Optimal Experiment Design For Dynamic System Identification

Dynamic System Identification: Experiment Design and Data Analysis

Dynamic System Identification: Experiment Design and Data Analysis

Optimal Experiment Design for Dynamic System Identification

This work is concerned with the problem of experiment design for the efficient identification of a linear single input, single output dynamic system from input-output data in the presence of disturbances. The experimenter is allowed to select certain factors under his control (input signal, output filter, sampling times), subject to suitable constraints, in order to maximise information from an experiment. A frequency domain approach to the test signal/sampling rate design problem is adopted and the cost criterion is chosen to be a suitable convex scalar function of the inverse Fisher information matrix. A geometrical approach to the design problem is developed for both continuous-time and discrete-time systems, based on the theory of Tchebycheff systems and their associated moment spaces. Conditions are derived for the existence of certain minimal representations of the optimal input spectrum, leading to a reduction in the dimension of the design optimization problem. In particular, for a restricted class of model structures, the optimal input spectrum contains the minimum number of frequencies consistent with a persistently exciting signal. A class of sequential design algorithms is proposed with proven global convergence to a D-optimal design. Comparison is made of the computational efficiency of a number of these algorithms.

Optimal Experiment Design for Dynamic System Identification