Use of random search and genetic algorithms to optimize stochastic robustness functions

Stochastic Robustness Synthesis is a framework for designing practical compensators. It uses Monte Carlo simulation to evaluate the quality of control laws, and it searches a parameter space for the best law. Search methods must find the global minimum of a probabilistic design criterion function, ideally with minimum numbers of Monte Carlo evaluations. This paper examines two approaches to minimizing the probabilistic function: random search and a genetic algorithm. The genetic algorithm is similar to previously published algorithms but has several modifications to improve its performance, most notably a clustering analysis at the beginning of each generation. Statistical tools are incorporated into the search algorithms, allowing intelligent search decisions to be based on the 'noisy' Monte Carlo estimates. Performance of the two methods is demonstrated by application to a 24-dimensional test function. The genetic algorithm is shown to be significantly better than the random search for this application. The genetic algorithm is then used to design compensators for a benchmark problem and produces control laws with excellent levels of stability and performance robustness.