Model Predictive Control With Wind Preview for Aircraft Forced Landing

Autonomous emergency landing capability of fixed-wing aircraft is essential for opening airspace for civil unmanned aviation. This article proposes a goal-oriented control scheme to exploit wind information for the benefit of forced landing. Different from general disturbances in a classic control system, a favorable wind would help aircraft to glide to a selected landing site more easily so increase the level of safety while an adverse wind may render a selected landing site infeasible. We formulate the forced landing problem with wind preview information in the framework of economic model predictive control (EMPC), which aims to maximize the aircraft's final altitude when reaching a target region. A double-layer model predictive control (MPC) scheme is adopted to lessen the computational burden and to increase the prediction time window for practical implementation, where a piecewise-constant disturbance-preview-based EMPC maximizes the altitude at the upper level, and a linear MPC is employed at the lower level to track the reference signal optimized by the upper-level planner. Moreover, the effectiveness of the goal-oriented optimal control scheme is illustrated by several case studies, where an unmanned aircraft is gliding toward potential landing sites under various conditions.


I. INTRODUCTION
With the advances and increasing maturity of unmanned aircraft technologies, there is a strong aspiration in future unmanned aviation where unmanned aircraft would safely operate with human-piloted aircraft in shared civil airspace. However, despite all the efforts in improving the reliability and the robustness of technologies/subsystems, aircraft is still prone to various faults, at all the levels from components to subsystems, under a wide range of operation conditions. As an integrated part of unmanned aviation, active contingency management is important to guarantee the safety of the aircraft and particularly the public. Among others, autonomous forced landing as the last resort simply aims to land aircraft in a suitable place as soon as possible to minimize the risk to the public and save the aircraft if possible [1], [2], [3], [4]. It is of particular importance in emergent situations, such as engine failure, and other critical or irreversible failures. Without this type of function in place, a significant risk would be imposed on the public when an unmanned aircraft flies over a residential area or safety-critical infrastructure.
Without engine power, an aircraft is only capable of gliding a certain distance based on its aerodynamic configuration, its flight status, and weather conditions. At a high level of selecting a suitable landing site, reachability analysis plays a key role in determining where the aircraft under concern is able to reach. A feasible path for forced landing with a minimum traveling time between two points was studied in [1] based on a kinematic aircraft model. Geometric curves, such as Dubins curves and trochoids, were utilized to drive a gliding aircraft to lose as little height as possible by flying the shortest path [2], [3], [4]. Seleckỳ et al. [5] designed a method, where the trajectory planner is able to generate reachable states for an unmanned aerial vehicle (UAV) by considering the wind effects.
After reachability analysis, a target landing site can be selected by weighing many other factors, such as the size and surface of potential landing sites [6]. Then, the control objective in the forced landing problem is to reach the selected site with a maximum altitude so that the aircraft has the most time to make decisions on how to land safely, e.g., continue its straight-line autolanding process or switch to another landing site if needed. Hence, it is desirable to develop a control algorithm, which can maximize the altitude directly, instead of tracking a reference signal as in the standard model predictive control (MPC). Motivated by this goal-oriented operation, we may adopt an economic MPC (EMPC) idea that provides an elegant way to undertake the economic optimization problem in real time (see [7], [8], [9], [10], [11], and references therein). To mitigate real-time implementation issues of nonlinear optimization involved in EMPC, our previous work proposes a two-level control strategy for the forced landing task [12]. In the high-level path planner, a piecewise constant input EMPC approach is employed for a nonlinear model to generate a reference path for the low-level controller, which is not only able to alleviate the computational burden but also to increase the prediction time window of the forced landing process. In the low-level controller, a linear time-varying MPC approach is adopted for a linearized model to track the desired trajectory optimized by the EMPC-based path planner.
