Lyapunov Theory-Based Fusion Neural Networks for the Identification of Dynamic Nonlinear Systems

2019 ◽  
Vol 29 (09) ◽  
pp. 1950015 ◽  
Author(s):  
Spyridon Plakias ◽  
Yiannis S. Boutalis
Keyword(s):  
Nonlinear Systems ◽  
Additive Noise ◽  
Learning Algorithm ◽  
Neural System ◽  
Lyapunov Theory ◽  
Identification Process ◽  
Neural Architecture ◽  
Parameter Variations ◽  
Error System ◽  
Task Simulation

This paper introduces a novel fusion neural architecture and the use of a novel Lyapunov theory-based algorithm, for the online approximation of the dynamics of nonlinear systems. The proposed neural system, in combination with the proposed update rule of the neural weights, achieves fast convergence of the identification process, ensuring at the same time stability of the error system in the sense of Lyapunov theory. The fusion neural system combines the features that are extracted from two-independent neural streams, a feedforward and a diagonal recurrent one, satisfying different design criteria of the identification task. Simulation results for five cases reveal the approximation strength of both proposed fusion neural architecture and proposed learning algorithm. Also, additional experiments demonstrate the effectiveness in cases of parameter variations and additive noise.

Improved learning algorithm for two-layer neural networks for identification of nonlinear systems

2019 ◽  
Vol 329 ◽  
pp. 86-96 ◽  
Author(s):  
José A.R. Vargas ◽  
Witold Pedrycz ◽  
Elder M. Hemerly
Keyword(s):  
Neural Networks ◽  
Nonlinear Systems ◽  
Learning Algorithm ◽  
Improved Learning

An Optimization Procedure of Model’s Base Construction in Multimodel Representation of Complex Nonlinear Systems

2021 ◽  
Author(s):  
Bennasr Hichem ◽  
M’Sahli Faouzi
Keyword(s):  
Nonlinear Systems ◽  
Learning Algorithm ◽  
Batch Reactor ◽  
Optimization Procedure ◽  
Base Number ◽  
Deterministic Approach ◽  
Modeling Analysis ◽  
Complex Nonlinear Systems ◽  
Definition Of ◽  
And Control

The multimodel approach is a research subject developed for modeling, analysis and control of complex systems. This approach supposes the definition of a set of simple models forming a model’s library. The number of models and the contribution of their validities is the main issues to consider in the multimodel approach. In this chapter, a new theoretical technique has been developed for this purpose based on a combination of probabilistic approaches with different objective function. First, the number of model is constructed using neural network and fuzzy logic. Indeed, the number of models is determined using frequency-sensitive competitive learning algorithm (FSCL) and the operating clusters are identified using Fuzzy K- means algorithm. Second, the Models’ base number is reduced. Focusing on the use of both two type of validity calculation for each model and a stochastic SVD technique is used to evaluate their contribution and permits the reduction of the Models’ base number. The combination of FSCL algorithms, K-means and the SVD technique for the proposed concept is considered as a deterministic approach discussed in this chapter has the potential to be applied to complex nonlinear systems with dynamic rapid. The recommended approach is implemented, reviewed and compared to academic benchmark and semi-batch reactor, the results in Models’ base reduction is very important witch gives a good performance in modeling.

scholarly journals Robust Preview Control for a Class of Uncertain Discrete-Time Lipschitz Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Xiao Yu ◽  
Fucheng Liao ◽  
Jiamei Deng
Keyword(s):  
Nonlinear Systems ◽  
Discrete Time ◽  
Tracking Error ◽  
Reference Signal ◽  
Original System ◽  
Linear Matrix ◽  
Preview Control ◽  
Lipschitz Nonlinear Systems ◽  
Error System ◽  
Discrete Integrator

This paper considers the design of the robust preview controller for a class of uncertain discrete-time Lipschitz nonlinear systems. According to the preview control theory, an augmented error system including the tracking error and the known future information on the reference signal is constructed. To avoid static error, a discrete integrator is introduced. Using the linear matrix inequality (LMI) approach, a state feedback controller is developed to guarantee that the closed-loop system of the augmented error system is asymptotically stable with H∞ performance. Based on this, the robust preview tracking controller of the original system is obtained. Finally, two numerical examples are included to show the effectiveness of the proposed controller.

Modeling The Tower Of Hanoi Using Neural Network

1993 ◽  
pp. 47-56
Author(s):  
Mohamed Othman ◽  
Mohd. Hassan Selamat ◽  
Zaiton Muda ◽  
Lili Norliya Abdullah
Keyword(s):  
Neural Network ◽  
Knowledge Representation ◽  
Network Architecture ◽  
Learning Algorithm ◽  
Learning Rule ◽  
Neural System ◽  
Neural Systems ◽  
Tower Of Hanoi ◽  
Artificial Neural ◽  
The Given

This paper discusses the modeling of Tower of Hanoi using the concepts of neural network. The basis idea of backpropagation learning algorithm in Artificial Neural Systems is then described. While similar in some ways, Artificial Neural System learning deviates from tradition in its dependence on the modification of individual weights to bring about changes in a knowledge representation distributed across connection in a network. This unique form of learning is analyzed from two aspects: the selection of an appropriate network architecture for representing the problem, and the choice of a suitable learning rule capable qf reproducing the desired function within the given network. Key words: Tower of Hanoi; Backpropagation Algorithm; Knowledge Representation;

Diagonal recurrent neural network observer-based adaptive control for unknown nonlinear systems

