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

Dynamic model reference control of a PMAC motor for automotive traction drives

The permanent magnet AC (PMAC) motor drive is a bilinear closely coupled system subject to saturation due to finite DC supply voltage and current limitation for hardware protection. Model reference control can be applied to the PMAC motor, with PI current controllers tracking the model reference current command values. The finite supply voltage constraint results in degradation of system performance when the current regulators saturate. In this paper, a dynamic model reference controller is presented which includes the current and voltage limits and constrains the magnitude of the current vector command signals, operating the system just within the limits of saturation. This allows the PI controllers to accurately track the command signals and retain control of the current vector. The controller ensures maximum possible dynamic performance of the system. The system and controller is presented and experimentally verified, and the PI controller gains are found by Monte Carlo simulation

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