Bounding set calculation for neural network-based output feedback adaptive control systems

Evaluating the bounding set of dynamic systems subject to direct neural-adaptive control is a critical issue in applications where the control system must undergo a rigorous verification process in order to comply with certification standards. In this paper, the boundedness problem is addressed for a comprehensive class of uncertain dynamic systems. Several common but unnecessary approximations that are typically performed to simplify the Lyapunov analysis have been avoided in this effort. This leads to a more accurate and general formulation of the bounding set for the overall closed loop system. The conditions under which boundedness can be guaranteed are carefully analyzed; additionally, the interactions between the control design parameters, the ‘Strictly Positive Realness’ condition, and the shape and dimensions of the bounding set are discussed. Finally, an example is presented in which the bounding set is calculated for the neuro-adaptive control of an F/A-18 aircraft, along with a numerical study to evaluate the effect of several design parameters.