A Nonlinear Adaptive Autopilot for Unmanned Aerial Vehicles Based on the Extension of Regression Matrix

In applications of the L-1 adaptive flight control system, we found two limitations to be extended: (1) the system cannot meet the demands of engineering in terms of nonlinearity and adaptation in most flight scenarios; (2) the adaptive control law generates a transient response in the tracking error, hindering the system from reaching the steady-state error, and ultimately decreasing control accuracy. In response to these problems, an extended flight control system for L-1 adaptive theory is proposed and rigorously proved. This system involves considering the nonlinear function matrix of state variables, which serves as an extension of the regression matrix in the original L-1 adaptive control system, thus enhancing its nonlinear characteristics. The problem of calculating the adaptive laws, caused by the extended regression matrix, is solved by using the pseudo-inverse matrix. To eliminate the transient response, the state vector and its estimate are recorded and employed just like an integrator. Finally, the proposed system is verified on a high-subsonic flight subject to nonlinear uncertainties, with simulation results showing improved control accuracy and enhanced robustness. The proposed system resolves the limitations of the L-1 adaptive control system in nonlinearity, providing the possibility for further theoretical development to improve the performance of adaptive control systems.