2020 ◽  
Vol 42 (15) ◽  
pp. 2833-2856
Author(s):  
Ahmed Elkenawy ◽  
Ahmad M El-Nagar ◽  
Mohammad El-Bardini ◽  
Nabila M El-Rabaie
Keyword(s):  
Neural Network ◽  
Optimal Control ◽  
Adaptive Control ◽  
Nonlinear Systems ◽  
Recurrent Neural Network ◽  
Learning Algorithm ◽  
Lyapunov Stability Theory ◽  
Adaptive Dynamic Programming ◽  
External Disturbances ◽  
System States

This paper proposes an observer-based adaptive control for unknown nonlinear systems using an adaptive dynamic programming (ADP) algorithm. First, a diagonal recurrent neural network (DRNN) observer is proposed to estimate the unknown dynamics of the nonlinear system states. The proposed neural network offers a simpler structure with deeper memory and guarantees the faster convergence. Second, a neural controller is constructed via ADP method using the observed states to get the optimal control. The optimal control law is determined based on the new structure of the critic network, which is performed using the DRNN. The learning algorithm for the proposed DRNN observer-based adaptive control is developed based on the Lyapunov stability theory. Simulation results and hardware-in-the-loop results indicate the robustness of the proposed ADP to respond the system uncertainties and external disturbances compared with other existing schemes.

scholarly journals Influence of Time Delay in Signal Transmission on Synchronization between Two Coupled FitzHugh-Nagumo Neurons

2019 ◽  
Vol 9 (10) ◽  
pp. 2159 ◽  
Author(s):  
Bin Zhen ◽  
Zhenhua Li ◽  
Zigen Song
Keyword(s):  
Time Delay ◽  
Energy Method ◽  
Signal Transmission ◽  
Coupled System ◽  
Original System ◽  
Neural System ◽  
Periodic Part ◽  
Change Rate ◽  
Error System ◽  
Synchronization Problems

In this paper, the energy method is employed to analytically investigate the influence of time delay in signal transmission on synchronization between two coupled FitzHugh-Nagumo (FHN) neurons. Unlike pre-existing methods that deal with synchronization problems, our major idea is to consider the change rate of the energy of the synchronization error system, since the original system’s synchronization is equivalent to the disappearance of the energy of the error system. In rewriting the original coupled system in the corresponding energy coordinates based on the energy method, we find that the change rate of energy of the error system can be divided into two parts (periodic and non-periodic). The synchronization criterion for the original system can then be obtained by letting the non-periodic part of the change rate of the energy be less than zero. The correctness of the analysis is illustrated with numerical simulations. Our analytical results show that time delay in signal transmission has very significant effects on the synchronization between two FHN neurons. If the time delay in signal transmission is not taken into account in the two coupled FHN neurons, synchronous spikes cannot be achieved in the system for any given coupling strength. By adjusting the value of the time delay in signal transmission, the neural system can freely switch between neural rest and synchronous spikes. This means that time delay in signal transmission is crucial for the occurrence of synchronous spikes in the FHN neural system, which contributes to our understanding of the interaction between neurons. We analytically show the influence of the time delay on the synchronization between two FHN neurons, which was seldom considered by other researchers.

A NEW APPROACH OF THE 2-AXES PAM ROBOT ARM IDENTIFICATION USING NEURAL MIMO NARX MODEL

2013 ◽  
Vol 22 (01) ◽  
pp. 1250039
Author(s):  
HO PHAM HUY ANH ◽  
KYOUNG KWAN AHN
Keyword(s):  
Learning Algorithm ◽  
Back Propagation ◽  
Training Data ◽  
The Novel ◽  
Robot Arm ◽  
New Approach ◽  
Identification Process ◽  
Highly Nonlinear ◽  
Model Scheme ◽  
Narx Model

In this paper, a novel MIMO Neural NARX model is used for simultaneously modeling and identifying both joints of the 2-axes PAM robot arm's inverse and forward dynamic model. The highly nonlinear cross effect of both links of the 2-axes PAM robot arm are thoroughly modeled through an Inverse and Forward Neural MIMO NARX Model-based identification process using experimental input-output training data. Consequently the proposed Inverse and Forward Neural MIMO NARX model scheme of the nonlinear 2-axes PAM robot arm has been investigated. The results show that the novel Inverse and Forward Neural MIMO NARX Model trained by Back Propagation learning algorithm yields outstanding performance and perfect accuracy.

Biologically Modeled Noise Stabilizing Neurodynamics for Pattern Recognition

1998 ◽  
Vol 08 (02) ◽  
pp. 321-345 ◽  
Author(s):  
Hung-Jen Chang ◽  
Walter J. Freeman ◽  
Brian C. Burke
Keyword(s):  
Gaussian Noise ◽  
Olfactory System ◽  
Additive Noise ◽  
Neural System ◽  
External Input ◽  
State Transitions ◽  
Anterior Olfactory Nucleus ◽  
Significant Stimulus ◽  
Unpredictable Environments ◽  
Hybrid Dynamics

We present a distributed KIII model for the olfactory neural system. Low-level Gaussian noise is introduced to the receptors and anterior olfactory nucleus, which biologically models the peripheral and central sources of noise. The additive noise numerically makes the model stable and robust in respect to repeated input-induced state transitions, while improving the simulations of EEG potentials and multiunit activity from the olfactory system. This hybrid dynamics generates a 1/f aperiodic state, which provides an unpatterned basal state for every module to stay in while there is no significant stimulus. Any external input may guide the system to a certain patterned state. The mechanism is fast, fully parallel, under modulatory control, and flexible in absorbing new patterns from unpredictable environments.

Sign in / Sign up

Export Citation Format

Share Document