In this paper, 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. Additionally, 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.

The strength of surgical repairs of the vertical shear femoral neck fractures can be significantly augmented with the 2.7-mm locking plate. The construct with the cannulated screws was significantly stronger than the DHS construct.

Persons with acquired flatfoot deformity demonstrate impaired walking performance, as indicated by slower walking speed and frequent reports of foot pain during activity and at rest. 25,29 There is no doubt that acquired flatfoot deformity is accompanied by some level of tibialis posterior tendon dysfunction. The tibialis posterior functions to create a rigid foot segment by stabilizing the midfoot 37 and assists in generating energy, by the plantar flexors in terminal stance, to produce successful propulsion. 41 Laboratory studies confirm that persons with acquired flatfoot deformity demonstrate T T STUDY DESIGN: Controlled laboratory study using a cross-sectional design. T T OBJECTIVES:To characterize ankle and hip muscle performance in women with posterior tibial tendon dysfunction (PTTD) and compare them to matched controls. We hypothesized that ankle plantar flexor strength, and hip extensor and abductor strength and endurance, would be diminished in women with PTTD and this impairment would be on the side of dysfunction. T T BACKGROUND:Individuals with PTTD demonstrate impaired walking abilities. Walking gait is strongly dependent on the performance of calf and hip musculature. T T METHODS:Thirty-four middle-aged women (17 with PTTD) participated. Ankle plantar flexor strength was assessed with the single-leg heel raise test. Hip muscle performance, including strength and endurance, were dynamometrically measured. Differences between groups and sides were assessed with a mixed-model analysis of variance. T T RESULTS:Females with PTTD performed significantly fewer single-leg heel raises and repeated sagittal and frontal plane non-weight-bearing leg lifts, and also had lower hip extensor and abductor torques than age-matched controls. There were no differences between sides for hip strength and endurance measures for either group, but differences between sides in ankle strength measures were noted in both groups. T T CONCLUSION:Women with PTTD demonstrated decreased ankle and hip muscle performance bilaterally.

An intensive, progressive exercise program combined with education reduces disability and improves function in patients who have undergone a single-level lumbar microdiskectomy.