Nonlinear systems identification and control via dynamic multitime scales neural networks.

To identify online a quite general class of nonlinear systems, this paper proposes a new stable learning law of the dynamic multilayer neural networks (DMNN). A Lyapunov-like analysis is used to derive this stable learning procedure for the hidden layer as well as for the output layer. An algebraic Riccati equation is considered to construct a bound for the identification error. The suggested learning algorithm is similar to the well-known backpropagation rule of the static multilayer perceptrons but with an additional term which assure the property of global asymptotic stability for the identification error. Two numerical examples illustrate the effectiveness of the suggested new learning laws.

An adaptive identification method of simple dynamic recurr ent neural network (SRNN) for nonlinear dynamic systems is presented in this paper. This method based on the theory that by using the inner-states feed-back of dynamic network to describe the nonlinear kinetic characteris tics of system can reflect the dynamic ch aracteristics more directly, deduces the recursive prediction error (RPE) learning algorithm of SRNNe and improves the algorithm by studying topological structure on recursion layer without the weight values. The simulation results indicate that this kind of neural network can be used in real-time control, due to its less weight values, simpler learning algorithm, higher identification speed, and higher precision of model. It solves the problems of intricate in training algorithm and slow rate in convergence caused by the complicate topologi cal structure in usual dynami c recurrent neural network. Keywords: non-linear system, system identification, dynamic recurrent neural network, RPE algorithm

An increasing number of applications of dynamic neural networks has been developed for digital signal processing (DSP), dynamic neural networks are feedforward neural networks with commonly used scalar synapses replaced by linear filters. This provides feedforward neural networks with the capability of performing dynamic mappings, which depend on past input values, dynamic neural networks are suitable for time series prediction, nonlinear system identification, and signal processing applications. Their most popular types are Finite Impulse Response (FIR) neural networks, which are obtained by replacing synapses with finite impulse response filters. Due to their guaranteed stability characteristic and easy to minimize error surface they have been used with great success in many applications such as signal enhancement, noise cancellation, classification of input patterns, system identification, prediction, and control.. Most of the works on system identification using neural networks are based on multilayer feedforward neural networks with backpropagation learning or more efficient variations of this algorithm, an elegant method for training layered networks. This paper is based on work in a Dynamic System Modeling (DYSMO) and as an application for speed control of DC motor drive.

Magnetic levitation system is a typical nonlinear and instable system. Based on the complexity and inaccuracy of modelling, in this paper identified magnetic levitation system using the speciality that neural network(NN) can approach any nonlinear function. A Radial Basis Function neural network (RBFNN) controller is designed based on the neural network adaptive control principle. This paper proposes a control method which combine neural network adaptive control method and state feedback control method based on RBFNN. A simulation of the system is proposed, and the result shows that RBFNN could approach magnetic levitation system very well, neural network adaptive state feedback controller has a good effect on this nonlinear system; this control system has a preferable stability and control property.

The Sixth International Symposium on Neural Networks (ISNN 2009)

The identification of nonlinear systems with artificial neural networks models has been successfully used in many applications. Most processes in industry are characterized by nonlinear and time-varying behavior. In this context, the identification of mathematical models for nonlinear systems is vital in many fields of engineering. The Radial Basis Function Neural Network (RBF-NN) is a powerful approach for nonlinear identification and can be improved using Particle Swarm Optimization (PSO) approaches. This paper presents a multivariable nonlinear system identification using RBF-NN combined with standard PSO and Constriction Factor PSO (CFPSO) approaches in order to determine the RBF-NN parameters. RBF-NN is considered to be a good choice for black-box modeling problems due to its rapid learning capacity and, therefore, has been applied successfully to nonlinear time series modeling and nonlinear identification. On the other hand, PSO was inspired by the choreography of bird flocks and fish schools and can be seen as a distributed behavior algorithm that performs multidimensional search. Furthermore, promising simulation results from performance analysis of the proposed RBF-NN with PSO training approaches are presented and discussed in this paper showing promising results.

The article is devoted to the problem of optimization of search request ranking algorithms in the digital information retrieval system. The algorithm of functioning of the neural network ranking unit based on Hopfield neural network is built. The ability to generate a ranked list of pages found as a result of the request in the digital information retrieval system can be provided by solving two problems of integer optimization: the problem of assignment of combinatorial sets of criteria for assessing the relevance of web page search and the problem of sorting of numbers—relevance values. The architecture of the neural network model based on the dynamic Hopfield neural network with binary output function designed for combinatorial optimization of the final list of documents found in the digital information retrieval system was synthesized. Promising variants of neural network models with binary output function of neurons for synthesis of the optimal evaluation plan with a combinatorial set of criteria by solving the problem of assignment were built. It has been proven that the built models differ in the rules for determining the coefficients of synaptic connections and external shifts; each of the created rules can be used independently or in different combinations with one another. In the course of analytical research, it was found that the optimization formulation of the problem of sorting of relevance values of search pages is identical to the problem of assignment of combinatorial groups of evaluation criteria provided that the elements of the performance matrix of the latter are defined as linear combinations of relevance values.

