Adaptive Control of Nonaffine Systems with Applications to Flight Control

Traditional flight control design is based on linearization of the equations of motion around a set of trim points and scheduling gains of linear (optimal) controllers around each of these points to meet performance specifications. For high angle of attack maneuvers and other aggressive flight regimes (required for fighter aircraft for example), the dynamic nonlinearities are dependent not only on the states of the system, but also on the control inputs. Hence, the conventional linearization-based logic cannot be straightforwardly extended to these flight regimes, and non-conventional approaches are required to extend the flight envelope beyond the one achievable by gain-scheduled controllers. Due to the nonlinear-in-control nature of the dynamical system in aggressive flight maneuvers, well-known dynamic inversion methods cannot be applied to determine the explicit form of the control law. Additionally, the aerodynamic uncertainties, typical for such regimes, are poorly modelled, and therefore there is a great need for adaptive control methods to compensate for dynamic instabilities. In this thesis, we present an adaptive control design method for both short-period and lateral/directional control of a fighter aircraft. The approach uses a specialized set of radial basis function approximators and Lyapunov-based adaptive laws to estimate the unknown nonlinearities. The adaptive controller is defined as a solution of fast dynamics, which verifies the assumptions of Tikhonov's theorem from singular perturbations theory. Simulations illustrate the theoretical findings.