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

Abstract

In applications of the L1 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 L1 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 L1 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 L1 adaptive control system in nonlinearity, providing the possibility for further theoretical development to improve the performance of adaptive control systems.