Nonlinear identification via connected neural networks for unsteady aerodynamic analysis

This paper presents an online modeling and control strategy for a class of linearizable nonlinear systems with unknown parameters and nonlinearities. A dynamic neural network (DNN) is utilized for modeling of nonlinear systems in their equivalent feedback linearized form. Lyapunov techniques are used to derive the adaptation rules for training the DNN's weight matrices. An adaptive state feedback stabilizing control is developed based on the equivalent DNN model of the systems. An observer is also designed to estimate the states of the DNN model of the system. Subsequently, an adaptive output feedback stabilizing control law is derived for unknown nonlinear systems, using their equivalent DNN model, with guaranteed closed-loop stability. Simulation results show the effectiveness of the proposed technique.

Discrete-time neural network output feedback control of nonlinear discrete-time systems in non-strict form

One of the difficulties encountered in the application of reinforcement learning methods to real-world problem is the generalization of large-scale or continuous state space. In order to solve the curse of dimensionality problem caused by discretizing continuous state space, a kind of Q-learning method for continuous state space based on a dynamic Elman neural network was proposed in this paper. The inputs and the output of Elman network are the system state-action pair and the corresponding Q-value. That is, Elman network is used to estimate the Q-value of state-action pair on-line. Eligibility trace for connecting weights is introduced by borrowing ideas from the eligibility trace mechanism of state in temporal difference algorithm to improve the learning speed of neural network. Computer simulations on mountain car control illustrate the performance and applicability of the proposed Q-learning scheme.

In this paper, a novel approximate optimal distributed controller for a class of uncertain nonlinear interconnected system with event-sampled state vector is presented by using approximate dynamic programming (ADP). The event-sampled function approximation property of the neural network (NN) is utilized to generate a solution to the Hamilton-Jacobi-Bellman (HJB) equation and subsequently to obtain an optimal control policy of each subsystem in a forward-in-time manner. To relax the accurate knowledge of subsystem and interconnection dynamics, and input gain matrix, a novel NN identifier with event sampled state vector is designed at each subsystem. An adaptive event sampling condition and novel weight tuning rules for the NN identifier and NN controller using the Lyapunov stability theory are derived. To attain optimality faster, an iterative learning scheme is embedded within the inter-event part of the sampling interval along with time-driven learning at the event sampled instants. Further, the benefit of incorporating exploration in this event sampled framework to improve optimality is discussed along with the challenges involved. The state vector of the interconnected system and the weight estimation errors of the NN identifier and controller are demonstrated to be locally uniformly ultimately bounded (UUB). Finally, the analytical design is verified via simulation.

A novel method for optimal trajectory tracking of uncertain nonlinear systems by using adaptive dynamic programming (ADP)-based integral reinforcement learning (IRL) and neural networks (NNs) is proposed. The method utilises an actor-critic framework with optimal backstepping to minimise a discounted value function and uses a single-layer NN identifier for estimating the unknown dynamics. For safety assurance, a time-varying barrier Lyapunov function (TVBLF) is used in the control design to handle the constraints. A novel weight-tuning law by using the control input error, integral Bellman error, and the NN identifier is used for the actor-critic framework. A novel lifelong learning (LL)-based method for critic NN is utilised in an optimal framework by incorporating the Bellman error to mitigate catastrophic forgetting in multitasking scenarios. Stability analysis using Lyapunov stability theory is obtained for the overall closed-loop system. Simulations of leader-follower mobile robot formation control show a 25% reduction in the cost in multitasking scenarios.

Intelligent Multivariable Modeling of Blast Furnace Molten Iron Quality Based on Dynamic AGA-ANN and PCA

The efficacy of the multimodel framework (MMF) in modeling and identification of complex, nonlinear, and uncertain systems has been widely recognized in the literature owing to its simplicity, transparency, and mathematical tractability, allowing the use of well-known modeling analysis and control design techniques. The approach proved to be effective in addressing some of the shortcomings of other modeling techniques such as those based on a single nonlinear autoregressive network with exogenous inputs model or neural networks. A great number of researchers have contributed to this active field. Due to the significant amount of contributions and the lack of a recent survey, the review of recent developments in this field is vital. In this two-part paper, we attempt to provide a comprehensive coverage of the multimodel approach for modeling and identification of complex systems. The study contains a classification of different methods, the challenges encountered, as well as recent applications of MMF in various fields. Part 1 of this paper presents an overview of MMF for modeling and identification of nonlinear systems as well as the review of recent developments in the partitioning strategies employed.