During the gliding, winds play an important role in unmanned aircraft's path and performance. Depending on the location of a selected landing site, a favorable wind would help the aircraft to reach it much easier with a larger safe margin (in terms of the altitude above the ground) while an adverse wind condition may render the aircraft impossible to reach it. Therefore, the flight controller shall harvest a favorable wind, rather than reject it as in the normal practice of a typical control system design. With the advances in sensor technology, wind sensors are able to provide reasonable accurate information about local wind conditions [13], [14], [15]. Additionally, with the past short-term collected data of wind conditions, the disturbance estimation [16], [17] and machine learning [18], [19] techniques are also able to predict the wind conditions in near future with a reasonable accuracy. As reported in [20], a nominal MPC approach with disturbance preview information is designed for linear systems, which is able to exploit the disturbance preview. More recently, a disturbance-preview-based MPC approach extends the relevant result to a general class of nonlinear systems, where the recursive feasibility and stability are also rigorously analyzed [21].
Inspired by the aforementioned works, a disturbancepreview-based EMPC (DP-EMPC) approach will be proposed for the forced landing task of an unmanned aircraft system, which aims to make full use of the wind to minimize the height loss. Moreover, due to the specific properties of the forced landing problem, it is quite difficult to select an appropriate terminal weight to cover the cost-to-go. Therefore, to establish the stability of the aircraft system with the DP-EMPC approach, a shrinking horizon mechanism is adopted, which can relax the requirements on terminal ingredients.
To the best of our knowledge, currently there is no work on exploiting real-time wind preview information for the benefit of maximizing the aircraft landing altitude and analyzing its impact on the aircraft forced landing behavior, in particular how to take advantage of winds to achieve better objectives. Moreover, to take the advantage of real-time implementable two-level framework [12], this article proposes an optimal controller design for the forced landing task under wind conditions. In summary, our main contributions include the following.
1) A DP-EMPC approach is proposed to take the opportunity raised by wind conditions to optimize highlevel economic criteria, i.e., to maximize the altitude of an unmanned aircraft system as it reaches the target area of a forced landing site. 2) A two-level controller is developed to reduce the computational complexity and to enhance the practicality of the unmanned aircraft system.
3) The recursive feasibility and stability are established with the shrinking horizon mechanism for the DP-EMPC approach.
Finally, we demonstrate the effectiveness of our proposed DP-EMPC algorithm by several forced landing scenarios under different wind conditions. It is clearly evident that making use of wind information (either precise or imprecise) could provide much better performances than without using it.
The remaining part is organized as follows: the mathematical model of fixed-wing UAVs and the selection of a terminal region for a landing site are presented in Section II. Section III presents the design of an implementable two-level controller to drive the unmanned aircraft to the landing site, which can take advantage of the wind condition to maximize its landing altitude. In Section IV, the stability analysis of the aircraft system is given. Section V verifies the effectiveness of the proposed controller with several case studies, whereas Section VI concludes the entire article.

A. Aircraft Modeling
This article investigates an optimal control strategy for forced landing tasks of a fixed-wing unmanned aircraft under wind conditions. This article considers the full nonlinear motion of a fixed-wing aircraft in wind conditions over a flat Earth presented in [22] and [23], which can be given with the following compact state-space form: where the state vector is taken in the form of z = {X, Y, Z, V, α, β, p, q, r, φ, θ, ψ}, denoting the position in three dimensions, speed, angle of attack and side slip angle, angular velocities in three dimensions, and Euler angles, respectively. The control vector v = {δ e , δ a , δ r } denotes the control signals of elevator deflection, aileron deflection, and rudder deflection, respectively. ω = {ω X , ω Y , ω Z } denotes the wind disturbances in three dimensions. Note that the detailed expression of this fullorder dynamic equation can be found in the literature [22], [23]. Due to the high complexity of the above full dynamic representation, a practical approach is employing the following reduced number of equations [24], [25], [26] for path planning and an autopilot block to control the aircraft described by the full nonlinear dynamic model to track the control command: where the state vector x = [X Y Z V γ ψ α φ] T , the control vector u = [ᾱφ], and the wind disturbance Note that γ represents the vertical flight path angle. Hence, the compact form of the nonlinear dynamics (2) is described bẏ In particular, it is noticed that two first-order equations with constant coefficients k α and k φ , respectively, are used to model the relationships for angle of attack α and roll angle φ with respect to their corresponding command signals [27], [28]. The parameters L(α, V ) and D(α, V ) denote the lift and drag forces, which are given by where ρ denotes the air density, AR = b 2 S denotes the wing aspect ratio with respect to the wing area S and the wingspan b. In addition, C L and C D are the aerodynamic lift force and drag force coefficients, respectively.
