Optimal Designs for Time—Dependent Responses

The purpose of this paper is to investigate methods for the design of optimal dynamic experiments. In Section 2, we introduce notation and a determinant criterion for dynamic experiments. In Section 3, optimal dynamic designs are constructed analytically in a number of simple cases. As will be seen, the dimension of the design problem increases with the dimension of the control vectors (equivalently, the response vector). In Section 4, we discuss the use of suitable parameterizations of the control variable trajectories to reduce the dimensionality of the optimization problem. The relationship between the design of optimal dynamic experiments and the results developed for marginally restricted designs is considered in Section 5. Numerical methods are discussed in Section 6. We close, in Section 7, with an extension of the methodology to the case where one or more linear combinations of the response trajectory is observed for each control trajectory.