I. Introduction n recent years, the investigation and development of flight control algorithms for nonlinear aircraft dynamics has been addressed by many researchers. The standard approach for designing control systems for nonlinear aircraft is gain-scheduling. In this strategy, linear approximation of dynamic equations at several important operation points within the flight envelope is achieved. Depending on these points, linear controllers are designed and then combined continuously as the vehicle flies from one operating point to another. Due to linearization, the actual system performance and stability can be significantly different from the design results due the approximated nonlinearities. Instead of the need of interpolation or of gain-fitting technique of several operation points, the application of a variable-gain optimal output feedback control design methodology is proposed in Ref. 1 in which the feedback gains are calculated and scheduled as a function of the angle of attack. In this approach, the feedback gains are calculated and scheduled by minimizing the cost function that is a function of state and control vectors. The proposed approach is not fully effective and robust for short period mode control due to the computational cost and convergence of the associated constrained optimization problem.

Nonlinear inverse dynamics (NDI) 2, 3 for flight control system is proposed to eliminate the drawbacks of gainscheduling based design. Reference 2 uses assumptions in which aerodynamic force coefficients and moment coefficients to be nonlinear functions of the angle of attack, sideslip angle, and thrust coefficient but linear functions of the elevator, aileron, and rudder, the motion equations can be rewritten as a triangular system of general form and then a nonlinear inverse dynamic controller is generated and proven valid over the entire flight envelope. The limitation of proposed strategy is that aerodynamic moments must be linearly represented in terms of stability derivatives and control variables. A better approach of NDI design for full nonlinear flight control is presented in Ref. 3 which uses a fact that control surface deflections do not affected directly to the slow dynamics. Therefore, full nonlinear flight dynamics are designed separately for slow-state variable dynamics and fast-state variable dynamics. With the designed fast-state controller, a separate and approximate inversion procedure is carried out to design slowstate controller for slow-state variable dynamics and the achieved slow-state controllers are used as commands for fast-state variable dynamics. A justification of reliability of proposed algorithm is confirmed analytically using the longitudinal dynamics. As general disadvantages of NDI approach that prevent the popularity of applying the method for nonlinear flight systems are the robustness of NDI based control design, ie, system parameters of the aircraft dynamics are included in control law. Therefore, aircraft model used for control design needs to be accurate in order to achieve good performance and stability of the system. In recent years, many researchers have addressed backstepping control design which are introduced for the first time in Ref. 4 and has been a motivated basis in exploring a new direction in control design for nonlinear dynamic systems. Backstepping control design is seen as a recursive design process which breaks a design problem on the full system down to a sequence of sub-problems on lower order systems. Considering each lower order system with a CLF and paying attention to the interaction between two subsystems makes it modular and easy to design the stabilizing controller. The advantages of …