The state and input variables of the aircraft are subject to some physical constraints and safety constraints, which are considered in the receding horizon optimization problem. Mathematically, the state and input constraint set (possibly coupled) is presented by where G(·, ·) denotes a set of real-valued continuous functions. For instance, a common form of the aircraft constraints could include which define the upper and lower bounds of these aircraft states.

B. Terminal Region of Gliding Task
In most literature, the landing site is simply modeled as a single point that may not be suitable for a large proportion of practical situations since heading and other attributes are also important. For example, when the aircraft is flying downwind at the moment when it reaches the targeted point, extra turns would be necessary to adjust the right heading angle which further induces undesired height losses. Furthermore, adopting geometric curves, such as Dubins curves and trochoids, does not take into account the physical constraints of the aircraft [2], [4]. In particular, it always requires the satisfaction of assumptions that the bank angle and speed are achieved instantly when the aircraft changes from the glide mode for minimum sink in the turn to the straight line path for a maximum glide ratio.
In this article, we adopt a partial cylinder with a fixed radius shown in Fig. 1 as the terminal target region, where the aircraft will execute the final landing procedure, consume extra altitude, and achieve the safe landing [2], [12], [29]. This terminal region can be formulated as the following set: where G f (·) are explicitly formulated in the form of the following inequalities: where P L = [XȲZ], d, and represent the critical point, the threshold distance, and the angle of the terminal region, respectively. S start = [X start Y start Z start ] and S end = [X end Y end Z end ] denote the starting and ending locations of the final landing site, respectively.ψ = arctan Y end −Y start X end −X start is the reference heading angle at the final straight line gliding stage.
The condition (8a) imposes that the distance between the location that the aircraft reaches and the specific point (X ,Ȳ ) is no more than d. The minimum requirement on aircraft altitude isZ, which is ensured by (8b). The condition (8c) ensures that the aircraft velocity must be no less than the stall speedV . Finally, the condition (8d) describes the required orientation of the aircraft as it flies to the target region.
When the unmanned aircraft suffers from engine failure, it is essential to exchange its height for flight distance to reach the desired landing site. Hence, it is necessary to plan a trajectory with the minimum altitude loss. More importantly, if the aircraft system keeps enough altitude, it retains the possibility to fly to other optional landing sites under the circumstances that unexpected events happen; for example, the selected site is assessed to be unsuitable after visual inspection with onboard cameras. More details on the advantages of extra altitude and more energy storage have been discussed in [2]. Therefore, this article focuses on the design of an optimization-based controller, which maximizes the terminal height when it reaches the selected landing site by exploiting wind preview information. Rather than online planning a path using EMPC by ignoring the wind condition as in our previous work [12], the favorable wind condition is considered as an opportunity in this goal-oriented operation. More specifically, the preview information of the wind condition is considered in the receding horizon optimization framework to take the opportunity to maximize the terminal altitude of the aircraft system as it glides to a selected landing site.
