A General Framework for Switched and Variable Gain Higher Order Sliding Mode Control

Sliding mode control is a widely used approach in different application domains, due to its versatility and ease of implementation. As is well known, one of its most serious drawbacks is the presence of chattering. To alleviate this problem, higher order sliding mode (HOSM) approaches have been proposed, which also allow dealing with high relative degree plants. To gain more flexibility in the controller design and to boost performance, switched and variable-gain approaches are being developed for first and second-order sliding mode controllers. This article introduces a conceptual framework to merge the two aspects, providing a general methodology for the design and tuning of high-order sliding mode controllers. The main strength of the method is its generality, in that it accommodates a generic order $r$ sliding mode controller, and it encompasses both continuous and discrete variation of the controller parameters, the latter giving rise to switched strategies. The properties of the closed-loop system are formally analyzed, and the effectiveness of the method is demonstrated in simulation on examples of switched and variable gain HOSM controllers.