Recurrent High Order Neural Network Research Articles

Convergence for HRNNs with Unbounded Activation Functions and Time-varying Delays in the Leakage Terms

In this paper, the exponential convergence problems are considered for a class of high-order recurrent neural networks (HRNNs) with time-varying delays in the leakage terms. Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of this system converge exponentially to zero point by using Lyapunov functional method and differential inequality techniques. It is believed that these results are significant and useful for the design and applications of HRNNs. Even for the system without leakage delays, the criterion is shown to be different from a recent publication. Moreover, some examples are given to show the effectiveness of the proposed method and results.

Real-Time Decentralized Neural Control for a Five Dof Redundant Robot

This paper presents a discrete-time decentralized control scheme for trajectory tracking of a five degrees of freedom (DOF) redundant robot. A modified recurrent high order neural network (RHONN) structure is used to identify the plant model and based on this model, a discrete-time control law is derived, which combines block control and sliding mode technique. The neural network learning is performed on-line by Kalman filtering. The local controllers for each joint use only local angular position and velocity measurements. The proposed control scheme is implemented in real-time. The experimental results for trajectory tracking show the effectiveness of the proposed approach.

State Estimation by Artificial Neural Networks in a Continuous Bioreactor

A based neural networks state observer to estimate biomass, substrate and methane in a continuous anaerobic reactor is introduced in this paper. The observer is designed from a recurrent high order neural network with a hyperbolic tangent as activation function and an extended Kalman filter as learning algorithm. The observer structure is validated via simulations and using experimental data obtained from an anaerobic continuous stirred tank at lab scale. This prototype is used to treat real slaughterhouse wastewater and it is operated in continuous mode. The obtained results show that the proposed observer is able to reproduce adequately the biomethane production and the substrate (related to chemical oxygen demand) in the methanogenesis stage; besides, methanogenic bacteria are also well estimated but some modifications are required in order to reach better results.

Particle Swarm Based Approach of a Real-Time Discrete Neural Identifier for Linear Induction Motors

This paper focusses on a discrete-time neural identifier applied to a linear induction motor (LIM) model, whose model is assumed to be unknown. This neural identifier is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high-order neural network (RHONN) trained with a novel algorithm based on extended Kalman filter (EKF) and particle swarm optimization (PSO), using an online series-parallel con figuration. Real-time results are included in order to illustrate the applicability of the proposed scheme.

Exponential convergence for HRNNs with continuously distributed delays in the leakage terms

This paper considers exponential convergence for a class of high-order recurrent neural networks (HRNNs) with continuously distributed delays in the leakage terms (i.e., “leakage delays”). Without assuming the boundedness on the activation functions, some sufficient conditions are derived to ensure that all solutions of this system converge exponentially to zero point by using Lyapunov functional method and differential inequality techniques, which are new and complement previously known results. In particular, we propose a new approach to prove the exponential convergence of HRNNs with continuously distributed delays in the leakage terms. Moreover, an example is given to show the effectiveness of the proposed method and results.

Special issue on ‘new results on neuro‐fuzzy adaptive control systems’

Special issue on ‘new results on neuro‐fuzzy adaptive control systems’

Decentralized neural identifier and control for nonlinear systems based on extended Kalman filter

A time-varying learning algorithm for recurrent high order neural network in order to identify and control nonlinear systems which integrates the use of a statistical framework is proposed. The learning algorithm is based in the extended Kalman filter, where the associated state and measurement noises covariance matrices are composed by the coupled variance between the plant states. The formulation allows identification of interactions associate between plant state and the neural convergence. Furthermore, a sliding window-based method for dynamical modeling of nonstationary systems is presented to improve the neural identification in the proposed methodology. The efficiency and accuracy of the proposed method is assessed to a five degree of freedom (DOF) robot manipulator where based on the time-varying neural identifier model, the decentralized discrete-time block control and sliding mode techniques are used to design independent controllers and develop the trajectory tracking for each DOF.

