Neural networks for identification of nonlinear systems under random piecewise polynomial disturbances

The problem of identification of a nonlinear dynamic system is considered. A two-layer neural network is used for the solution of the problem. Systems disturbed with unmeasurable noise are considered, although it is known that the disturbance is a random piecewise polynomial process. Absorption polynomials and nonquadratic loss functions are used to reduce the effect of this disturbance on the estimates of the optimal memory of the neural-network model.

Dynamic recurrent neural network for system identification and control

A dynamic recurrent neural network (DRNN) that can be viewed as a generalisation of the Hopfield neural network is proposed to identify and control a class of control affine systems. In this approach, the identified network is used in the context of the differential geometric control to synthesise a state feedback that cancels the nonlinear terms of the plant yielding a linear plant which can then be controlled using a standard PID controller.

Purification and functional characterisation of Rhinocerase, a novel serine protease from the venom of Bitis gabonica rhinoceros

Background: Serine proteases are a major component of viper venoms and are thought to disrupt several distinct elements of the blood coagulation system of envenomed victims. A detailed understanding of the functions of these enzymes is important both for acquiring a fuller understanding of the pathology of envenoming and because these venom proteins have shown potential in treating blood coagulation disorders. Methodology/Principal Findings: In this study a novel, highly abundant serine protease, which we have named rhinocerase, has been isolated and characterised from the venom of Bitis gabonica rhinoceros using liquid phase isoelectric focusing and gel filtration. Like many viper venom serine proteases, this enzyme is glycosylated; the estimated molecular mass of the native enzyme is approximately 36kDa, which reduces to 31kDa after deglycosylation. The partial amino acid sequence shows similarity to other viper venom serine proteases, but is clearly distinct from the sequence of the only other sequenced serine protease from Bitis gabonica. Other viper venom serine proteases have been shown to exert distinct biological effects, and our preliminary functional characterization of rhinocerase suggest it to be multifunctional. It is capable of degrading α and β chains of fibrinogen, dissolving plasma clots and of hydrolysing a kallikrein substrate. Conclusions/Significance: A novel multifunctional viper venom serine protease has been isolated and characterised. The activities of the enzyme are consistent with the known in vivo effects of Bitis gabonica envenoming, including bleeding disorders, clotting disorders and hypotension. This study will form the basis for future research to understand the mechanisms of serine protease action, and examine the potential for rhinocerase to be used clinically to reduce the risk of human haemostatic disorders such as heart attacks and strokes.

Neurofuzzy design and model construction of nonlinear dynamical processes from data

A common problem in many data based modelling algorithms such as associative memory networks is the problem of the curse of dimensionality. In this paper, a new two-stage neurofuzzy system design and construction algorithm (NeuDeC) for nonlinear dynamical processes is introduced to effectively tackle this problem. A new simple preprocessing method is initially derived and applied to reduce the rule base, followed by a fine model detection process based on the reduced rule set by using forward orthogonal least squares model structure detection. In both stages, new A-optimality experimental design-based criteria we used. In the preprocessing stage, a lower bound of the A-optimality design criterion is derived and applied as a subset selection metric, but in the later stage, the A-optimality design criterion is incorporated into a new composite cost function that minimises model prediction error as well as penalises the model parameter variance. The utilisation of NeuDeC leads to unbiased model parameters with low parameter variance and the additional benefit of a parsimonious model structure. Numerical examples are included to demonstrate the effectiveness of this new modelling approach for high dimensional inputs.

Dual-orthogonal radial basis function networks for nonlinear time series prediction

A new structure of Radial Basis Function (RBF) neural network called the Dual-orthogonal RBF Network (DRBF) is introduced for nonlinear time series prediction. The hidden nodes of a conventional RBF network compare the Euclidean distance between the network input vector and the centres, and the node responses are radially symmetrical. But in time series prediction where the system input vectors are lagged system outputs, which are usually highly correlated, the Euclidean distance measure may not be appropriate. The DRBF network modifies the distance metric by introducing a classification function which is based on the estimation data set. Training the DRBF networks consists of two stages. Learning the classification related basis functions and the important input nodes, followed by selecting the regressors and learning the weights of the hidden nodes. In both cases, a forward Orthogonal Least Squares (OLS) selection procedure is applied, initially to select the important input nodes and then to select the important centres. Simulation results of single-step and multi-step ahead predictions over a test data set are included to demonstrate the effectiveness of the new approach.

