Input Design in Worst-Case System Identification Using Binary Sensors

This technical note addresses system identification using binary-valued sensors in a worst-case set-membership setting. The main contribution is the solution of the optimal input design problem for identification of scalar gains, which is instrumental to the construction of suboptimal input signals for identification of FIR models of arbitrary order. Two different cost functions are considered for input design: the maximum parametric identification error and the relative uncertainty reduction with respect to the minimum achievable error. It is shown that in the latter case, the solution enjoys the property of being independent of the length of the identification experiment and as such it can be implemented as an optimal recursive procedure over a time interval of arbitrary length.