Overview

Dynamic systems abound in the real-life practical environment as biological, mechanical, electrical, civil, chemical, aerospace, road traffic and a variety of other systems. Understanding the dynamic behaviour of these systems is of primary interest to scientists as well as engineers. Mathematical modelling via parameter estimation is one of the ways that leads to deeper understanding of the system's characteristics. These parameters often describe the stability and control behaviour of the system. Estimation of these parameters from input-output data (signals) of the system is thus an important step in the analysis of the dynamic system.

Actually, analysis refers to the process of obtaining the system response to a specific input, given the knowledge of the model representing the system. Thus, in this process, the knowledge of the mathematical model and its parameters is of prime importance. The problem of parameter estimation belongs to the class of 'inverse problems' in which the knowledge of the dynamical system is derived from the input-output data of the system. This process is empirical in nature and often ill-posed because, in many instances, it is possible that some different model can be fitted to the same response. This opens up the issue of the uniqueness of the identified model and puts the onus of establishing the adequacy of the estimated model parameters on the analyst. Fortunately, several criteria are available for establishing the adequacy and validity of such estimated parameters and models. The problem of parameter estimation is based on minimisation of some criterion (of...