Optimal design of periodic test input signals for multivariable impulse response models

This paper considers an optimal test input design problem occurring in a control-relevant, iterative system identification scheme. The optimization is based on minimizing the expected a posteriori closed-loop error based on the a priori information given by the data already collected. Instead of directly solving the resulting nonlinear optimization to obtain the test input sequences, two different computationally efficient approaches are proposed. The first approach is cast in the frequency domain and we solve for optimal discrete spectra of the periodic signals under some reasonable approximation. The solution can be realized as an input sequence by performing a spectral factorization and implementing the spectral factor as a digital Finite Impulse Response filter. A second approach is suggested by reformulating the optimal design problem as a linear matrix inequalities problem. The efficacy of these approaches is demonstrated through a numerical example.