Design of state observers with error limitation using cluster analysis

Abstract

The design of full-order state observers with error limitation can be performed by using set invariance concepts, together with the multiparametric programming technique, which presents, as solution, piecewise affine (PWA) output injection laws over polyhedral regions. However, this technique has some disadvantages when applied to multiple-output systems, such as complex calculations, high computational cost, and considerable memory requirements. In order to reduce the computational complexity of the offline solution in multiple-output systems, this paper shows how the K q-flat data cluster analysis algorithm can be used to establish a smaller number of polyhedral regions which are able to confine the estimation error in a constraints set. Optimization problems are also formulated in order to significantly reduce the number of regions, but resulting in sub-optimal observers. Finally, a comparison between the proposed approach and the multiparametric programming technique is presented through a numerical example which shows how the complexity of the set-invariant observers can be reduced by our technique.