Adaptive identification and control of dynamical systems using neural networks

The goal of this paper is to introduce a new neural network architecture called Sigmoid Diagonal Recurrent Neural Network (SDRNN) to be used in the adaptive control of nonlinear dynamical systems. This is done by adding a sigmoid weight victor in the hidden layer neurons to adapt of the shape of the sigmoid function making their outputs not restricted to the sigmoid function output. Also, we introduce a dynamic back propagation learning algorithm to train the new proposed network parameters. The simulation results showed that the (SDRNN) is more efficient and accurate than the DRNN in both the identification and adaptive control of nonlinear dynamical systems.

In this paper, the use of radial basis function network (RBFN) for simultaneous online identification and indirect adaptive control of nonlinear dynamical systems is demonstrated. The motivation of using RBFN comes from the simplicity of its structure and simpler mathematical formulation, which gives it an advantage over multi-layer feed-forward neural network (MLFFNN). Since most processes are nonlinear, the use of conventional proportional-integral-derivative controller is not useful. Most of the time plant’s dynamics information is not available. This creates another limitation on the use of conventional control techniques, which works only if plant’s dynamics information is available. The proposed controller is tested for parameter variations and disturbance effects. Simulation results showed that RBFN is able to capture the unknown dynamics as well as simultaneously able to adaptively control the plant. It is also found to compensate the effects of parameter variations and disturbances. The comparative analysis is also done with MLFFNN in each simulation example, and it is found that performance of RBFN is better than that of MLFFNN.

A multilayer recurrent neural network-based approach for the identification and self-tuning adaptive control of multi-input multi-output nonlinear dynamical systems is developed. An efficient online implementation of the control strategy, by a fast updating of the control actions to track the dynamical variations in the system, is facilitated by the recurrent neural network, which is trained by a supervised training scheme that uses a simple updating rule. An application of this approach for the adaptive control of synchronous power generators under fault conditions is described, and a quantitative performance evaluation is given to bring out certain important characteristic features of the neural network used for control. >

This chapter presents a robust Adaptive Fuzzy Neural Controller (AFN C) suitable for identification and control of uncertain Multi-Input-Multi-Output (MIMO) nonlinear systems. The proposed controller has the following salient features: (1) Self-organizing fuzzy neural structure, i.e. fuzzy control rules can be generated or deleted automatically; (2) Online learning ability of uncertain MIMO nonlinear systems; (3) Fast learning speed; (4) Fast convergence of tracking errors; (5) Adaptive control, where structure and parameters of the AFNC can be self-adaptive in the presence of disturbances to maintain high control performance; (6) Robust control, where global stability of the system is established using the Lyapunov approach. Two simulation examples are used to demonstrate excellent performance of the proposed controller.

A method for identifying nonlinear dynamic systems with noise is proposed by using probabilistic universal learning networks (PrULNs). PrULNs are extensions of universal learning networks (ULNs). ULNs form a superset of neural networks and were proposed to provide a universal framework for modeling and control of nonlinear large-scale complex systems. But the ULN does not provide any stochastic characteristics of the signals propagating through it. The PrULNs are equipped with machinery to calculate stochastic properties of signals and to train network parameters so that the signals behave with the pre-specified stochastic properties. On the other hand it is generally recognized that there exists an overfitting problem when identification of nonlinear dynamic systems with noise is done by neural networks. In this paper, it is shown from simulation results of identification of a nonlinear robot dynamics that PrULNs are useful for avoiding the overfitting.

Teaching Aids for Modeling and Control of Hybrid Systems (CAMCHS)

Neural networks have been applied very successfully in the identification and control of nonlinear dynamic systems. The paper presents a design of neural network based control system for 2DOF nonlinear laboratory helicopter model (Humusoft CE 150). The main objective of this paper is to develop artificial neural networks to control helicopter's motors, or consequently elevation and azimuth angles. Neural networks are obtained by cloning various type of controllers designed in our previous papers. Those procedures included a cloning linear PID controller, gain scheduling controller and fuzzy controller.

This paper presents a discussion of the applicability of neural networks in the identification and control of dynamic systems. Emphasis is placed on the understanding of how the neural networks handle linear systems and how the new approach is related to conventional system identification and control methods. Extensions of the approach to nonlinear systems are then made. The paper explains the fundamental concepts of neural networks in their simplest terms. Among the topics discussed are feed forward and recurrent networks in relation to the standard state-space and observer models, linear and nonlinear auto-regressive models, linear, predictors, one-step ahead control, and model reference adaptive control for linear and nonlinear systems. Numerical examples are presented to illustrate the application of these important concepts.

This paper analyzes, theoretically and by computer simulation, the capabilities and limitations of neural networks to be used for the identification and optimal control of nonlinear dynamical systems. It is shown how neural networks can be efficiently trained to identify the forward and inverse dynamics of systems and also to work as optimal controllers which minimize some peformance measures of the system to be controlled. The performance of neural networks when applied to the optimal control of nonlinear vehicle suspensions is analyzed and compared with the performance of passive suspensions and that of active suspensions with linear (LQ) controllers designed by linearizing the nonlinear characteristics of the suspensions around the equilibrium point. It is found that nonlinear vehicle suspensions with neuro-control show better performance than suspensions controlled with conventional LQ regulators. Some issues about the implementation of neural networks to improve its convergence and generalization properties are analyzed.

