A Review of Smooth Variable Structure Filters: Recent Advances in Theory and Applications

Abstract

The smooth variable structure filter (SVSF) is a relatively new state and parameter estimation technique. Introduced in 2007, it is based on the sliding mode concept, and is formulated in a predictor-corrector fashion. The main advantages of the SVSF, over other estimation methods, are robustness to modeling errors and uncertainties, and its ability to detect system changes. Recent developments have looked at improving the SVSF from its original form. This review paper provides an overview of the SVSF, and summarizes the main advances in its theory.

A fuzzy-smooth variable structure filtering strategy: For state and parameter estimation

“…Since its introduction, the SVSF has been significantly developed and expanded [13][14][15][16]. The SVSF estimation process may be summarized by the following sets of equations [10].…”

“…The SVSF is based on sliding mode estimation and is formulated in a predictor-corrector fashion. The sliding mode strategy allows the estimation strategy to be very robust to modeling uncertainties and errors [10]. Since its introduction, the SVSF has been significantly developed and expanded [13][14][15][16].…”

“…Furthermore, the noise must be Gaussian and white. These conditions lead to a statistically optimal solution to a linear stochastic estimation problem [10]. The following equations, used recursively, make up the KF process.…”

“…The SVSF estimated trajectory is smoothed when the smoothing subspace encompasses the existence subspace [10]. In other words, the uncertainties are being suppressed in the estimation process.…”

Dynamic Model and Motion Control of a Robotic Manipulator

“…For instance, autonomous ground vehicles with robotic manipulators are used in bomb disarming, search and rescue, and reconnaissance. To conduct surgery or translate human movement with a robotic manipulator on military missions remotely, it is important to control the robotic manipulator in sync with the movement of the operator [5][6][7][8][9][10][11][12][13].…”