Real-time torque control using discrete-time recurrent high-order neural networks

This paper presents a discrete-time direct current (DC) motor torque tracking controller, based on a recurrent high-order neural network to identify the plant model. In order to train the neural identifier, the extended Kalman filter (EKF) based training algorithm is used. The neural identifier is in series-parallel configuration that constitutes a well approximation method of the real plant by the neural identifier. Using the neural identifier structure that is in the nonlinear controllable form, the block control (BC) combined with sliding modes (SM) control techniques in discrete-time are applied. The BC technique is used to design a nonlinear sliding manifold such that the resulting sliding mode dynamics are described by a desired linear system. For the SM control technique, the equivalent control law is used in order to the plant output tracks a reference signal. For reducing the effect of unknown terms, it is proposed a specific desired dynamics for the sliding variables. The control problem is solved by the indirect approach, where an appropriate neural network (NN) identification model is selected; the NN parameters (synaptic weights) are adjusted according to a specific adaptive law (EKF), such that the response of the NN identifier approximates the response of the real plant for the same input. Then, based on the designed NN identifier a stabilizing or reference tracking controller is proposed (BC combined with SM). The proposed neural identifier and control applicability are illustrated by torque trajectory tracking for a DC motor with separate winding excitation via real-time implementation.

Avoiding singularities in recurrent neural control for induction motors

In this paper, a master–slave synchronization scheme based on parameter identification is proposed to overcome the controller singularity problem that appears when linearization-like techniques are applied in indirect adaptive neural control, like Neural Block Control (NBC). Such a synchronization strategy requires an identifier-like recurrent neural network and an adaptive law to update the neural weights. The proposed adaptive law prevents both, specific adaptive weights zero-crossing and the ‘parameter drift’ phenomenon. NBC consists of two tasks; synchronizing an identifier-like recurrent neural network (slave) with the plant (master) and controlling the system based on the slave model. The effectiveness of the synchronization law is tested using NBC for controlling the angular speed and magnetic flux magnitude of an induction motor. Usingit a priori knowledge about the real plant, a high-order recurrent neural network is proposed as the slave system. Based on the slave neural model, a discontinuous control law is derived, which combines Block Control and Sliding Modes. NBC with the proposed synchronization strategy is tested via simulations, comparing results with a standard parameters adaptive law. Copyright © 2011 John Wiley & Sons, Ltd.

Finding MAPs using strongly equivalent high order recurrent symmetric connectionist networks

Belief revision is the problem of finding the most plausible explanation for an observed set of evidences. It has many applications in various scientific domains like natural language understanding, medical diagnosis and computational biology. Bayesian Networks (BN) is an important probabilistic graphical formalism widely used for belief revision tasks. In BN, belief revision can be achieved by finding the maximum a posteriori (MAP) assignment. Finding MAP is an NP-Hard problem. In previous work, we showed how to find the MAP assignment in BN using High Order Recurrent Neural Networks (HORN) through an intermediate representation of Cost-Based Abduction. This method eliminates the need to explicitly construct the energy function in two steps, objective and constraints. This paper builds on that previous work by providing the theoretical foundation and proving that the resultant HORN used to find MAP is strongly equivalent to the original BN it tries to solve.

Real-Time Recurrent Neural State Estimation

A nonlinear discrete-time neural observer for discrete-time unknown nonlinear systems in presence of external disturbances and parameter uncertainties is presented. It is based on a discrete-time recurrent high-order neural network trained with an extended Kalman-filter based algorithm. This brief includes the stability proof based on the Lyapunov approach. The applicability of the proposed scheme is illustrated by real-time implementation for a three phase induction motor.

Recurrent High Order Neural Network Modeling for Wastewater Treatment Process

Due to the multi-variable, nonlinear, large time delay and strong coupling features of the wastewater treatment process, a recurrent high-order neural network is used to model the key water quality parameters(Chemical Oxygen Demand, Biological Oxygen Demand, Suspended Solid and Ammonia Nitrogen) for the wastewater treatment process, and the neural network is trained by an filtering algorithm. Operational data of a wastewater treatment plant is employed to illustrate the efficacy of the proposed modeling method. Meanwhile, the results are compared with feed-forward neural network and the general recurrent neural network to indicate the modeling accuracy of the recurrent high-order neural network.

Rollover Prediction and Control in Heavy Vehicles Via Recurrent High Order Neural Networks

Abstract In this paper, a predictor is developed in order to estimate roll angle and lateral acceleration for tractor-semitrailers. Based on this prediction, an active control system is designed to prevent rollover for these vehicles. In order to develop this control structure, a high order recurrent neural network is used to model the unknown tractor semitrailer system; a learning law is obtained using the Lyapunov methodology. Then a control law, which stabilizes the reference tracking error dynamics, is developed using Control Lyapunov Functions and the inverse optimal control approaches. Via simulations, the control scheme is applied to the speed-only and speed-yaw rate trajectory tracking in atractor-semitrailer during a cornering situation.

