Tuning of A Random Search Algorithm for Controller Design.

Abstract

Fixed structure controllers display numerous local minima for quadratic performance measures and high dimensional plants. In fact, minimizing a quadratic function with nonlinear constraints is known to be an NP-hard problem. This implies a severe computational burden for higher dimensional problems. One class of multi -modal optimization approach that could overcome this problem is random search optimization. However, very little is known about how different parameters of such algorithms should be adjusted in order to achieve a desired convergence speed. This paper presents a systematic analysis of an Adaptive Random Search Algorithm similar to that of Pronzato. The analysis reveals the key parameters affecting convergence time and provides insight on ways to tune the algorithm for more rapid convergence. A new stopping criterion is also proposed that eliminates the need to estimate the optimum function value beforehand.