D-optimal input design for parameter estimation of linear and distributed parameter systems

thesis is concerned with the optimal input design problem for parameter estimation of linear, single input single output, discrete-time dynamic systems. Some aspects of experimental design for parameter estimation of distributed parameter systems are also studied. The experiment design problem is to choose the experimental conditions subject to constraints such that the information from an experiment is maximized in some sense. The optimality criterion employed in this thesis is the determinant of Fisher information matrix (D-optimality). The design of optimal inputs for parameter estimation of linear dynamic systems comprises the major contribution of this thesis. The open-loop input design is studies for systems subject to input and output power constraints. A method is given to obtain an optimal input design for an autoregressive model with output power constraints. It is shown that the optimal input frequencies can be obtained by solving a set of non-linear equations without recourse to optimization techniques involving the calculation of determinants. The problem of optimal input design for estimating part of the system parameters of a general model is investigated. Some results from D-optimal designs are extended for the D -optimal case. A comparison of minimal uniform input designs and a D-optimal design is also carried out, and the D-efficiency of minimal uniform input designs is illustrated by considering first order systems. The relationship between the experimental conditions and the achievable accuracy in parameter estimation for distributed parameter systems is also investigated. In distributed parameter systems, besides the boundary perturbations, another important design variable is available, namely, the spatial location of measurement sensors. A method to design optimal experiments for parameter estimation of a general distributed parameter system is proposed and illustrated by typical designs for a parabolic and a hyperbolic system.