The computer image processing is useful for identifying each particle from a picture of overlapping particles like particles of fine powder or droplets of atomized liquid. For this purpose we propose a new approach in which a binary image of overlapping particles is approximated in one of overlapping circles. This approach selects the best among a number of alternative patterns of overlapping circles, each of which is produced based on a combination of numbers of circles and their intersections. The validity and performance of this approach are examined through both a real picture and some computer simulation.
In this paper, optimization methods for hierarchical systems are dealt with. We consider a problem in which the upper level objective function includes the lower level optimal value function. First, we review several useful results in sensitivity analysis which are already obtained by many resarchers. Moreover we point out that information on sensitivity analysis for optimal value function (i.e. gradient, generalized gradient or directional derivative) depends on the uniqueness of the optimal solution and of the Lagrange multiplier vector. Next, under the uniqueness of optimal solution and Cottle constraint qualification, we consider a problem for finding the upper level descent direction. This problem is formulated as a quadratic programming problem. Therefore, we may apply a proper solution method to the problem to obtain the upper level descent direction. Finally, we construct an optimization algorithm for the two-level hierarchical system based on the above results.
We will focus on computational aspects of hierarchical overlapping coordination, the concept of which was first introduced in Haimes and Macko, and propose new coordination methodology in this paper. The overlapping coordination formulated mathematically by Macko and Haimes as the optimization methodology for large scale systems is a feasible decomposition method in the sense that every constraint is satisfied during the optimization process. Here, we will develop a new overlapping coordination method which uses a non-feasible decomposition method. The Kuhn-Tucker or Lagrange multipliers for the coupling constraints of different decompositions are used as the coordination variables. The coupling constraints may not be satisfied, untill the optimal solution is found. Numerical examples will be solved in order to show how the proposed method works and the results show that it is very promising. The proposed method keeping the attributes of overlapping coordination concepts can be applied effectively for many types of real large scale problems.
A new canonical form for descriptor system Ex=Ax+Bu, y=Cx+Du is presented. In this canonical form the structures concerning impulse controllability and impulse observability of the descriptor system are indicated. Therefor the presented canonical form is the natural extension to descriptor system from Kalman's canonical form for state equation.Io this paper the problem of eliminating impulsive modes by output feedback for descriptor system is also considered. By using the canonical form the necessary and suffcient condition is proposed.