A global optimization approach to fractional optimal control

In this paper, we consider a fractional optimal control problem governed by system of linear differential equations, where its cost function is expressed as the ratio of convex and concave functions. The problem is a hard nonconvex optimal control problem and application of Pontriyagin's principle does not always guarantee finding a global optimal control. Even this type of problems in a finite dimensional space is known as NP hard. This optimal control problem can, in principle, be solved by Dinkhelbach algorithm [10]. However, it leads to solving a sequence of hard D.C programming problems in its finite dimensional analogy. To overcome this difficulty, we introduce a reachable set for the linear system. In this way, the problem is reduced to a quasiconvex maximization problem in a finite dimensional space. Based on a global optimality condition, we propose an algorithm for solving this fractional optimal control problem and we show that the algorithm generates a sequence of local optimal controls with improved cost values. The proposed algorithm is then applied to several test problems, where the global optimal cost value is obtained for each case

Evaluating Pillar Industry's Transformation Capability: A Case Study of Two Chinese Steel-Based Cities.

Many steel-based cities in China were established between the 1950s and 1960s. After more than half a century of development and boom, these cities are starting to decline and industrial transformation is urgently needed. This paper focuses on evaluating the transformation capability of resource-based cities building an evaluation model. Using Text Mining and the Document Explorer technique as a way of extracting text features, the 200 most frequently used words are derived from 100 publications related to steel- and other resource-based cities. The Expert Evaluation Method (EEM) and Analytic Hierarchy Process (AHP) techniques are then applied to select 53 indicators, determine their weights and establish an index system for evaluating the transformation capability of the pillar industry of China's steel-based cities. Using real data and expert reviews, the improved Fuzzy Relation Matrix (FRM) method is applied to two case studies in China, namely Panzhihua and Daye, and the evaluation model is developed using Fuzzy Comprehensive Evaluation (FCE). The cities' abilities to carry out industrial transformation are evaluated with concerns expressed for the case of Daye. The findings have policy implications for the potential and required industrial transformation in the two selected cities and other resource-based towns