Input design using Markov chains for system identification

This paper studies the input design problem 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 in the input model by properly choosing the state space of the Markov chain, which is defined so that the Markov chain generates a multi-level sequence. The probability distribution of the Markov chain is shaped in order to minimize the cost function considered in the input design problem. Stochastic approximation is used to minimize that cost function. With this approach, the input signal to apply to the system can be easily generated by extracting samples from the optimal distribution. A numerical example shows how this method can improve estimation with respect to other input realization techniques.