Applying the extended Kalman filter to systems described by nonlinear differential-algebraic equations

This paper describes a method for the state estimation of nonlinear systems described by a class of differential-algebraic equation models using the extended Kalman filter. The method involves the use of a time-varying linearisation of a semi-explicit index one differential-algebraic equation. The estimation technique consists of a simplified extended Kalman filter that is integrated with the differential-algebraic equation model. The paper describes a simulation study using a model of a batch chemical reactor. It also reports a study based on experimental data obtained from a mixing process, where the model of the system is solved using the sequential modular method and the estimation involves a bank of extended Kalman filters.

Model predictive control using dynamic integrated system optimisation and parameter estimation (DISOPE)

DISOPE is a technique for solving optimal control problems where there are differences in structure and parameter values between reality and the model employed in the computations. The model reality differences can also allow for deliberate simplification of model characteristics and performance indices in order to facilitate the solution of the optimal control problem. The technique was developed originally in continuous time and later extended to discrete time. The main property of the procedure is that by iterating on appropriately modified model based problems the correct optimal solution is achieved in spite of the model-reality differences. Algorithms have been developed in both continuous and discrete time for a general nonlinear optimal control problem with terminal weighting, bounded controls and terminal constraints. The aim of this paper is to show how the DISOPE technique can aid receding horizon optimal control computation in nonlinear model predictive control.

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.

Modelling and control of Hammerstein system using B-spline approximation and the inverse of De Boor algorithm

In this article a simple and effective controller design is introduced for the Hammerstein systems that are identified based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a B-spline neural network. The controller is composed by computing the inverse of the B-spline approximated nonlinear static function, and a linear pole assignment controller. The contribution of this article is the inverse of De Boor algorithm that computes the inverse efficiently. Mathematical analysis is provided to prove the convergence of the proposed algorithm. Numerical examples are utilised to demonstrate the efficacy of the proposed approach.

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.

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.

The system identification and control of Hammerstein system using non-uniform rational B-spline neural network and particle swarm optimization

In this paper a new system identification algorithm is introduced for Hammerstein systems based on observational input/output data. The nonlinear static function in the Hammerstein system is modelled using a non-uniform rational B-spline (NURB) neural network. The proposed system identification algorithm for this NURB network based Hammerstein system consists of two successive stages. First the shaping parameters in NURB network are estimated using a particle swarm optimization (PSO) procedure. Then the remaining parameters are estimated by the method of the singular value decomposition (SVD). Numerical examples including a model based controller are utilized to demonstrate the efficacy of the proposed approach. The controller consists of computing the inverse of the nonlinear static function approximated by NURB network, followed by a linear pole assignment controller.

Study of the nonlinear optical properties of a crosslinkable chromophore for use in guest host polymer films

A guest/host material system in which the guest molecule is a functionalized, optically nonlinear, chromophore is described. A verification of the crosslinking process, an assessment of the nonlinear properties of the chromophore, using Solvatochromic methods, and an investigation of the electric field induced molecular orientation using second-harmonic generation are included.

Exact design manifold control of a class of nonlinear singularly perturbed systems

The integral manifold approach captures from a geometric point of view the intrinsic two-time-scale behavior of singularly perturbed systems. An important class of nonlinear singularly perturbed systems considered in this note are fast actuator-type systems. For a class of fast actuator-type systems, which includes many physical systems, an explicit corrected composite control, the sum of a slow control and a fast control, is derived. This corrected control will steer the system exactly to a required design manifold.