Mixed H2/H∞ residual generator design via Heuristic Kalman Algorithm

Abstract

This paper presents a simple but effective synthesis strategy for observers based faults detection in linear time-invariant (LTI) systems which are simultaneously affected by two classes of unknown inputs: Noises having fixed spectral densities and unknown finite energy disturbances. The problem of designing such an observer, also called a residual generator, is formulated as a mixed H2/H∞ optimization problem. This is done to obtain an optimal residual generator, i.e. with minimal sensitivity to unknown inputs. Unfortunately, there is no known solution to this difficult optimization problem. Finding such a residual generator is known to be computationally intractable via the conventional techniques. This is mainly due to the non-convexity of the resulting optimization problem. To solve this kind of problem easily and directly, without using any complicated mathematical manipulations, we utilize the Heuristic Kalman Algorithm (HKA) for the resolution of the underlying constrained non-convex optimization problem. A numerical example is given to illustrate the advantage of the mixed H2/H∞ optimization approach against techniques based on optimization of H2 or H∞ criteria.