On the design of optimal input signals in system identification

The problem of designing optimal inputs in the identification of multi-input multi-output linear systems with unknown time varying parameters is considered using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop system inputs. The computation of the optimal closed-loop mappings is shown to be a nontrivial exercise in stochastic control with no analytic solution, but optimal open-loop and affine laws yield much more tractable problems. For time invariant systems, the sensitivity index considered is shown to be equivalent to the trace of the (strictly positive definite) Information Matrix associated with the system. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback, is also given.