When system identification methods are used to construct mathematical models of real systems, it is important to collect data that reveal useful information about the systems dynamics. Experimental data are always corrupted by noise and this causes uncertainty in the model estimate. Therefore, design of input signals that guarantee a certain model accuracy is an important issue in system identification.
This thesis studies input design problems for system identification where time domain constraints have to be considered. A finite Markov chain is used to model the input of the system. This allows to directly include input amplitude constraints into the input model, by properly choosing the state space of the Markov chain. The state space is defined so that the model generates a binary signal. The probability distribution of the Markov chain is shaped in order to minimize an objective function defined in the input design problem.
Two identification issues are considered in this thesis: parameter estimation and NMP zeros estimation of linear systems. Stochastic approximation is needed to minimize the objective function in the parameter estimation problem, while an adaptive algorithm is used to consistently estimate NMP zeros.
One of the main advantages of this approach is that the input signal can be easily generated by extracting samples from the designed optimal distribution. No spectral factorization techniques or realization algorithms are required to generate the input signal.
Numerical examples show how these models can improve system identification with respect to other input realization techniques.
2009. , 58 p.