On the other hand, as stated in [12], the conventional single-layer controller based on nonlinear MPC technology is generally not applicable for real-time implementation for forced landing since an unrealistic long prediction horizon is required. In order to stabilize the fast aircraft dynamics with a flight controller designed for a discrete-time model, it is necessary to select a sufficiently small sampling time to approximate the continuous-time dynamics with an adequate accuracy. However, the small value of sampling time drastically increases the computational complexity, as there are more decision variables to be optimized. A two-level optimal control strategy proposed in [12] is adopted to address this implementation issue. Furthermore, the preview information of wind is fully exploited at the high level to maximize the terminal height by proposing disturbance-previewbased EMPC (DP-EMPC) algorithm. The two-level framework of the controller is depicted in Fig. 2. The upper-level DP-EMPC planner optimizes a reference trajectory for the low-level controller, as well as achieves the maximum terminal height with the exploitation of profitable wind conditions. The low-level controller is designed with the linear time-varying MPC algorithm, which aims to track the reference trajectory and to generate the control commands u = [ᾱφ]. Additionally, the built-in autopilot calculates the actual control signals v = {δ e , δ a , δ r } to drive the unmanned aircraft vehicle. The time setup of the proposed two-level framework is briefly introduced as follows [12]. A sampling time T s defined as the interval of the high-level DP-EMPC is used to update system states and to generate a new control sequence. Different from the conventional discretetime EMPC, the holding time interval T s is computed by T s = P · T d with an integer P ≥ 1, where T d is the sampling time of the low-level controller. N ∈ I >0 and N ∈ I >0 denote the prediction horizons of the high-level DP-EMPC and low-level MPC, respectively. The control command (reference signal) optimized by the DP-EMPC planner keeps constant over P integration steps T d of the low-level MPC, i.e., u ·P+i = u ·P+ j , ∀ ∈ I [0,N −1] , and ∀i, j ∈ I [0,P−1] . Before introducing the two-level optimization problem, let us discretize the continuous-time system (3) into the following discrete-time state equation: where T d represents the discretization sampling time. Based on the above discrete-time dynamics, further notations will be introduced: denoting N t as the prediction horizon, x t:t+N t |t represents the sequence of predicted states from instant t to t + N t , u t:t+N t −1|t denotes the sequence of future control moves, and ω t:t+N t −1|t is the sequence of wind preview information, considered at sampling instant t.
A. High-Level: DP-EMPC for Trajectory Planning The piecewise constant shrinking horizon DP-EMPC scheme is designed to form the high-level planner of the unmanned aircraft. It aims to generate a reference trajectory for the low-level controller, as well as to maximize the terminal height, which takes the wind condition as the opportunity to optimize economic criteria, rather than rejecting the wind disturbance.
Before designing the high-level DP-EMPC planner, the following assumption is made.
Assumption 1 The preview information of the wind condition at sampling instant t is precise and available Under the piecewise constant setup, we call an ordered P-tuple of points x P t = {x t (0), x t (1), . . . , x t (P − 1)} fulfilling ∀k ∈ I [0,P−1] , as a P-step system which aims at describing the original system (9) every T s sampling time. Then, after implementing u t over P integration steps, the ordered Ptuple of points can be given with the following compact form: where F (x t , u t , ω t:t+P−1|t ) is the vector function resulting from (11), u t is the constant control input over the P-step, and ω t:t+P−1|t = [ω t|t , . . . , ω t+P−1|t ] is the P-step preview information of wind. Based on the P-step system, we formulate the optimal control problem (OCP) which aims to maximize the aircraft altitude when it reaches the predefined target region. The economic cost function is defined by h(x N P|t ) = −Z N P|t denoting the predicted terminal height. The initial condition is specified by constraint (13a). Constraint (13b) is introduced to describe the dynamic equations with constant input and preview information of the wind condition for the P-step system. (13c) denotes the state and input constraints, and (13d) ensures the entry of the terminal region for the aircraft system. The decision variables of the OCP (13) are explicitly given with the expression of u t:(N −1)P|t = {u t|t , u t+P|t , u t+2P|t , . . . , u (N −1)P|t }, which include the angle of attackᾱ and roll angleφ over the prediction horizon N . After solving this OCP, the resulting optimal control sequence is and the corresponding state sequence is Notice that the preview information of the wind condition ω t+ |t is included in the prediction model (13b) of the OCP, where the DP-EMPC provides an elegant mechanism to maximize the benefit of wind condition for the aircraft altitude by making use of the preview information of disturbances. In particular, the proposed DP-EMPC scheme not only rejects unfavorable wind uncertainties as necessary but also harvests favorable ones if it is beneficial to lifting the altitude of an unmanned aircraft in the forced landing task. REMARK 1 With the advances in sensor technology [13], [14], [15], disturbance estimation algorithm [16], [17], and machine learning technique [18], [19], we are able to predict reasonable accurate information about wind conditions in near future. Furthermore, the preview errors of the wind conditions are considered in the simulations, where the effects of the preview errors are analyzed to demonstrate the flexibility and robustness of the proposed DP-EMPC scheme. Simulation results verify that the proposed DP-MPC scheme is able to not only make use of the favorable preview information but also reject the detrimental disturbance despite the existence of preview errors.

