Time-domain optimal experimental design in human postural control testing

We are developing a series of systems science-based clinical tools that will assist in modeling, diagnosing, and quantifying postural control deficits in human subjects. In line with this goal, we have designed and constructed an experimental device and associated experimental task for identification of the human postural control system. In this work, we present a Quadratic Programming (QP) technique for optimizing a time-domain experimental input signal for this device. The goal of this optimization is to maximize the information present in the experiment, and therefore its ability to produce accurate estimates of several desired postural control parameters. To achieve this, we formulate the problem as a non-convex QP and attempt to maximize a measure (T-optimality condition) of the experiment's Fisher Information Matrix (FIM) under several constraints. These constraints include limits on the input amplitude, physiological output magnitude, subject control amplitude, and input signal autocorrelation. Because the autocorrelation constraint takes the form of a Quadratic Constraint (QC), we replace it with a conservative linear relaxation about a nominal point, which is iteratively updated during the course of optimization. We show that this iterative descent algorithm generates a convergent suboptimal solution that guarantees monotonic non-increasing of the cost function while satisfying all constraints during iterations. Finally, we present example experimental results using an optimized input sequence.