Concurrent learning adaptive control for systems with unknown sign of control effectiveness

Most Model Reference Adaptive Control methods assume that the sign of control effectiveness is known. These methods cannot be used in situations that require adaptation in presence of unknown sign of control effectiveness, such as when controls reverse on an flexible aircraft due to wing twist, or when actuator mappings are unknown. To handle such situations, a Concurrent Learning Model Reference Adaptive Control method is developed for linear uncertain dynamical systems where the sign of the control effectiveness, and parameters of the control allocation matrix, are unknown. The approach relies on simultaneous estimation of the control allocation matrix using online recorded and instantaneous data concurrently, while the system is being actively controlled using the online updated estimate. It is shown that the tracking error and weight error convergence depends on how accurate the estimates of the unknown parameters are. This is used to establish the necessity for purging the concurrent learning history stacks, and three algorithms for purging the history stack for eventual re-population are presented. It is shown that the system states will not grow unbounded even when the sign of the control effectiveness is unknown, and the control allocation matrix is being estimated online. Simulations validate the theoretical results.