B. Low-Level: MPC With Linearized System for Tracking
The design of the low-level controller is almost the same as our previous work [12]. However, to illustrate the whole idea of the two-layer control scheme clearly, we introduce the low-level controller briefly in this section.
The low-level controller adopts the time-varying MPC technique based on the linearized aircraft model with small sampling time T d to achieve accurate tracking performance for the optimized reference trajectory generated by the high-level planner. The constant baseline control signal u r t:t+P−1 = {u * t|t , . . . , u * t|t } and the state reference x r t:t+P−1 = {x * t|t , . . . , x * t+k|t , . . . , x * t+P−1|t } are sent to the low-level MPC controller in every time interval T s = P · T d .
The linearized equation of system (9) is described bỹ , with a parameter vector σ k = [x r k , u r k , ω r k ] T for x r k = x * t+k|t and u r k = u * t|t generated by the high-level DP-EMPC planner, and ω r k = ω t+k|t denoting the disturbance preview information.
For the time instant k and prediction horizon N , the low-level MPC problem is formulated by With the obtained optimal solutionũ * k:k+N −1|k = {ũ * k|k ,ũ * k+1|k ,ũ * k+2|k , . . . ,ũ * k+N −1|k } of (15), the sum of the first elementũ * k|k and the signal u * t|t provided by the upperlevel DP-EMPC will be used in the autopilot (see Fig. 2) to calculate the deflection control signals δ e , δ a , and δ r of the unmanned aircraft system. This process will be repeated for P steps until the next time instant to execute the high-level DP-EMPC trajectory planner. (14) is clarified here. The complete linearized error system is given byx k+1 = A(σ k )x k + B(σ k )ũ k + D(σ k )ω k . Furthermore, according to Assumption 1, we have that the disturbance preview information is precise, which implies that the preview errorω k = 0. Hence, the disturbance information will not explicitly appear in the prediction model (14) adopted for the inner-loop controller. Additionally, it shall be mentioned that the matrices A(σ k ), B(σ k ), and D(σ k ) are independent of the disturbance ω = [ω X ω Y ω Z ], since ω in the nonlinear system (2) is an additive disturbance. REMARK 3 It is necessary to clarify the main contribution of this article with respect to our previous work [12]. The main work of [12] is to propose a two-level framework for the forced landing task. However, it does not consider the wind condition in the controller design at all. In this article, a DP-EMPC approach is proposed in the high-level trajectory planner, which is able to not only take the opportunity raised by favorable wind conditions to optimize high-level economic criteria but also reject detrimental wind disturbances to strengthen the robustness of the closed-loop system. Hence, this article is a significant extension of our previous work.

IV. RECURSIVE FEASIBILITY AND STABILITY ANALYSIS
The stability analysis of the upper-level DP-EMPC planner and the low-level MPC controller will be briefly given in this section.

A. Stability Analysis of the High-Level DP-EMPC
A key point in the stability analysis of the EMPC algorithm is to select a suitable Lyapunov function candidate based on the economic cost criteria, which was analyzed in [8] and [30]. Following this idea, we investigate the stability analysis of the DP-EMPC approach for a forced landing task of the unmanned aircraft system when the wind information is exploited.
The main result of the high-level DP-EMPC planner is presented as follows.
THEOREM 1 Suppose that Assumption 1 is satisfied, and the OCP (13) is feasible at the initial time. Then, the proposed DP-EMPC scheme is recursively feasible and the unmanned aircraft is able to enter the target region X f in finite time even in the presence of the wind condition.
PROOF In the first step, we will give the analysis of the recursive feasibility of the DP-EMPC scheme.
