Identification Of Time-varying Nonlinear Systems Research Articles

Identification of Time-Varying Non-Linear Systems for Brain Connectivity Analysis

Many control systems encountered in physical, automobile engineering, economic phenomena and biomedical engineering fields are nonlinear and nonstationary to some extent. In general, nonlinear processes can be adequately characterized by a nonlinear model. Recently, a system can be obtained directly from experimental input/ output data by determining the system structure and the numerical values of the unknown parameters, this process is known as system identification. System identification techniques for linear and nonlinear systems have received such attention and have been widely applied to reveal fundamental properties of the system which are not apparent. Billings [1] surveyed the available approaches of non-linear system identification by considering the functional series of Volterra and Wiener, and the identification algorithms developed by Ku and Wolf [2]. Narendra and Parthasarathy [3] considered the orthogonal expansion methods and the kernel identification algorithms. All these methods discussed above were considered numerous alternatives and related topics which have been developed over the last decade or so.

Identification of time-varying nonlinear systems using minimal radial basis function neural networks

An identification algorithm for time-varying nonlinear systems using a sequential learning scheme with a minimal radial basis function neural network (RBFNN) is presented. The learning algorithm combines the growth criterion of the resource allocating network of Platt with a pruning strategy based on the relative contribution of each hidden unit of the RBFNN to the overall network output. The performance of the algorithm is evaluated on the identification of nonlinear systems with both fixed and time-varying dynamics and also on a static function approximation problem. The nonlinear system with the fixed dynamics have been studied extensively earlier by Chen and Billings and the study with the time-varying dynamics reported is new. For the identification of fixed dynamics case, the resulting RBFNN is shown to be more compact and produces smaller output errors than the hybrid learning algorithm of Chen and Billings. In the case of time-varying dynamics, the algorithm is shown to adjust (add/drop) the hidden neurons of the RBFNN to ‘adaptively track’ the dynamics of the nonlinear system with a minimal RBF network.

Identification of time-varying nonlinear systems using Chebyshev polynomials

This paper is devoted to an identification of time-varying nonlinear systems using Chebyshev polynomials of the first kind. For systems being linear relatively unknown functional parameters, a method of approximate determination of these parameters has been worked out. As the identification problems are ill-posed to solve the obtained redefinite system of linear algebraic equations, a regularization method is used.