a novel method to compute the stability region in power system transient stability analysis is presented. this method is based on the set analysis. the key to this method is to construct the hamilton-jacobi-isaacs (hji) partial differential equation (pde) of a nonlinear system, using which we can compute the backward reachable set by applying the level set methods. the backward reachable set of...

A novel method to compute the stability region in power system transient stability analysis is presented. This method is based on the set analysis. The key to this method is to construct the Hamilton-Jacobi-Isaacs (HJI) partial differential equation (PDE) of a nonlinear system, using which we can compute the backward reachable set by applying the level set methods. The backward reachable set of...

The problem of dexterous manipulation of objects, i.e. of arbitrary relocation and reorientation of rigid bodies by action of some mechanism, is considered. We build upon previous results on the possibility of implementing dexterous “robot hands” with few actuators, which can be afforded through the exploitation of nonholonomic rolling of regular surfaces. In this paper we focus on the manipula...

We investigate and analyze a computational method for the approximation of reachable sets for nonlinear dynamic systems. The method uses grids to cover the region of interest and the distance function to the reachable set evaluated at grid points. A convergence analysis is provided and shows the convergence of three different types of discrete set approximations to the reachable set. The distan...