Assume that the OCP (13) is feasible at t = P. The sequence of optimal control signal is given by According to Assumption 1 that the preview information of the wind condition is precisely known, the following tail of the optimal control sequence (16) is a feasible solution of the shrinking horizon OCP (13) at time t + P = ( + 1)P: Hence, the proposed DP-MPC scheme is recursively feasible.
Next, we will analyze the stability of the system under the proposed DP-EMPC scheme.
The main idea of the stability analysis borrows from the literature [31]. Define a positive function at time t = P V x P:N P|t , u P: (18) whereh is a large constant to make the condition h(x N P|t ) + h > 0 always holds. The nonnegative parameter σ i|t satisfies that σ i|t = 0 if the aircraft enters the target region, otherwise σ i|t = 1. Therefore, V (x P:N P|t , u P:(N −1)P|t ) > 0 holds for all ≥ 0.
Define the optimal value of the function (18) at t = P According to the inherent property of the optimization problem, it is easy to obtain So we get the descent property of the positive function (19), which can be regarded as a Lyapunov function. Hence, the aircraft system under the DP-EMPC scheme is stable, which implies that the unmanned aircraft will enter the target region X f in a finite time.

B. Stability Analysis of the Low-Level MPC
The low-level MPC scheme is a linear time-varying MPC approach. Hence, we give the following result of the proposed MPC scheme straightforwardly. THEOREM 2 Suppose that the MPC algorithm (15) is feasible at the initial time. Then, the proposed MPC scheme is recursively feasible and stable.
PROOF The proof of this theorem is quite similar to the stability analysis of the standard linear time-varying MPC approach in literatures [12], [32]. Therefore, the proof is omitted here for brevity. REMARK 4 It is reasonable to use the terminal equality constraintx k+N |k = 0 in a low-level MPC scheme. Because the main task of the low-level controller is to drive the tracking errorx k in (14) to zero. Additionally, the terminal equality constraint (15d) can simplify the terminal ingredients of the MPC algorithm largely, for that the calculation of terminal ingredients for time-varying system is quite complex, especially for a higher-order dynamic system like unmanned aircraft [33], [34]. Furthermore, the terminal equality was also adopted in our previous work [12].

V. SIMULATIONS
This section gives representative simulation results for the forced landing task of an unmanned aircraft system under various conditions, which demonstrates the effectiveness and superiority of the proposed controller with preview information of wind conditions. In these simulation tests, a high-fidelity dynamic model (1) of Aerosonde [22], [23] is used to demonstrate the performance of the proposed optimal controller. First of all, the performance to maximize the landing altitude of unmanned aircraft by making use of the wind condition is presented. Furthermore, the capability of driving the aircraft to different selected landing sites under various wind conditions is also verified.
In this simulation scenario, the Aerosonde system suffers from an engine failure in the presence of the wind condition, which is assumed to be like a "1-cos" wind environment [35]. The wind velocities on three axes are depicted in Fig. 3. The positive value of the wind velocity implies that the wind blows along the positive direction of the relative axis, and vice versa.
To demonstrate the superior performance of our proposed DP-EMPC scheme and its robustness, three control schemes are tested and compared for all these simulation studies. In addition to the proposed DP-EMPC with precise preview information of the wind condition, the scheme of EMPC without making use of preview information of the wind condition [12] and the DP-EMPC with imprecise wind information (i.e., with preview error) are also considered. In the latter case, it is presumed that the wind is estimated aŝ ω = [1, −1. 3,0] in the prediction and online optimization, which is different from the actual wind profile shown in Fig. 3.
In this scenario, the landing site is denoted as S 1 , whose critical point, the starting and ending locations of the fi-  Table I. It is evident that the DP-EMPC scheme is able to take advantage of the preview information of the wind condition to maximize the landing altitude of the aircraft system when reaching the selected landing site while the aircraft with the conventional EMPC rejects the favorable wind and is forced to track the path planned without consideration of winds. Even when the wind condition is not precisely   known, the proposed DP-EMPC is still able to achieve much less height loss. This also demonstrates the robustness and flexibility of the proposed DP-EMPC scheme. Finally, Fig. 6 gives the deflection control signals of the aircraft system, which shows that all the signals are within the bounds of the constraints ±5 deg.
