Identification of singularly perturbed nonlinear system using recurrent high-order neural network

An Artificial Neural Network (ANN) works by creating connections between different processing elements (artificial neurons). ANNs have been extensively used for Data Mining, which extracts hidden patterns and valuable information from large databases. This paper introduces a new adaptive Higher Order Neural Network (HONN) model and applies it in data mining tasks such as determining breast cancer recurrences and predicting incomes base on census data. An adaptive hyperbolic tangent function is used as the neuron activation function for the new adaptive HONN model. The paper compares the new HONN model against a Multi-Layer Perceptron (MLP) with the sigmoid activation function, an RBF Neural Network with the Gaussian activation function, and a Recurrent Neural Network (RNN) with the sigmoid activation function. Experimental results show that the new adaptive HONN model offers several advantages over conventional ANN models such as better generalisation capabilities as well as abilities in handling missing values in a dataset.

Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis. Artificial Neural Networks (ANN) have been widely used in applications such as bankruptcy prediction, predicting costs, forecasting revenue, forecasting share prices and exchange rates, processing documents and many more. This chapter introduces an Adaptive Higher Order Neural Network (HONN) model and applies the adaptive model in business applications such as simulating and forecasting share prices. This adaptive HONN model offers significant advantages over traditional Standard ANN models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors, due to their ability to better approximate complex, non-smooth, often discontinuous training data sets. The generalisation ability of this HONN model is explored and discussed.

The data in the real world are complex and varied. When we apply artificial neural networks to simulate the real-world commerce data through simple functions, accuracy could become problematic. To overcome this issue, we could choose Higher Order Neural Network (HONN) models, which can simulate a data set very accurately. This paper has developed a new open-box HONN model with fractional functions, called a Fractional High Frequency Cosine and Sine HONN (FHFCSHONN) model. FHFCSHONN structure and learning algorithm formulas are studied too. This paper also built a new software package called a FHFCSHONN simulator. Based on the commerce data testing results, the FHFCSHONN model's average error is 0.6980%, while the other three HONN model average errors are 4.0160%, 4.2370%, and 4.3556% respectively.

Business is a diversified field with general areas of specialisation such as accounting, taxation, stock market, and other financial analysis. Artificial Neural Networks (ANNs) have been widely used in ap- plications such as bankruptcy prediction, predicting costs, forecasting revenue, forecasting share prices and exchange rates, processing documents and many more. This chapter introduces an Adaptive Higher Order Neural Network (HONN) model and applies the adaptive model in business applications such as simulating and forecasting share prices. This adaptive HONN model offers significant advantages over traditional Standard ANN models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors, due to their ability to better approximate complex, non-smooth, often discontinuous training data sets. The generalisation ability of this HONN model is explored and discussed.

This paper introduces an adaptive Higher Order Neural Network (HONN) model and applies it in data mining such as simulating and forecasting government taxation revenues. The proposed adaptive HONN model offers significant advantages over conventional Artificial Neural Network (ANN) models such as much reduced network size, faster training, as well as much improved simulation and forecasting errors. The generalization ability of this HONN model is explored and discussed. A new approach for determining the best number of hidden neurons is also proposed.

The authors study the stability and convergence properties of recurrent high-order neural networks (RHONNs) as models of nonlinear dynamical systems. The overall structure of the RHONN consists of dynamical elements distributed throughout the network in the form of dynamical neurons, which are interconnected by high-order connections. It is shown that if a sufficiently large number of high-order connections between neurons is allowed, the RHONN model is capable of approximating the input-output behavior of general dynamical systems to any degree of accuracy. Based on the linear-in-the-weights property of the RHONN model, the authors have developed identification schemes and derived weight adaptive laws for adjustment of the weights. The convergence and stability properties of these weight adaptive laws have been analyzed. In the case of no modeling error, the state error between the system and the RHONN model converges to zero asymptotically. If modeling errors are present, the sigma -modification is proposed as a method of guaranteeing the stability of the overall scheme. The feasibility of applying these techniques has been demonstrated by considering the identification of a simple rigid robotic system. >

