## 1 Introduction  
Driven by advanced computing technologies, open-source systems, investigations and applications of unmanned aerial vehicles (UAVs) have progressed at an astounding speed in the past decades. To extend the applications of UAVs in wide area or long range, the fuel efficiency of the propulsion system plays a key role in this topic. In general, a fixed-wing aircraft has higher aerodynamic efficiency than a rotorcraft, which implies that it has better endurance and range than the rotorcraft. It can provide the advantage of longer flight durations at higher speeds thus enabling larger survey areas per given flight. Both the range and endurance of an aircraft depend on rate of fuel consumption of the engine. Therefore, the flight control design plays an important role in the optimization of the fuel consumption for an aircraft or UAV. In conventional flight control design, the autopilot and the autothrottle systems are usually considered separately [1]. The autothrottle unit is mainly used to adjust the engine throttle valve to achieve the desired flight speed, and the autopilot unit is designed to regulate the control surfaces for attitude and altitude maneuvers. However, since the dynamic model of an aircraft is nonlinear and uncertain, interaction between autopilot and autothrottle systems actually exists, and dynamic coupling between speed and altitude always occurs. According to the study proposed by [PERSON] [2], a pilot who tries to control airspeed and altitude separately winds up controlling one or the other rather poorly. Often times, the airspeed gets too low, whereupon the wing stalls and the pilot abruptly loses control. There is a coupling effect between airspeed and altitude, and controlling either one will affect another. In conventional flight control system, airspeed is controlled by throttle and altitude is controlled by elevator. This method will cause the undesirable flight path and airspeed coupling, and loss of airspeed control when thrust is limited. Therefore, by utilizing the relationship between airspeed and altitude, a control system was introduced by utilizing the energy of an aircraft. The first energy-based flight control system, named total energy control system (TECS), was developed by [PERSON] [3; 4]. TECS is a generic control technique that integrates all longitudinal flight-path and speed control functions, which does not depend on a particular aircraft type [5]. For fixed-wing aircraft, the mechanism and applications of TECS were used in guidance [6; 7] and flight control [5; 8; 9]. TECS based controllers have been successfully implemented on many aircrafts, such as the National Aeronautics and Space Administration (NASA) B737 technology demonstration plane [10], a general aviation aircraft [11], and a motor glider [12]. For helicopter, the design of a flight control system using TECS and H\({}_{\infty}\) control theory was introduced in the study [1]. Recently, studies based on TECS for UAVs have attracted more and more attention. However, compared to manned aircrafts, there are relatively few studies focused on the fuel efficiency of UAVs [13; 14]. To enhance the performance and usability of UAVs, there is a need for UAVs to increase endurance and/or reduce the amount of fuel carried. Many studies of UAVs focused on the problem of determining the optimal trajectory required to improve the fuel consumption [15; 16; 17]. Therefore, the design of the flight controllers emphasized on how to keep on the desired trajectory. For example, [PERSON] et al. used a Linear Quadratic Regulator (LQR) to stabilize the UAV on its nominal trajectory whilst rejecting disturbances and modeling errors [16]. However, for a typical flight profile of an aircraft, the level flight, climbing, and descending maneuvers are performed all the time after the aircraft leaves the ground. Therefore, the longitudinal flight control plays a significant role in fuel efficiency of an aircraft.