Geometric Identification and Control of Nonlinear Dynamic Systems Based on Floating Basis Vector Representation

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 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 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.

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 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.

This paper presents a method for obtaining optimal stable control for general nonlinear nonautonomous dynamical systems. The approach is inspired by recent developments in analytical dynamics and the observation that the Lyapunov criterion for stability of dynamical systems can be recast as a constraint to be imposed on the system. A closed-form expression for control is obtained that minimizes a user-defined control cost at each instant of time and enforces the Lyapunov constraint simultaneously. The derivation of this expression closely mirrors the development of the fundamental equation of motion used in the study of constrained motion. For this control method to work, the positive definite functions used in the Lyapunov constraint should satisfy a consistency condition. A class of positive definite functions has been provided for mechanical systems that meet this criterion. To illustrate the broad scope of the method, for linear systems it is shown that a proper choice of these positive definite functions results in conventional LQR control. Control of the Lorenz system and a multi-degree of freedom nonlinear mechanical system are considered. Numerical examples demonstrating the efficacy and simplicity of the method are provided.

In recent years, multilayer neural networks and recurrent networks have emerged as important components for representing nonlinear transformations and have proved particularly successful in pattern recognition and optimization problems. The authors explore methods for incorporating such networks in adaptive systems for the identification and control of complex nonlinear dynamical systems. >

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

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 two simple adaptive controllers are outlined that create only temporal and situation-dependent system models. They may be plausible alternatives of the more sophisticated soft computing approaches that aim at the identification of permanent and complete models. In both cases the temporal models 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, but in quite different manners. Both methods apply simple elimination of the casual algebraic singularities the occurrence of which cannot be evaded in the practice. The operation of the methods is illustrated by the control of a 2-degrees-of-freedom dynamic system as a typical paradigm via simulation

Linear stabilization of the programmed motions of non-linear controlled dynamical systems under parametric perturbations

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.

The paper demonstrates that radial basis function network (RBFN) with adaptive centers and width can be used effectively for identification of nonlinear dynamic system. The proposed RBFN is trained by hybrid learning algorithm, which uses conjugate gradient optimization algorithm to obtain the center and width of each radial basis function and the least squares method to obtain the weights. To avoid capturing a local optimum, regularization error energy function is used and the centers of basis functions are initialized using a fuzzy C-means clustering method. Simulation results reveal that the identification schemes based on RBFN gives considerably better performance and show faster learning in comparison to previous methods

This paper is concerned with neural-learning control of nonlinear dynamical systems. Two control schemes using neural-learning techniques are introduced. One is adaptive neural control and the other is predictive neural control. An application of neural-learning control to an industrial combustion system is also included. (7 pages)