A Hybrid Evolutionary-Algebraic Approach to Optimal and Robust Controller Design (Hybride evolutionär-algebraische Verfahren für den Entwurf optimaler und robuster Regler)

Abstract

Abstract Modern control techniques – such as H 2 or H ∞ optimal controller design – offer powerful synthesis tools, provided the controller has the same order as the plant, and there are no constraints on the information structure of the feedback loop (e. g. decentralized control). If these assumptions do not hold – as is often the case in practical applications – the synthesis problem becomes non-convex and hard to solve. A frequently encountered situation is however that a synthesis problem is intractable, whereas the corresponding analysis problem is convex and easy to solve. In this case, it is often more efficient to use the easily available analysis results to guide a stochastic search for the solution, rather than to address the hard synthesis problem directly. In this paper, such an approach – based on a combination of algebraic tools from optimal control theory and evolutionary search techniques – is presented. Four benchmark problems representing “hard” control problems are used to illustrate the approach and to compare its efficiency with that of previously published solutions.