Optimal experiment design and system identification: Human testing applications

In this work, we demonstrate novel techniques for system identification and the optimization of experimental input sequences. The goal of these techniques is to extend traditional methods to the analysis of human motor control systems. We first demonstrate a Monte-Carlo technique for producing a robust optimal experimental input design for identification of the human head-neck target tracking system. In this technique, we use nonlinear least-squares fitting to match a nominal and noisy model of the head-neck tracking system. Using Monte-Carlo simulation in combination with a simultaneous min-max optimization technique, we find a parameterized experimental input that guarantees a lower bound of parameter estimation performance for any subject in some pre-defined population. We show that this technique produces better results for a worst-case subject than an experiment optimized for an average subject from within the same population. Next, we show the development of an inverse LQR technique for recovering underlying goals behind a given control design. In this technique, we use known system state matrices and a known full-state feedback gain matrix K. We then "invert" the LQR design procedure to find cost matrices Q and R that would generate K in the forward LQR problem. When this problem is feasible, we show a convex Linear Matrix Inequality (LMI) technique that will produce a unique solution. When the problem is infeasible, we demonstrate a method using a Ricatti equation gradient for finding a local optimal solution. We demonstrate this technique in the recovery of control goals for a single human subject, and show that it produces results that are consistent with explicit goals given to the subject. This technique is then extended using inverse LQG methods. In this formulation, we consider problems of the traditional controller-observer LQG form. From known system state matrices, known full-state feedback gain matrix K, and known observer gain L, we find noise covariance matrices W and V and control cost matrices Q and R. We demonstrate the usefulness of this technique in several simulation examples. Finally, we demonstrate a technique for performing time-domain optimal input design for experimental parameter estimation. In this technique, we consider each point in a discrete-time input signal to be a free variable, and locally maximize a measure of the experiment's Fischer Information Matrix. This optimization is subject to a number of constraints on input amplitude, output amplitude, human control effort, and a unique constraint on the signal's autocorrelation so as to minimize signal predictability. By recasting this quadratically-constrained quadratic program as a series of linearly constrained quadratic programs, we are able to solve the problem efficiently and produce a maximally informative input sequence. We demonstrate this technique experimentally and show that it reduces the variance of parameters estimated from the experimental response of a single human subject.