Towards the supervisory control of uncertain nonholonomic systems

Control systems with nonholonomic motion constraints have been extensively studied in the recent years, particularly in the context of robotics. Robotic manipulators, especially mobile ones, are described by complicated models about which there is likely to be significant uncertainty [4]. This is just one source of motivation for studying the challenging problem of controlling nonholonomic mechanical systems in the presence of modeling uncertainty. The status of this problem as of December 1995 is perhaps best expressed by the following quote from the survey article by Kolmanovsky and McClamroch [11]: “There are many important research problems for nonholonomic control systems that have been little studied. Here we identify the problem of control of nonholonomic systems when there are model uncertainties, as arise from parameter variations or from neglected dynamics. It is not necessary to motivate the importance of this problem, but it is curious that there is little published literature that deals directly with these questions”. In the last few years, however, several researchers have made a considerable amount of progress on this problem [3, 4, 9, 10, 17, 18]. One well known reason for the difficulties that arise in control of nonholonomic systems is the fact that they fail to meet Brockett’s necessary condition for smooth feedback stabilizability [2]. As a result, the development of adaptive stabilizing controllers for such systems becomes a challenging task. The goal of this paper is to demonstrate that a promising alternative to conventional adaptive control for nonholonomic systems is provided by the supervisory control techniques which have been developed for linear continuous-time systems in [13, 14], for linear discrete-time systems in [1, 12], and most recently for certain classes of nonlinear systems in [7, 8]. One of the advantages of supervisory control is that