While the kip movements of expert gymnasts have been explained under the minimum torque-change criterion with assumption of a via-point, the meaning of the via-point has been unclear. On the other hand, expert gymnasts say that their movements are associated with effortless skill to achieve a task, in comparison with a movement without the via-point. We consider an integral of square of joint-torques as the effort cost, in addition to the commanded torque-change cost, and propose two approaches to reproduce the kip movement as follows: 1) a combined criterion that minimizes weighted sum of the torque-change and effort costs without assuming via-points, and 2) a hierarchical criterion that allocates via-points such that the effort cost of whole movement is minimized. The results of numerical analysis suggest that both the approaches can improve predictions of the kip movement compared with the results under the minimum torque-change model alone.
This paper proposes a new critical chain scheduling method in project management. The authors have already proposed a theoretical model, which provides an optimal total size of dummies to be inserted in the initial project schedule. Dummies, which are occasionally referred to as buffer, are useful to absorb schedule delays caused by a variety of uncertainties. Given the total size of dummies, this study explores for some useful rules under which we should allocate the dummies in the initial project schedule to generate buffered schedule. Some computational experiments derives several important properties of buffered schedules with a view to demonstrating the effectiveness of those rules particularly in critical chain scheduling.
In this paper, a numerical optimization method of static output feedback gain for the H∞ control problem is presented. This is a descent method that gives a monotonically nonincreasing sequence of the H∞ performance index starting from a stabilizing gain. A feasible direction is calculated using an inner point of a linear matrix inequality derived from the bilinear matrix inequality with respect to the feedback gain and the Lyapunov matrix. A stabilizing problem can be also treated similarly.