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Generation of excitation signals with prescribed autocorrelation for input and output constrained systems

This paper considers the problem of realizing an input signal with a desired autocorrelation sequence satisfying both input and output constraints for the system it is to be applied to. This is a important problem in system identification. Firstly, the properties of the identified model are highly dependent on the used excitation signal during the experiment and secondly, on real processes, due to actuator saturation and safety considerations, it is important to constrain the inputs and outputs of the process. The proposed method is formulated as a nonlinear model predictive control problem. In general this corresponds to solving a non-convex optimization problem. Here we show how this can be solved in one particular case. For this special case convergence is established for generation of pseudo-white noise. The performance of the algorithm is successfully verified by simulations for a few different auto-correlation sequences, with and without input and output constraints.