Active identification of unknown systems: an information theoretic approach

The problem of identifying the value of a set of a priori unknown parameters of a discrete-time dynamic system is faced. To this end, a control law that minimizes the "information gain" about such parameters is required. The Shannon entropy is proposed (and justified) as a suitable information measure. After formulating the general statement of the problem, a viable approximation consisting in formulating a receding horizon problem is proposed. When the measurement channel is linear in the parameters, the optimal solution of the latter is given involving the minimization of a (finite dimensional) cost at each step.