Direct adaptive regulation of unknownnonlinear systems with analysis of themodel order problem

A new method for the direct adaptive regulation of unknown nonlinear dynamical systems is proposed in this paper, paying special attention to the analysis of the model order problem. The method uses a neurofuzzy (NF) modeling of the unknown system, which combines fuzzy systems (FSs) with high order neural networks (HONNs). We propose the approximation of the unknown system by a special form of an NF-dynamical system (NFDS), which, however, may assume a smaller number of states than the original unknown model. The omission of states, referred to as a model order problem, is modeled by introducing a disturbance term in the approximating equations. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. An adaptive modification method, termed ‘parameter hopping’, is incorporated into the weight estimation algorithm so that the existence and boundedness of the control signal are always assured. The applicability and potency of the method are tested by simulations on well known benchmarks such as ‘DC motor’ and ‘Lorenz system’, where it is shown that it performs quite well under a reduced model order assumption. Moreover, the proposed NF approach is shown to outperform simple recurrent high order neural networks (RHONNs).

A NEW DIRECT ADAPTIVE REGULATOR WITH ROBUSTNESS ANALYSIS OF SYSTEMS IN BRUNOVSKY FORM

The direct adaptive regulation of unknown nonlinear dynamical systems in Brunovsky form with modeling error effects, is considered in this paper. Since the plant is considered unknown, we propose its approximation by a special form of a Brunovsky type neuro-fuzzy dynamical system (NFDS) assuming also the existence of disturbance expressed as modeling error terms depending on both input and system states plus a not-necessarily-known constant value. The development is combined with a sensitivity analysis of the closed loop and provides a comprehensive and rigorous analysis of the stability properties. The existence and boundness of the control signal is always assured by introducing a novel method of parameter hopping and incorporating it in weight updating laws. Simulations illustrate the potency of the method and its applicability is tested on well known benchmarks, as well as in a bioreactor application. It is shown that the proposed approach is superior to the case of simple recurrent high order neural networks (HONN's).

Discrete-time recurrent high order neural networks for nonlinear identification

This paper focuses on the problem of discrete-time nonlinear system identification via recurrent high order neural networks. It includes the respective stability analysis on the basis of the Lyapunov approach for the NN training algorithm. Applicability of the proposed scheme is illustrated via simulation for a discrete-time nonlinear model of an electric induction motor.

Exponential convergence for high-order recurrent neural networks with a class of general activation functions

In this paper, we consider high-order recurrent neural networks with a class of general activation functions. By using some mathematical analysis techniques, we establish new results to ensure that all solutions of the networks converge exponentially to zero point.

DISCRETE-TIME REDUCED ORDER NEURAL OBSERVERS FOR UNCERTAIN NONLINEAR SYSTEMS

This paper focusses on a novel discrete-time reduced order neural observer for nonlinear systems, which model is assumed to be unknown. This neural observer is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high order neural network (RHONN) trained with an extended Kalman filter (EKF)-based algorithm, using a parallel configuration. This work includes the stability proof of the estimation error on the basis of the Lyapunov approach; to illustrate the applicability, simulation results for a nonlinear oscillator are included.

A NEW NEURAL OBSERVER FOR AN ANAEROBIC BIOREACTOR

In this paper, a recurrent high order neural observer (RHONO) for anaerobic processes is proposed. The main objective is to estimate variables of methanogenesis: biomass, substrate and inorganic carbon in a completely stirred tank reactor (CSTR). The recurrent high order neural network (RHONN) structure is based on the hyperbolic tangent as activation function. The learning algorithm is based on an extended Kalman filter (EKF). The applicability of the proposed scheme is illustrated via simulation. A validation using real data from a lab scale process is included. Thus, this observer can be successfully implemented for control purposes.

Neurofuzzy Control Strategy for an Abattoir Wastewater Treatment Process

In this paper a neurofuzzy control strategy, composed by a neural observer and a fuzzy supervisor, for an anaerobic wastewater treatment process is proposed. The neural observer is based on a recurrent high order neural network (RHONN) which is trained by an extended Kalman filter. The main objective of the observer is to estimate methanogenic biomass, which is employed by a fuzzy supervisor. The tasks of this supervisor are: to detect the biological activity inside the bioreactor, to select and to apply an adequate control action depending on the operating conditions in order to avoid washout. The applicability of the proposed scheme is illustrated via simulations considering the model of a prototype bioreactor which is used to treat effluents collected from an abattoir.