Adaptive Extremum Seeking Control Design

The paper focuses on an adaptive output-tracking problem using on-line extremum seeking command generation. Two interconnected dynamic uncertain subsystems are considered. Using direct adaptive neural network based control, both subsystems are forced to follow their corresponding trajectories. While the command for the first subsystem is predetermined, the command for the second subsystem is computed on-line such that the influence of the second subsystem on the first one is minimized, The problem is motivated by the need to design an autopilot for autonomous formation flight. The autopilot must perform in an aerodynamically uncertain environment. The control problem reflects two aircraft flying in a closed-coupled formation wherein the trailing aircraft must constantly seek an optimal relative position that minimizes the aerodynamic drag force induced by the wing vortices of the lead aircraft. Using feedforward neural networks and on-line extremum seeking command generation, the proposed control scheme provides bounded output tracking and minimizes the effect of uncertainty on the first subsystem's dynamics. Closed-loop system stability is shown using Lyapunov's direct method.