Data-Guided Regulator for Adaptive Nonlinear Control

A critical aspect of autonomous operations in safety-critical scenarios is learning from available data for quick adaptation to new environments while maintaining safety. Examples include aircraft emergency landing scenarios in adverse weather conditions and agile quadrotor flights through low clearance gates in the presence of dynamic and strong wind conditions [1]. From a system theoretic perspective, this system feature maps to having the autonomous agent handle parametric model uncertainties and disturbances with control-theoretic guarantees such as stability and tracking error convergence, common in adaptive control settings [2, 3]. A rich body of literature has analyzed classical adaptive control algorithms' stability and convergence properties for continuous-time dynamical systems. Such studies include the use of PI (proportional integral) controllers [4] for a class of linear time-varying systems to guarantee (I) infinite-time convergence of the tracking error to zero, i.e., the difference between actual and nominal states () = () (), for any constant exogenous disturbance (denoted by), (II) infinite-time convergence of the tracking error () to a bound which is proportional to the bound on the magnitude of the rate of the exogenous signal ().