The main objective of this special issue is to present readers with the significantly extended and improved versions of several high-quality articles presented at the Third International Conference on Natural Computation (ICNC’07). ICNC’07 was held jointly with The Fourth International Conference on Fuzzy Systems and Knowledge Discovery (FSKD’07) from August 24 to 27, 2007 in Haikou, Hainan, China. ICNC’07 featured the most upto-date research results in computational paradigms inspired from nature, including biological, ecological, linguistic, and physical systems. It is an exciting and emerging interdisciplinary area in which a wide range of techniques and methods are being studied for dealing with large, complex, and dynamic problems. It received 1752 submissions from 35 countries/regions. After rigorous reviews, 770 papers were published in the ICNC’07 proceedings. The acceptance rate for publication was 44%. Through a careful selection from the papers in the ICNC’07 proceedings published by IEEE Press, authors of 18 papers were invited to submit extended versions to this special issue. All authors except one submitted their version to Elsevier Editorial System for Neurocomputing. Each paper had gone though reviewing by at least three reviewers. Based on reviewers’ comments, authors made further revisions. We present 12 papers in this special issue. The first paper entitled ‘‘Behavioral task processing for cognitive robots using artificial emotions’’ authored by Evren Daglarli, Hakan Temeltas, and Murat Yesiloglu presents an artificial emotional-cognitive system-based autonomous robot control architecture. There are three levels, namely, behavioral system level, behavioral selection level, and emotion–motivation module, in its general control architecture. ‘‘Binary classification using ensemble neural networks and interval neutrosophic sets’’ by Pawalai Kraipeerapun and Chun Che Fung proposes two approaches for binary classification. The first one applies a single pair of neural networks while the second one uses an ensemble of pairs of neural networks for the binary classification. Interval neutrosophic sets are used in both methods in order to represent imperfection in the prediction. ‘‘Identification and control of nonlinear systems by a timedelay recurrent neural network’’ by Hongwei Ge, Wenli Du, Feng Qian, and Yanchun Liang introduces time-delay and recurrent mechanisms into a recurrent neural network. A dynamic recurrent back-propagation algorithm is developed for training the proposed neural network. Experiments show that the proposed network is very effective for identification and control for dynamic systems.

A procedure based on the use of artificial neural networks for the identification of nonlinear dynamic systems is developed and applied to the damped Duffing oscillator under deterministic excitation. The “generalization” ability of neural networks is invoked to predict the response of the same nonlinear oscillator under stochastic excitations of differing magnitude. The analogy between the neural network approach and a qualitatively similar nonparametric identification technique previously developed by the authors is illustrated. Some of the computational aspects of identification by neural networks, as well as their fault-tolerant nature, are discussed. It is shown that neural networks provide high-fidelity mathematical models of structure-unknown nonlinear systems encountered in the applied mechanics field.

This paper presents a self-adaptive recurrent neuro-fuzzy inference system (R-SANFIS) for dealing with dynamic problems. The proposed recurrent system possesses two salient features: 1) it incorporates fuzzy basis functions (FBFs) with dynamic elements for better approximation of nonlinear dynamic functions, and 2) it is capable of translating the complicated behaviors of dynamic systems into a set of simple linguistic "dynamic" rules and state-space equations as well. A systematic self-adaptive learning algorithm has been developed to construct the R-SANFIS with a parsimonious network structure and fast parameter learning convergence. Computer simulations and the performance comparisons with some existing recurrent networks on identification and control of nonlinear dynamic systems have been conducted to validate the effectiveness of the proposed R-SANFIS.

A new dynamical sliding mode control algorithm is proposed for robust adaptive learning in analog multilayer feedforward networks with a scalar output. These type neural structures are widely used for modeling, identification and control of nonlinear dynamical systems. The zero level set of the learning error variable is considered as a sliding surface in the space of network learning parameters. The convergence of the algorithm is established and conditions are given. Its effectiveness is shown when applied to on-line learning of nonmonotonic function using a two-layered feedforward neural network.KeywordsHide LayerFeedforward Neural NetworkSliding ModeScalar OutputLinear Activation FunctionThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This article presents a theoretical framework for the identification of nonlinear dynamic MISO systems with orthonormal base function models on fundamental basics of the Volterra theory. In the past the Volterra theory was used for the identification of nonlinear dynamic SISO systems (e.g. Hammerstein and Wiener models). In principle it is possible to extend these approaches to systems with more than one input (i.e. MISO systems). In former times this failed due to a lack of computational performance. In this paper an approach is presented which allows the identification of arbitrary coupled Hammerstein and Wiener models with multiple inputs. Some fundamental considerations for the identification of MISO systems based on arbitrary coupled Hammerstein models are made and extended to MISO systems based on arbitrary coupled Wiener models. This extended Volterra theory results in equations where the unknown parameters can be separated of the input values in a linear manner. In order to approximate the truncated impulse responses of the linear dynamic systems and to reduce the number of unknown parameters orthonormal base functions (OBFs) are introduced. As an example the proposed identification method is applied to a MISO system based on forward and backward coupled Hammerstein and Wiener models.

In this paper a simple adaptive controller is outlined that creates only temporal and situation-dependent system model. It may be a plausible alternative of the more sophisticated soft computing approaches that aim the identification of permanent and complete models. The temporal model can be built up and maintained step-by-step on the basis of slow elimination of fading information by the use of simple updating rules consisting of finite algebraic steps of lucid geometric interpretation. It may be used for filling in the “lookup tables” or rule bases of the more sophisticated representations experimentally. The method applies simple elimination of the the casual algebraic singularities the occurrence of which cannot be evaded in the practice. The operation of the method is illustrated by the control of a 2 Degrees Of Freedom dynamic system as a typical paradigm via simulation.