A variable structure controller for a class of uncertain systems with unknown uncertainty bounding function

In designing variable structure controllers when the upper bounding function for the matched system uncertainty is not known, the controller design remains to be a challenge. The main purpose of this paper is to solve this problem for a class of uncertain systems with matched uncertainties. To this end, a variable structure controller is proposed whose novelty lies in the form of the controller structure and also the mechanism introduced to update the controller\u27s gain. Unlike most existing variable structure controllers, the new design does not require the upper bounding function for the uncertainty to be exactly known (for the bounded uncertainty case, the knowledge of the upper bound is not needed). It is proved that asymptotic stability of closed-loop systems can be guaranteed globally. One drawback for this controller is that the controller gain may go unbounded if the noises or other system uncertainties are not considered and are present. The other drawback is the well known controller chattering problem. To deal with these drawbacks, we modify the controller\u27s gain update law and replace its discontinuous term with a continuous approximation, and hence propose a modified variable structure controller. With the modified variable structure controller, all the closed-loop signals are guaranteed to be bounded and the states can be driven to an arbitrarily small neighborhood of the origin. The price paid for this is the loss of asymptotic stability. Inspired by the equivalent control concept, a method for estimating the uncertainty is also derived when the modified variable structure controller is applied. Simulation examples are given to show the effectiveness of the controller and uncertainty estimation scheme. © 2006 IEEE