Various authors have investigated the applicability of nonlinear control methodologies to advanced flight vehicles. These methods offer both increases in aircraft performance as well as reduction of development times by dealing with the complete dynamics of the vehicle rather than local operating point designs (see Section 5.1.3). Feedback linearization, in its various forms, is perhaps the most commonly employed nonlinear control method in flight control [14, 34, 143, 165, 166, 250]. Backstepping-based approaches are discussed for example in [77, 98, 106, 107, 245]. Reference [135] presents a nonlinear model predictive control approach that relies on a Taylor series approximation to the system's differential equations. Optimal control techniques are applied to control load-factor in [96]. Prelinearization theory and singular perturbation theory are applied for the derivation of inner and outer loop controllers in [165]. The main drawback to the nonlinear control approaches mentioned above is that, as model-based control methods, they require accurate knowledge of the plant dynamics. This is of significance in flight control since aerodynamic parameters always contain some degree of uncertainty. Although some of these approaches are robust to small modeling errors, they are not intended to accommodate significant unanticipated errors that can occur, for example, in the event of failure or battle damage. In such an event, the aerodynamics can change rapidly and deviate significantly from the model used for control design. Uninhabited Air Vehicles (UAVs) are particularly susceptible to such events since there is no pilot onboard. For high performance aircraft and UAVs, improved control may be achievable if the unknown nonlinearities are approximated adaptively.

This chapter presents detailed design and analysis of adaptive approximation based controllers applied to fixed-wing aircraft.¹ Therefore, we begin the chapter in Section 8.l with a brief introduction to aircraft dynamics and the industry standard method for representing the aerodynamic forces and moments that act on the vehicle. The dynamic model for an aircraft is presented in Subsection 8.1.1. Subsection 8.1.2 introduces the nondimensional coefficient representation for the aerodynamic forces and moments in the dynamic model. For ease of reference, tables summarizing aircraft notation are included at the end of the chapter in Section 8.4.

Two control situations are considered. In Section 8.2, an angular rate controller is designed and analyzed. That controller is applicable in piloted aircraft applications where the stick motion of the pilot is processed into body-frame angular rate commands. That section will also discuss issues such as the effect of actuator distribution. In Section 8.3, we develop a full vehicle controller suitable for UAVs. The controller inputs are commands for climb rate γ, ground track χ, and airspeed V. An adaptive approximation based backstepping approach is used.