In this brief, we present a set of techniques for finding a cost function to the time-invariant linear quadratic regulator (LQR) problem in both continuous- and discrete-time cases. Our methodology is based on the solution to the inverse LQR problem, which can be stated as: does a given controller K describe the solution to a time-invariant LQR problem, and if so, what weights Q and R produce K as the optimal solution? Our motivation for investigating this problem is the analysis of motion goals in biological systems. We first describe an efficient linear matrix inequality (LMI) method for determining a solution to the general case of this inverse LQR problem when both the weighting matrices Q and R are unknown. Our first LMI-based formulation provides a unique solution when it is feasible. In addition, we propose a gradient-based, least-squares minimization method that can be applied to approximate a solution in cases when the LMIs are infeasible. This new method is very useful in practice since the estimated gain matrix K from the noisy experimental data could be perturbed by the estimation error, which may result in the infeasibility of the LMIs. We also provide an LMI minimization problem to find a good initial point for the minimization using the proposed gradient descent algorithm. We then provide a set of examples to illustrate how to apply our approaches to several different types of problems. An important result is the application of the technique to human subject posture control when seated on a moving robot. Results show that we can recover a cost function which may provide a useful insight on the human motor control goal.

Context: The evidence for the efficacy of osteopathic manipulative treatment (OMT) in the management of low back pain (LBP) is considered weak by systematic reviews, because it is generally based on low-quality studies. Consequently, there is a need for more randomized controlled trials (RCTs) with a low risk of bias. Objectives: The objective of this study is to evaluate the efficacy of an OMT intervention for reducing pain and disability in patients with chronic LBP. Methods: A single-blinded, crossover, RCT was conducted at a university-based health system. Participants were adults, 21–65 years old, with nonspecific LBP. Eligible participants (n=80) were randomized to two trial arms: an immediate OMT intervention group and a delayed OMT (waiting period) group. The intervention consisted of three to four OMT sessions over 4–6 weeks, after which the participants switched (crossed-over) groups. The primary clinical outcomes were average pain, current pain, Patient-Reported Outcomes Measurement Information System (PROMIS) 29 v1.0 pain interference and physical function, and modified Oswestry Disability Index (ODI). Secondary outcomes included the remaining PROMIS health domains and the Fear Avoidance Beliefs Questionnaire (FABQ). These measures were taken at baseline (T₀), after one OMT session (T₁), at the crossover point (T₂), and at the end of the trial (T₃). Due to the carryover effects of OMT intervention, only the outcomes obtained prior to T₂ were evaluated utilizing mixed-effects models and after adjusting for baseline values. Results: Totals of 35 and 36 participants with chronic LBP were available for the analysis at T₁ in the immediate OMT and waiting period groups, respectively, whereas 31 and 33 participants were available for the analysis at T₂ in the immediate OMT and waiting period groups, respectively. After one session of OMT (T₁), the analysis showed a significant reduction in the secondary outcomes of sleep disturbance and anxiety compared to the waiting period group. Following the entire intervention period (T₂), the immediate OMT group demonstrated a significantly better average pain outcome. The effect size was a 0.8 standard deviation (SD), rendering the reduction in pain clinically significant. Further, the improvement in anxiety remained statistically significant. No study-related serious adverse events (AEs) were reported. Conclusions: OMT intervention is safe and effective in reducing pain along with improving sleep and anxiety profiles in patients with chronic LBP.

Estimating many parameters of biomechanical systems with limited data may achieve good fit but may also increase 95% confidence intervals in parameter estimates. This results in poor identifiability in the estimation problem. Therefore, we propose a novel method to select sensitive biomechanical model parameters that should be estimated, while fixing the remaining parameters to values obtained from preliminary estimation. Our method relies on identifying the parameters to which the measurement output is most sensitive. The proposed method is based on the Fisher information matrix (FIM). It was compared against the nonlinear least absolute shrinkage and selection operator (LASSO) method to guide modelers on the pros and cons of our FIM method. We present an application identifying a biomechanical parametric model of a head position-tracking task for ten human subjects. Using measured data, our method (1) reduced model complexity by only requiring five out of twelve parameters to be estimated, (2) significantly reduced parameter 95% confidence intervals by up to 89% of the original confidence interval, (3) maintained goodness of fit measured by variance accounted for (VAF) at 82%, (4) reduced computation time, where our FIM method was 164 times faster than the LASSO method, and (5) selected similar sensitive parameters to the LASSO method, where three out of five selected sensitive parameters were shared by FIM and LASSO methods.

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 a seated balance device and associated experimental task for identification of the human seated 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 seated postural control parameters. To achieve this, we formulate the problem as a nonconvex QP and attempt to locally 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 nonincreasing of the cost function value while satisfying all constraints during iterations. Finally, we present successful experimental results using an optimized input sequence.