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Thus, a better approach is proposed to improve the performance in this situation.

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On the other hand, the method might lead to a poor quality across the full flight envelope due to uncertain system parameters. By numerical simulation and experimental study, the backstepping control method can prove a very good performance and stability if system parameter modeling is accurate.

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After a series of control design for subsystems, a nonlinear feedback controller is obtained. By considering each subsystem in relation with interconnected subsystems, a virtual feedback control is selected from satisfying the requirement of LyapunovвЂ™s theorem. The achieved model will be divided into subsystems for control objectives. In approaches, a full nonlinear dynamic system is transformed directly or indirectly into a strict-feedback form or a lower-triangular model for applicability via assumptions or state transformations. In recent years, backstepping or recursive control design for a strict-feedback form of nonlinear dynamic systems is introduced firstly by authors and is applied extensively for flight control of the nonlinear flight dynamic system. Thus, a new type of the robust controller, in which a robust property for a nonlinear dynamic system must be included, is necessary to improve stability and performance of aircraft longitudinal dynamics. However, mentioned control design methods are mostly focused on design of control parameters that are not fully able to adapt internal dynamics in order to ensure the stability and performance robustness. In this approach, the control parameters of dynamic inversion are designed to minimize the probability of violating design specifications and so provide a better design with good robustness in stability and performance subject to modeling uncertainties. A better approach in robust control methods is proposed to improve the handling qualities across the specified flight envelope without the use of gain scheduling. Then, a genetic algorithm is used to search a feasible design coefficient space that is evaluated by Monte Carlo for stability and performance robustness. Twenty-eight uncertain parameters are used to model aircraft motion in nonlinear longitudinal dynamics. Recently, robust control design methods for nonlinear aircraft flight dynamics have been addressed by many researchers. However, these works neglected the effects of uncertainties that can lead to instability and poor performance of an aircraft system due to complex variations in aerodynamic models. Therefore, a direct application of a nonlinear flight system should be addressed for a new generation of flight control design. In, it is indicated that actual system performance and stability can be significantly different from design results due to linearized nonlinearities. From those selected points, linear controllers are designed and then combined continuously as the aircraft flies from one operating point to another. In this method, a linearized model of the nonlinear flight dynamic system at key operating points within the flight envelope is achieved. IntroductionДЄ standard design method of the flight control system for nonlinear aircraft dynamic systems is based on gain scheduling from linear control system designs. Also, an external disturbance on different loading/unloading conditions in flight is applied to verify and validate robustness of the proposed control method. A closed-loop system is achieved for in-flight simulation with different flight profiles for a comparison of the existing methods. Under some assumptions, full nonlinear longitudinal dynamics is reformed into a lower-triangular system for a direct application to formulate a control law. The application of flight-path angle control corresponding to the longitudinal dynamics of a high-performance F-16 aircraft simulation model is implemented. The achieved control method proves a well-tracking command with asymptotic stability, provides a robustness in the presence of uncertainties, and eliminates completely a chattering phenomenon. Then, a smooth switching function of the sliding surface is introduced and enforced to include in virtual feedbacks and a real control law from the control selection phrases of the backstepping design loop. In this approach, a family of the вЂњsliding surfaceвЂќ is introduced in state transformations. In this paper, a novel control design is presented systematically to synthesize a robust nonlinear feedback controller, called backstepping sliding mode control (BSMC), for the proposed system by a combined approach of backstepping design and sliding mode control. This paper presents a hybrid robust control design method for a third-order lower-triangular model of nonlinear dynamic systems in the presence of disturbance.

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