The fixed-order and fixed structure controller design problems are difficult ones, because they often lead to a non-convex problem(s) which is difficult to solve. With exception to some specific controller structures or assumptions for the underlying plant to analytic solution exist for such problems. 

Under the name of "Metaheuristics", also known as "Modern heuristics", are grouped algorithms like simulated annealing, evolutionary algorithms, particle swarm optimization, etc. [Glover and Kochenberger (2003)], which are designed for attacking hard optimization problems, as the ones already mentioned. These algorithms have successful record of applications on variety of difficult problems and due to the randomized operators they used are believe to be able to avoid getting trapped in local optima and therefore being suitable for attacking global optimization problems.

However recent advances in the non-smooth function analysis and gradient based techniques provide algorithms that appear to successfully attack non-smooth and non-convex problems. Two algorithms for designing fixed structure H-infinity controllers ([Burke et al. (2006)] and [Apkarian and Noll (2006)]) are example for these methods. Although that they converge to a local comparison analysis show that they perform good in many cases.

The task of this project is to research the area of application of the various metaheuristic, gradient-based and non-smooth optimization methods and extend them (or make a "clever combination" of them) to other design problems, such as H-2, mu and LPV controller design. Furthermore, since according to the "No-free lunch theorem for Optimization" no "best" optimization technique exists, it is reasonable to assume that the choice of the algorithm should be made problem dependent. In the view of the above a tool supporting the design and decision-making process is also of an interest. 

Algorithms of interest include, but are not limited to: gradient-based and quasi-neuton methods, evolutionary algorithms, covariance matrix adaptation, genetic programming, differential evolution, greedy randomized adaptive search, particle swarm optimization, simulated annealing, gradient sampling.