Inverse optimal nonlinear recurrent high order neural observer

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. >

In this paper, a new discrete time identification scheme for a singularly perturbed nonlinear system using recurrent high order multi-time scale neural network is presented. The high-order neural network (HONN) is known for its simple structure and powerful nonlinearity approximation property, which make it more suitable for modeling the singularly perturbed nonlinear systems than the multi-layer neural network [10]. An on-line identification scheme—optimal bounded ellipsoid (OBE) algorithm is developed for the recurrent high order neural network (RHONN) model. By adaptively changing the learning rate, the on-line identification scheme can achieve faster convergence compared to the other widely used learning schemes, such as backpropagation. Simulation results are presented to demonstrate the effectiveness of the proposed algorithm.

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 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.

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.

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.

Model Predictive Control is a well-suited control strategy; however, it needs to solve two main problems in order to be applied, first, it is necessary to have a suitable model of the plant to be controlled, in order to allow an adequate prediction, second, it is necessary to solve an optimization problem. These two problems not always can be solved particularly for nonlinear complex systems. Therefore, in this chapter we propose two variations for Model Predictive Control, in a first stage a recurrent high order neural network is proposed to obtain a fitting model for the plant to be controlled, and, at the same time this neural model identifies the system on-line through available measurements. Then, in a second stage, the optimization problem is solved using a particle swarm optimization algorithm. Using these two modifications, it is proposed a Neural Evolutionary Predictive Control for discrete-time nonlinear systems under disturbances under disturbances, and its effectiveness is shown in the experimental results by using data obtained from a linear induction motor prototype.

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

This work presents an alternative solution of the trajectory tracking problem for a two degrees of freedom (DOF) robot manipulator using a discrete-time decentralized control strategy. The local controller for each joint uses only local angular position and velocity measurements. A recurrent high order neural network (RHONN) structure is used to aproximate the manipulator dynamics, and based on this model, a discrete-time control law is computed, which combines block control and the sliding mode techniques. The neural network learning is performed on-line by Unscented Kalman filter (UKF) algorithm, a variation of nonlinear Kalman Filter.

This paper presents a solution of the trajectory tracking problem for robotic manipulators using a recurrent high order neural network (RHONN) structure to identify the robot arm dynamics, and based on this model a discrete-time control law is derived, which combines block control and the sliding mode techniques. The block control approach is used to design a nonlinear sliding surface such that the resulting sliding mode dynamics is described by a desired linear system. The neural network learning is performed on-line by Kalman filtering. The local controller for each joint uses only local angular position and velocity measurements. The applicability of the proposed control scheme is illustrated via simulations.

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.

Chapter 8 - Learning-Based Identification of Viral Infection Dynamics

This paper describes a neural inverse optimal control approach for a three-phase induction motor position trajectory and flux magnitude tracking. A recurrent high order neural network (RHONN) is used to identify the plant model, trained with an Extended Kalman Filter (EKF) algorithm; the control law minimize a cost functional avoiding to solve the Hamilton Jacobi Bellman (HBJ) equation. The applicability of the approach is illustrated via experimental results. The proposed scheme allows the easy integration of this kind of motors into a system of systems configuration.

The Sixth International Symposium on Neural Networks (ISNN 2009)