Accelerated quantitative feedback theory interval automatic loop shaping algorithm

Abstract

The quest for an efficient quantitative feedback theory (QFT) Automatic Loop Shaping algorithm is an open research problem. Different approaches have been adopted in the literature to efficiently solve this optimization problem, which is computationally hard due to its nonlinear and nonconvex nature. The first algorithms focused on different forms of simplification of the original problem, leading to faster but not accurate results. Stochastic algorithms have been another popular way of dealing with the complexity of this problem. These algorithms are faster than an exhaustive search, but do not guarantee, in general, the globally optimal solution. A third, more recent, approach, consists of using interval analysis global search algorithms, which are able to accurately solve the original problem, and are very suitable for execution speed optimization. In this work, one of these algorithms is taken as a basis to propose and develop an improved algorithm which is more efficient in terms of the execution time needed to solve a given problem. This improved efficiency is achieved by using two new information sources: Phase information and feasible boxes information. The main contribution of this work is to propose the use of these two new information sources to reduce execution time and to integrate this idea in the original algorithm. Their individual and joint associated speedups are measured by solving two classical QFT example problems: Matlab® QFT Toolbox example 2 and ACC ’90 benchmark problem. The results show that the new algorithm’s performance is significantly better.