The aim of this project is to research the possibilities for applying modern heuristic methods in the problems of low order and fixed structure controller designs.

Evolutionary algorithms, particle swarm optimization and simulated annealing are just some of the global optimization methods grouped under the term of metaheuristics [Glover and Kochenberger (2003)]. Such algorithms are designed for attacking hard optimization problems, which are often non-smooth, have non-convex feasible sets and multiple optima. In most cases, cannot be solved by local search methods, but are of high interest in many areas, as they often appear in practice.

In the area of control systems, such problems are the design of fixed order and low order controllers. Several recently developed techniques address the problem of designing low and fixed order H-infinity controllers [Burke et al. (2006)] and [Apkarian and Noll (2006)], but although they perform well on many problems they cannot escape the local character of the gradient based search they are based on, and converge to a local optimum.

The task of this project is to research the area of application of the various metaheuristic methods existing nowadays. According to the No free lunch theorem for optimization [Wolpert and Macready (1997)], no optimization algorithms performs on average better than random search, the applicability of each of the metaheuristics method will strongly depend on the extend to which it can be adapted to the problem considered. Therefore a part of this project will be concentrated on researching the possibilities and extending the available methods with operators, incorporating domain dependent knowledge.

Furthermore, since it is in general difficult for an engineer to know, given a problem which optimization method is the most suitable for it, an abstraction of the domain knowledge could be done, and a higher level heuristic algorithm let to perform this choice. Such approach is known as hyper-heuristics and has been already successfully applied in other domains [Glover and Kochenberger (2003)].

Algorithms of interest include, but are not limited to: evolutionary algorithms, covariance matrix analysis, genetic programming, greedy randomized adaptive search, memetic algorithms, particle swarm optimization, simulated annealing.

[Glover and Kochenberger (2003)] F. Glover and G. Kochenberger. Handbook in Metaheuristics. Kluwer's International Series on Operation Research. 2003

[Burke et al. (2006)] J. Burke, D. Henrion, A. Lewis, M. Overton. HIFOO - A Matlab package for fixed-order controller design and H-infinity optimization. IFAC Symposium on Robust Control Design . 2006

[Apkarian and Noll (2006)] P. Apkarian and D. Noll. Nonsmooth H-infinity Synthesis. IEEE Transactions on Automatic Control. 2006

[Wolpert and Macready (1997)] D. Wolpert and W. Macready. No Free Lunch Theorems for Optimization. IEEE Transactions on Evolutionary Computation. 1997

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