modeling error(s). The tracking errors converge to the required accuracy through the adaptive control algorithm derived by combining the variable neural network and Lyapunov synthesis techniques. The operation of an adaptive control scheme using the variable neural network is demonstrated using two simulated example

Parameter estimation and inference for stochastic reaction-diffusion systems: application to morphogenesis in D. melanogaster

Background: Reaction-diffusion systems are frequently used in systems biology to model developmental and signalling processes. In many applications, count numbers of the diffusing molecular species are very low, leading to the need to explicitly model the inherent variability using stochastic methods. Despite their importance and frequent use, parameter estimation for both deterministic and stochastic reaction-diffusion systems is still a challenging problem. Results: We present a Bayesian inference approach to solve both the parameter and state estimation problem for stochastic reaction-diffusion systems. This allows a determination of the full posterior distribution of the parameters (expected values and uncertainty). We benchmark the method by illustrating it on a simple synthetic experiment. We then test the method on real data about the diffusion of the morphogen Bicoid in Drosophila melanogaster. The results show how the precision with which parameters can be inferred varies dramatically, indicating that the ability to infer full posterior distributions on the parameters can have important experimental design consequences. Conclusions: The results obtained demonstrate the feasibility and potential advantages of applying a Bayesian approach to parameter estimation in stochastic reaction-diffusion systems. In particular, the ability to estimate credibility intervals associated with parameter estimates can be precious for experimental design. Further work, however, will be needed to ensure the method can scale up to larger problems

New insights for applications of Kreisselmeier's structure in robust and fault tolerant control

This paper addresses a two degree of freedom structure discussed by Kreisselmeier for the SISO case in 1999. The discussion herein considers a MIMO setting, and aims at the use of this control topology for robust and fault tolerant control. It is also shown how design barriers can be obtained for robust I/O transfer behavior assignment and robustness evaluation schemes can be devised which allow for the quantitative valuation of I/O transfer behavior degradation in the presence of plant model uncertainty. The concepts and techniques are illustrated and assessed using an in-flight simulation problem

Person-specific gesture set selection for optimised movement classification from EMG signals

© 2016 IEEE.Movement classification from electromyography (EMG) signals is a promising vector for improvement of human computer interaction and prosthetic control. Conventional work in this area typically makes use of expert knowledge to select a set of movements a priori and then design classifiers based around these movements. The disadvantage of this approach is that different individuals might have different sets of movements that would lead to high classification accuracy. The novel approach we take here is to instead use a data-driven diagnostic test to select a set of person-specific movements. This new approach leads to an optimised set of movements for a specific person with regards to classification performance

Stability analysis and nonlinear current-limiting control design for DC micro-grids with CPLs

In this study, a DC micro‐grid consisting of multiple paralleled energy resources interfaced by both bidirectional AC/DC and DC/DC boost converters and loaded by a constant power load (CPL) is investigated. By considering the generic dq transformation of the AC/DC converters' dynamics and the accurate nonlinear model of the DC/DC converters, two novel control schemes are presented for each converter‐interfaced unit to guarantee load voltage regulation, power sharing and closed‐loop system stability. This novel framework incorporates the widely adopted droop control and using input‐to‐state stability theory, it is proven that each converter guarantees a desired current limitation without the need for cascaded control and saturation blocks. Sufficient conditions to ensure closed‐loop system stability are analytically obtained and tested for different operation scenarios. The system stability is further analysed from a graphical perspective, providing valuable insights of the CPL's influence onto the system performance and stability. The proposed control performance and the theoretical analysis are first validated by simulating a three‐phase AC/DC converter in parallel with a bidirectional DC/DC boost converter feeding a CPL in comparison with the cascaded PI control technique. Finally, experimental results are also provided to demonstrate the effectiveness of the proposed control approach on a real testbed

Power sharing of parallel operated DC-DC converters using current-limiting droop control

In this paper, a nonlinear current-limiting droop controller is proposed to achieve accurate power sharing among parallel operated DC-DC boost converters in a DC micro-grid application. In particular, the recently developed robust droop controller is adopted and implemented as a dynamic virtual resistance in series with the inductance of each DC-DC boost converter. Opposed to the traditional approaches that use small-signal modeling, the proposed control design takes into account the accurate nonlinear dynamic model of each converter and it is analytically proven that accurate power sharing can be accomplished with an inherent current limitation for each converter independently using input-to-state stability theory. When the load requests more power that exceeds the capacity of the converters, the current-limiting capability of the proposed control method protects the devices by limiting the inductor current of each converter below a given maximum value. Extensive simulation results of two paralleled DC-DC boost converters are presented to verify the power sharing and current-limiting properties of the proposed controller under several changes of the load

Design of a UDE Frequency Selective Filter to Reject Periodical Disturbances

In this paper a new filter design for the Uncertainty and Disturbance Estimator (UDE) is proposed to reject periodical disturbances when a limited bandwidth is required for the control output. The motivation comes from several applications where the system actuator may introduce a bandwidth limitation, as a result of internal delays, or when the actuator itself is a limited bandwidth closed-loop system. When the traditional UDE approach is applied in these systems, the stability requirements impose a limitation over the effective bandwidth of the UDE filter and therefore disturbances cannot be fully rejected by the filter. In the case where the expected disturbance is periodical with a known fundamental frequency, the proposed UDE filter is designed as a chain of filters to match selected bands of the expected disturbance spectrum and fully reject them while maintaining the desired stability margins. A design example of a power inverter application is investigated and extensive simulation results are provided to verify the proposed UDE filter design

A temporal-to-spatial neural network for classification of hand movements from electromyography data

Deep convolutional neural networks (CNNs) are appealing for the purpose of classification of hand movements from surface electromyography (sEMG) data because they have the ability to perform automated person-specific feature extraction from raw data. In this paper, we make the novel contribution of proposing and evaluating a design for the early processing layers in the deep CNN for multichannel sEMG. Specifically, we propose a novel temporal-to-spatial (TtS) CNN architecture, where the first layer performs convolution separately on each sEMG channel to extract temporal features. This is motivated by the idea that sEMG signals in each channel are mediated by one or a small subset of muscles, whose temporal activation patterns are associated with the signature features of a gesture. The temporal layer captures these signature features for each channel separately, which are then spatially mixed in successive layers to recognise a specific gesture. A practical advantage is that this approach also makes the CNN simple to design for different sample rates. We use NinaPro database 1 (27 subjects and 52 movements + rest), sampled at 100 Hz, and database 2 (40 subjects and 40 movements + rest), sampled at 2 kHz, to evaluate our proposed CNN design. We benchmark against a feature-based support vector machine (SVM) classifier, two CNNs from the literature, and an additional standard design of CNN. We find that our novel TtS CNN design achieves 66.6% per-class accuracy on database 1, and 67.8% on database 2, and that the TtS CNN outperforms all other compared classifiers using a statistical hypothesis test at the 2% significance level