A neural network enhanced generalized minimum variance self-tuning proportional, integral and derivative control algorithm for complex dynamic systems

A neural network enhanced proportional, integral and derivative (PID) controller is presented that combines the attributes of neural network learning with a generalized minimum-variance self-tuning control (STC) strategy. The neuro PID controller is structured with plant model identification and PID parameter tuning. The plants to be controlled are approximated by an equivalent model composed of a simple linear submodel to approximate plant dynamics around operating points, plus an error agent to accommodate the errors induced by linear submodel inaccuracy due to non-linearities and other complexities. A generalized recursive least-squares algorithm is used to identify the linear submodel, and a layered neural network is used to detect the error agent in which the weights are updated on the basis of the error between the plant output and the output from the linear submodel. The procedure for controller design is based on the equivalent model, and therefore the error agent is naturally functioned within the control law. In this way the controller can deal not only with a wide range of linear dynamic plants but also with those complex plants characterized by severe non-linearity, uncertainties and non-minimum phase behaviours. Two simulation studies are provided to demonstrate the effectiveness of the controller design procedure.

Neurofuzzy network model construction using Bézier-Bernstein polynomial functions

Neurofuzzy modelling systems combine fuzzy logic with quantitative artificial neural networks via a concept of fuzzification by using a fuzzy membership function usually based on B-splines and algebraic operators for inference, etc. The paper introduces a neurofuzzy model construction algorithm using Bezier-Bernstein polynomial functions as basis functions. The new network maintains most of the properties of the B-spline expansion based neurofuzzy system, such as the non-negativity of the basis functions, and unity of support but with the additional advantages of structural parsimony and Delaunay input space partitioning, avoiding the inherent computational problems of lattice networks. This new modelling network is based on the idea that an input vector can be mapped into barycentric co-ordinates with respect to a set of predetermined knots as vertices of a polygon (a set of tiled Delaunay triangles) over the input space. The network is expressed as the Bezier-Bernstein polynomial function of barycentric co-ordinates of the input vector. An inverse de Casteljau procedure using backpropagation is developed to obtain the input vector's barycentric co-ordinates that form the basis functions. Extension of the Bezier-Bernstein neurofuzzy algorithm to n-dimensional inputs is discussed followed by numerical examples to demonstrate the effectiveness of this new data based modelling approach.

An introduction to radial basis functions for system identification: a comparison with other neural network methods

A look is taken at the use of radial basis functions (RBFs), for nonlinear system identification. RBFs are firstly considered in detail themselves and are subsequently compared with a multi-layered perceptron (MLP), in terms of performance and usage.

Belowground biomass functions and expansion factors in high elevation Norway spruce

Biomass allocation to above- and belowground compartments in trees is thought to be affected by growth conditions. To assess the strength of such influences, we sampled six Norway spruce forest stands growing at higher altitudes. Within these stands, we randomly selected a total of 77 Norway spruce trees and measured volume and biomass of stem, above- and belowground stump and all roots over 0.5 cm diameter. A comparison of our observations with models parameterised for lower altitudes shows that models developed for specific conditions may be applicable to other locations. Using our observations, we developed biomass functions (BF) and biomass conversion and expansion factors (BCEF) linking belowground biomass to stem parameters. While both BF and BCEF are accurate in belowground biomass predictions, using BCEF appears more promising as such factors can be readily used with existing forest inventory data to obtain estimates of belowground biomass stock. As an example, we show how BF and BCEF developed for individual trees can be used to estimate belowground biomass at the stand level. In combination with existing aboveground models, our observations can be used to quantify total standing biomass of high altitude Norway spruce stands.

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

A simple and effective algorithm is introduced for the system identification of Wiener system based on the observational input/output data. The B-spline neural network is used to approximate the nonlinear static function in the Wiener system. We incorporate the Gauss-Newton algorithm 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 initialization scheme. The efficacy of the proposed approach is demonstrated using an illustrative example.

Asymptotic expansions for Taylor coefficients of the composition of two functions

We give an asymptotic expansion for the Taylor coe±cients of L(P(z)) where L(z) is analytic in the open unit disc whose Taylor coe±cients vary `smoothly' and P(z) is a probability generating function. We show how this result applies to a variety of problems, amongst them obtaining the asymptotics of Bernoulli transforms and weighted renewal sequences.