Input Signal Generation for Constrained Multiple-Input Multple-Output Systems

We consider a recent method for generating an input signal with a desired auto correlation while satisfying both input and output constraints for the system it is to be applied to. This is an important problem in system identification, since the properties of the identified model depend on the used excitation signal while on real processes, due to actuator saturation and safety considerations, it is important to constraint the process inputs and outputs. Here, we extend an earlier method to work for longer input horizons and to the multiple-input multipleoutput case. This corresponds to solving a fourth order multivariate polynomial in each time step. Two different methods for solving this problem are considered: one based on convex relaxation and the other based on a cyclic algorithm. The performance of the algorithm is successfully verified by simulations and the effects of the input horizon length are discussed.