No abstract

Extending the domain of attraction is an intresting topic in nonlinear system's survey. In this paper we focus on extending DA along a spesific direction which is denoted by fault running vector. Directional extension is presented by a nonlinear conditioanal optimization problem. As the proposed cost function includes the initial state, a proper choice of starting point which converges to global minimum is difficult. To overcome this problem we use Homotopy Optimization method(HOM). In this method the algorithm starts from minimizing a simple function with a well defined global minimum and during the next iterations the starting cost function is converges to the actual one by uniform variations of homotopy coefficiant. To avoid local minimums we use a combinational algorithm which contains SA and HOM in Homotopy Optimization with Perturbation and Ensembles (HOPE). The simulation results show the eficiency of HOPE method in solving optimization problem of directional enlargement of DA. Moreover, using this idea we effectively increase the critical clearing time of power systems.

One of the restrictions for uncertain biological systems is that there are uncertain parameters which are not measurable with non-invasive instrument. A problem of interest is that proposing a method which estimates this parameter from measurable outputs of system. By declining homotopy parameter the initial problem which has the form of a high gain observer gradually transforms to a parameter estimation problem. With the gradual transform to the main problem provide the ability of finding the global value of uncertain parameter. This approach is applied for the model of cancer to illustrate the effectiveness of the homotopy method to achieve the best estimate for uncertain parameters by finding the minimum of a proposed optimization problem.