Advancements in functional state estimation using sliding mode observers

This thesis explores the development of functional state estimation schemes using sliding mode observers. In many practical situations, the internal state of a system cannot be determined by direct measurement, and an observer may be use to estimate the unavailable states based on the measured outputs and control inputs. Existing work has shown that the functional observer (which estimates only a subset of the states) can be used to eliminate the redundancy possessed in full-state estimation, and also reduce computational burden. The sliding mode observer has been shown to have excellent performance in robust state estimation, and also has the extra ability of estimating the unknown input. Its use for functional state estimation is still very much in its infancy with no significant works being reported. This thesis combines the theories of functional state estimation and sliding mode observer to reduce the observer complexity as well as improve the overall performance of the observer. The first contribution of this thesis is the reformulation of the system such that the sliding mode observer can be implemented directly to achieve functional state estimation. The next contribution is the development of a two-observer scheme (which uses two observers in cascade) for functional state estimation and the investigation of its existence conditions, which were found to be weaker and more general than previous work. Following that, the work of cascading observers was extended to multiple sliding mode observers is explored, together with the investigation of its existence conditions in terms of the original system matrices; these conditions enable the user to know at the outset whether the observer scheme is applicable to their system or not, and also systematically calculates the number of observers necessary and sufficient. Following that, a new functional state estimation method is introduced, where the functional state is modeled as an unknown input, and then estimated using the ability of the sliding mode observer to estimate unknown inputs. Finally, the functional observer is implemented on the a class of descriptor systems, and the necessary and sufficient conditions are investigated. The efficiency of the functional observer schemes presented in this thesis are demonstrated by simulation examples.