D-optimal input design for nonlinear FIR-type systems: A dispersion-based approach

Abstract

Optimal input design is an important step of the identification process in order to reduce the model variance. In this work a D-optimal input design method for finite-impulse-response-type nonlinear systems is presented. The optimization of the determinant of the Fisher information matrix is expressed as a convex optimization problem. This problem is then solved using a dispersion-based optimization scheme, which is easy to implement and converges monotonically to the optimal solution. Without constraints, the optimal design cannot be realized as a time sequence. By imposing that the design should lie in the subspace described by a symmetric and non-overlapping set, a realizable design is found. A graph-based method is used in order to find a time sequence that realizes this optimal constrained design. These methods are illustrated on a numerical example of which the results are thoroughly discussed. Additionally the computational speed of the algorithm is compared with the general convex optimizer cvx.

Optimal Estimation of Neural Recruitment Curves Using Fisher Information: Application to Transcranial Magnetic Stimulation

“…Instead, some real-valued FIM summary metric (optimality criterion) is maximized. A widely used criterion is D-optimality, which maximizes the determinant of FIM [44], [45]. Other criteria include E-and ED-optimality which maximize the FIM minimum eigenvalue and determinant expectation, respectively [46].…”

Quadrotor aircraft intelligent system identification experiment design

“…The information matrix elements contain the partial derivatives (sensitivities) of the dynamic response with respect to the model parameters. 21,22,3 The information matrix is defined based on the log likelihood function as shown in equation (9). 3,2,23 where E is the conditional expectation taken over all possible measurement realizations Y , p is the conditional probability of realizing a sequence of measurements, and λ is a vector model parameters.…”

“…Information content of an aircraft dynamic response (states and outputs) is embodied in a matrix called the information matrix, M. The information matrix elements contain the partial derivatives (sensitivities) of the dynamic response with respect to the model parameters. 21,22,3 The information matrix is defined based on the log likelihood function as shown in equation 9…”

On Optimal Test Signal Design and Parameter Identification Schemes for Dynamic Takagi-Sugeno Fuzzy Models Using the Fisher Information Matrix

“…This contribution addresses the details of using optimal model-based designs for dynamic nonlinear modelling like the necessity of a (high quality) initial simulation model (obtained using process model-free designs) to run the optimization. In many other works, the determinant is used as a measure for the FIM [27,28]. In this contribution, the impact of different measures is investigated.…”