Robust Adaptive Quadratic Programming and Safety Performance of Nonlinear Systems with Unstructured Uncertainties

This paper presents a robust optimal neuro-adaptive controller for nonlinear systems with unstructured uncertainties. This work is also the first step towards employing control barrier functions (CBFs) for such systems to create safety constraints in the presence of disturbances. The proposed controller consists of three parts: feedforward term, adaptive term, and optimal term. The unknown dynamics of the system are estimated by a joint neural network and concurrent learning adaptation mechanism (NNCL) to inform the adaptive term. The optimal term uses an online quadratic program (QP) formulated to generate the optimal signal while providing system stability via a control Lyapunov function (CLF). The CBFs and control bounds (CBs) constraints are incorporated into the QP structure to create safety conditions on the system and bound the control effort. A robust term robustifies the proposed controller to disturbances and uncancelled uncertainty. The end result is a QP-RCLBF-NNCL controller for which uniformly ultimately boundedness of all system signals is proven using Lyapunov synthesis. The proposed controller is validated on an inverted pendulum. Simulation results show that the controller achieves good tracking performance and model identification. Two safety tests are performed to show that the proposed controller is able to bound the control signal and velocity by their predefined values when a disturbance acts on the system.