This paper discusses a novel initialization algorithm for the estimation of nonlinear state-space models. Good initial values for the model parameters are obtained by identifying separately the linear dynamics and the nonlinear terms in the model. In particular, the nonlinear dynamic problem is transformed into an approximate static formulation, and simple regression methods are applied to obtain the solution in a fast and efficient way. The proposed method is validated by means of two measurement examples: the Wiener-Hammerstein benchmark problem and the identification of a crystal detector.
State-space models parametrized as feedforward NNs with one hidden layer and @math as activation function are presented in @cite_4 and @cite_10 . For these neural state-space models, prediction error learning algorithms are discussed. In particular, as an alternative to the Extended Kalman Filter, the Kalman gain is directly parametrized in order to obtain simpler expressions. In this way, the gradient of the cost function can be computed in a straightforward manner by following Narendra's sensitivity model approach. To deal with local minima problems two different heuristics are proposed: the initialization of nonlinear neural state-space models as linear state-space models, and learning complex models starting from less complex ones, by increasing the number of hidden neurons in the model.
@cite_10 @cite_4
1494912895 2004175622
Artificial neural networks possess several properties that make them particularly attractive for applications to modelling and control of complex non-linear systems. Among these properties are their universal approximation ability, their parallel network structure and the availability of on- and off-line learning methods for the interconnection weights. However, dynamic models that contain neural network architectures might be highly non-linear and difficult to analyse as a result. Artificial Neural Networks for Modelling and Control of Non-Linear Systems investigates the subject from a system theoretical point of view. However the mathematical theory that is required from the reader is limited to matrix calculus, basic analysis, differential equations and basic linear system theory. No preliminary knowledge of neural networks is explicitly required. The book presents both classical and novel network architectures and learning algorithms for modelling and control. Topics include non-linear system identification, neural optimal control, top-down model based neural control design and stability analysis of neural control systems. A major contribution of this book is to introduce NLq Theory as an extension towards modern control theory, in order to analyze and synthesize non-linear systems that contain linear together with static non-linear operators that satisfy a sector condition: neural state space control systems are an example. Moreover, it turns out that NLq Theory is unifying with respect to many problems arising in neural networks, systems and control. Examples show that complex non-linear systems can be modelled and controlled within NLq theory, including mastering chaos. The didactic flavor of this book makes it suitable for use as a text for a course on Neural Networks. In addition, researchers and designers will find many important new techniques, in particular NLq Theory, that have applications in control theory, system theory, circuit theory and Time Series Analysis. Prediction error learning algorithms for neural state space models are developed, both for the deterministic case and the stochastic case with measurement and process noise. For the stochastic case, a predictor with direct parametrization of the Kalman gain by a neural net architecture is proposed. Expressions for the gradients are derived by applying Narendra's sensitivity model approach. Finally a linear fractional transformation representation is given for neural state space models, which makes it possible to use these models, obtained from input output measurements on a plant, in a standard robust performance control scheme.