"Loop-at-a-time" design of dynamic surface controllers for nonlinear systems

The use of multiple surface sliding controllers for robust control of systems with mismatched uncertainties has produced a number of impressive applications, but also raised a few nagging questions. Among the latter are the use of numerical differencing to obtain derivatives of desired trajectories, robustness to uncertainties in the gain terms and the common practice of filtering desired trajectories for implementation. We seek to address these issues through the concept of a dynamic surface controller (DSC), in which filters form an integral part of the structure. This filtering removes the need for numerical differencing and guarantees a certain smoothness, enabling other assumptions of smoothness to be relaxed. In this paper, the DSC is coupled with a sequential design procedure that carves a system workspace out of the state space. Within this bounded region, tracking performance can be rigorously guaranteed in the presence of uncertainty while constraints such as rate limits and saturation are systematically avoided.