Reformulating The Minimum Eigenvalue Maximization In Optimal Experiment Design Of Nonlinear Dynamic Biosystems

摘要

Experiments that yield as much information as possible are desired for estimating parameters in nonlinear dynamic bioprocesses. Techniques for optimal experiment design ensure the systematic design of such informative experiments. A possible objective function in optimal experiment design is the E-criterion which corresponds to the maximization of the smallest eigenvalue of the Fisher information matrix. However, a potential problem with the minimal eigenvalue function is that it can be nondifferentiable. In addition, a closed form expression does not exist for the computation of eigenvalues of a matrix larger than a 4 by 4 one. A reformulation strategy from the field of convex optimization is presented in this paper to circumvent the aforementioned difficulties. It requires the inclusion of a matrix inequality constraint involving positive semidefiniteness. The positive semidefiniteness constraint is imposed via Sylverster's criterion. By applying the suggested reformulation, the maximization of the minimum eigenvalue function can be implemented in standard optimal control solvers through the addition of nonlinear constraints.