Input design in worst-case system identification with quantized measurements

This paper addresses the problem of set membership system identification with quantized measurements. Following the work developed for binary measurements, the problem of optimal input design with multiple sensor thresholds is tackled. For a FIR model of order n, the problem is decomposed into n static gain problems. The one-step optimal input problem is solved both for equispaced and generic sensor threshold distribution. Moreover, the N-step optimal input problem for the case of equispaced thresholds is addressed, and a solution is provided under a suitable assumption on the sensor range and resolution. The obtained results allow us to construct an upper bound on the time complexity of the FIR identification problem for the case of equispaced thresholds. Numerical application examples are reported to show the effectiveness of the proposed algorithms.