ABSTRACT
Although it is not intended to provide a review of the developments in the field of nonlinear system parameter identification, a succinct description of the key developments that are particularly relevant to robot dynamics and control is essential. The field of system parameter identification has a fascinating history dating back to the period of Gauss, Euler, Chebyshev and two of his illustrious students, Aleksandr Lyapunov and Andrey Markov. A complete review of the developments in linear system parameter identification has been presented in the reviews by Kailath [1] and Harris [2]. The textbooks by Ljung [3] and Juang [4] provide an excellent introduction to the subject of linear system parameter identification. Serious research into nonlinear system identification began in the 1970s but has matured into an independent field characterized by a number of dedicated reviews (Ljung [5], Kerschen et al. [6], Hunter and Kornberg [7], Janczak [8]). A recent book by Nelles [9] on the subject summarizes the subject. Dynamic nonlinear system parameter identification is a model structure and/or model parameter estimation process essential to establish the system dynamics using measured input-output data. Nonlinear system parameter identification is a very important prerequisite for nonlinear controller design in most practical robotic and autonomous vehicle systems which are patently nonlinear. A good model structure representation facilitates the inclusion of an array of relevant system dynamics and provides for both the accuracy of modeling and compactness of structure. Therefore, obtaining an optimum fit for the measured data with just a few parameters is vital for the selection of model structure representation. Much of the literature has a range of non-parametric and parametric model representations for nonlinear system identification problems. Among the parametric model representations are included black box-type models, physical and semi-physical models, empirical models, block-oriented models, composite local models and hybrid and linear parameter varying models (LPV). The black box-type representations are particularly suitable for modeling neural networks using artificial neural net representations, wavelets and neuro-fuzzy logic representations. The universal approximation properties of neural networks provide a powerful basis for modeling several robot dynamic nonlinear systems. The block-oriented models are composed of dynamic linear blocks and static nonlinear blocks and possess the flexibility of selecting blocks to represent the features of a given unknown system. The choices of different linear and nonlinear blocks result in various structures. Two of the notable nonlinear models are the Hammerstein and Wiener models, consisting of a dynamic linear part cascaded with an input or output static nonlinear component, respectively. Discrete representations of component blocks almost invariably reduce to nonlinear autoregressive moving average models with exogenous inputs (NARMAX) or a subset of a NARMAX model. In the final step on the identification process, one resorts to some form of regression, linear or nonlinear or classification. Notable amongst the regression-like methods are blind signal identification, extended and adaptive Kalman filter-based approaches and approaches rooted in variational principles.
To introduce the concept of parameter identification, consider the problem of transfer function identification. Consider a single-input, single-output system with a transfer function given by