In this scenario, the simulation results demonstrate that the proposed DP-EMPC method can take the opportunity of the wind condition to maximize the terminal altitude of the unmanned aircraft system in the forced landing task.

B. Capability to Enter Different Selected Landing Sites
In this simulation scenario, the unmanned aircraft system will be driven to different landing sites under various wind conditions, which aims to verify the capability to enter different selected landing sites, as well as to further examine the robustness of the proposed DP-EMPC scheme. Furthermore, to verify the robustness of the proposed DP-EMPC scheme, much stronger wind conditions are considered in    Fig. 3.
First of all, we examine the capability of the proposed DP-EMPC method to drive the unmanned aircraft to different landing sites with a roughly similar heading direction but different distances under wind conditions. The critical point and the location of the closer landing site (denoted as According to Fig. 7, the unmanned aircraft is able to enter the closer landing site S 2 under these three control schemes. Hence, the histories of height and the terminal heights of the aircraft flying to S 2 are depicted in Fig. 8 and Table II, respectively, which also verifies that the less height loss can be achieved by the proposed DP-EMPC scheme with the exploitation of profitable wind conditions.  Additionally, the conventional EMPC scheme cannot steer the unmanned aircraft to the farther landing site S 3 (see Fig. 7). Since the conventional EMPC scheme plans the reference trajectory without considering the wind condition, the planned reference trajectory could be unsuitable for the unmanned aircraft system under wind conditions. In other words, the low-level MPC controller is incapable of attenuating the wind disturbance with its inherent robustness to drive the unmanned aircraft to track this reference trajectory. On the other hand, the proposed DP-EMPC scheme considering the wind condition in the optimization problem makes it possible to generate an appropriate reference trajectory, which can be tracked by the low-level controller. Hence, the whole proposed control framework is able to reject the wind disturbance when it generates negative effects on the control task, which implies that the proposed DP-EMPC possesses stronger robustness to wind disturbances.
Next, we will examine the capability of the proposed DP-EMPC method to drive the unmanned aircraft system to landing sites with different directions under wind con- From Fig. 9, we can see that the unmanned aircraft can enter both landing sites under these three control schemes. Furthermore, the time histories of the heights are given in Figs. 10 and 11, respectively. In addition, the terminal heights of aircraft flying to the landing sites S 4 and S 5 are given in Table III. The terminal heights of the aircraft under   DP-EMPC with imprecise/precise preview information are larger than the height under conventional EMPC. Hence, all the aforementioned simulations verify that the proposed DP-EMPC method is able to harvest the favorable wind condition to maximize the altitude when the aircraft flies to the selected landing sites. Furthermore, it shall be mentioned that these two landing sites are symmetric with respect to the X -axis, and the wind directions relative to the final runways of two landing sites are different. Particularly, Table III shows that the terminal heights to the landing site S 4 are larger than those to the landing site S 5 , which implies that the wind direction relative to the final runway can affect the performances of the MPC approaches.
In this scenario, the simulation results verify that the proposed DP-EMPC scheme not only can take the opportunity of the wind condition when it is in favor of a specific landing task but also reject the unfavorable wind disturbance as necessary. The proposed DP-EMPC scheme possesses strong robustness to wind disturbances.

VI. CONCLUSION
A novel optimization control scheme for fixed-wing unmanned aircraft has been presented to accomplish a forced landing task. In this designed controller, a high-level DP-EMPC explores an optimal trajectory to the target region by using the preview information of wind conditions, and a low-level MPC is responsible for fast tracking while considering all the constraints. Case studies confirm that the proposed controller exhibits promising performance under different scenarios in the presence of persistent winds. In particular, it is verified that the proposed controller can take advantage of favorable wind and optimize its performance in terms of the high-level specifications, i.e., landing aircraft in a selected landing site safely. Furthermore, the future work will focus on the systematic design and theoretical analysis of the DP-EMPC scheme with preview error, particularly considering the estimation error of disturbance observers and sensor measurement noise.