The Sixth International Symposium on Neural Networks (ISNN 2009)

The regulation of unknown nonlinear dynamical systems using an indirect adaptive control technique is considered in this paper. The proposed scheme uses the concept of Fuzzy Dynamical Systems (FDS) operating in conjunction with High Order Neural Network Functions (F-HONNFs). Since the plant is considered unknown, we first propose its approximation by a special form of a fuzzy dynamical system (FDS) and in the sequel the fuzzy rules are approximated by appropriate HONNFs. Thus the identification scheme leads up to a Recurrent High Order Neural Network, which however takes into account the fuzzy output partitions of the initial FDS. Once the system is identified around an operation point is regulated to zero adaptively. Weight updating laws for the involved HONNFs are provided, which guarantee that both the identification error and the system states reach zero exponentially fast, while keeping all signals in the closed loop bounded. The applicability of the method is tested on a DC Motor system where it is shown that by following the proposed procedure one can obtain asymptotic regulation.

An adaptive discrete-time tracking controller for a direct current (DC) motor with controlled excitation flux is presented. A high order neural network is used to identify the plant model; this network is trained with an extended Kalman filter. Then, the discrete-time block control and sliding mode techniques are used to develop the reference tracking control for the angular position of a DC motor with separate winding excitation. The scheme is illustrated via simulations.

A neural network composed of a finite number of continuous value output neurons is known to be able to simulate any deterministic Turing machine. Several simulation models have been proposed, but there remains the problem that a massive number of neurons is needed to simulate the tape part in real time. In this paper the authors demonstrate that a recurrent higher‐order neural network can simulate any Turing machine, then specify the lower limit for the number of neurons required and the time needed for the simulation. First, the authors show that a recurrent higher‐order neural network consisting of a limited number of neurons using a threshold input/output function and a linear input/output function can simulate any deterministic Turing machine in real time, and that the number of neurons required to simulate the tape can be reduced to six. Then the authors show that if a saw‐type function is used, the number of neurons required for the simulation can be reduced to four. A simplified simulation model is then offered as a viable framework for learning formal language using a neural network. © 2001 Scripta Technica, Syst Comp Jpn, 32(10): 42–50, 2001

This chapter develops a new nonlinear model, Ultra high frequency Trigonometric Higher Order Neural Networks (UTHONN), for time series data analysis. Results show that UTHONN models are 3 to 12% better than Equilibrium Real Exchange Rates (ERER) model, and 4 – 9% better than other Polynomial Higher Order Neural Network (PHONN) and Trigonometric Higher Order Neural Network (THONN) models. This study also uses UTHONN models to simulate foreign exchange rates and consumer price index with error approaching 0.0000%.

State Estimation by Artificial Neural Networks in a Continuous Bioreactor

SummaryThis work presents a neural observer‐based controller for uncertain nonlinear discrete‐time systems with unknown time‐delays. The proposed neural observer does not need previous knowledge of the model about the system under consideration, neither the value of its parameters, delays, nor their explicit estimations. The proposed neural observer is based on a neural network composed of two recurrent high order neural networks (RHONNs) for nonmeasurable state variables, one in a parallel configuration, and for measurable state variables one in a series‐parallel configuration. The neural network is trained on‐line with an extended Kalman filter algorithm. The proposed RHONN observer provides a mathematical model for the system. Based on such a resulting mathematical model, a control law is designed using discrete‐time sliding mode block control. Applicability is presented using real‐time results that show the performance of the proposal using a linear induction motor prototype as the selected system; this prototype is under the presence of varying time‐delays. A Lyapunov analysis is included to prove the semi‐globally uniformly ultimately boundedness (SGUUB) of the proposed RHONN observer‐controller scheme for uncertain nonlinear discrete‐time systems with unknown delays.

This paper presents a discrete-time direct current (DC) motor torque tracking controller, based on a recurrent high order neural network (RHONN) to identify the plant model. Using this model, a control law is derived, which combines block control and sliding modes techniques. The applicability of the scheme is illustrated via real time implementation for a DC motor with separate winding excitation.

Decentralized neural identification and control for uncertain nonlinear systems: Application to planar robot