Recent large-scale power outages demonstrated the limitations of percolationand epidemic-based tools in modeling failures in power grids. Hence, we study the impact of line failures on the flow changes and cascade in the transmission system of the power grid by using a linearized power flow model. We use the pseudo-inverse of the power grid admittance matrix to obtain upper bounds on the flow c...

In the medical imaging field, discrete gradient transform (DGT) is widely used as a sparsifying operator to define the total variation (TV). Recently, TV minimization has become a hot topic in image reconstruction and is usually implemented using the steepest descent method (SDM). Since TV minimization with the SDM takes a long computational time, here we construct a pseudo-inverse of the DGT a...

We present in this work the performances of a mobile omnidirectional robot through evaluating its management of the redundancy of actuation. Thus we come to the predictive control implemented. The distribution of the wringer on the robot actions, through the inverse pseudo of Moore-Penrose, corresponds to a « geometric ›› distribution of efforts. We will show that the load on vehicle wheels wou...

The hierarchical control decomposition provided by inverse kinematics is seldom used in the field of Computer Animation. In this chapter we first review the properties and limitations of inverse kinematics compared to other techniques dedicated to the motion control of complex articulated figures. Then, beyond the sole pseudo-inverse solution, we examine the homogeneous solution allowing the pa...