Robust static output feedback controller synthesis using Kharitonov’s theorem and evolutionary algorithms

This paper presents a simple but effective tuning strategy for robust static output feedback (SOF) controllers with minimal quadratic cost in the context of multiple parametric uncertainties. Finding this type of controller is known to be computationally intractable using conventional techniques. This is mainly due to the non-convexity of the resulting control problem, which has a fixed structure. To solve this kind of control problem easily and directly, without using any complicated mathematical manipulations, we utilize Kharitonov’s theorem and an evolutionary algorithm (EA) for the resolution of the underlying constrained optimization problem. Using Kharitonov’s theorem, a family of bounded, robustly stable static output feedback controllers can be defined and EA is used to select the controller that ensures a minimal quadratic cost within this family. The resulting tuning strategy is applicable to both stable and unstable systems, without any limitations on the order of the process to be controlled. A numerical study was conducted to demonstrate the validity of the proposed tuning procedure.