A learning control strategy is preferred for the control and guidance of a fixedwing unmanned aerial vehicle to deal with lack of modeling and flight uncertainties. For learning the plant model as well as changing working conditions online, a fuzzy neural network (FNN) is used in parallel with a conventional P (proportional) controller. Among the learning algorithms in the literature, a derivativefree one, sliding mode control (SMC) theorybased learning algorithm, is preferred as it has been proved to be computationally efficient in realtime applications. Its proven robustness and finite time converging nature make the learning algorithm appropriate for controlling an unmanned aerial vehicle as the computational power is always limited in unmanned aerial vehicles (UAVs). The parameter update rules and stability conditions of the learning are derived, and the proof of the stability of the learning algorithm is shown by using a candidate Lyapunov function. Intensive simulations are performed to illustrate the applicability of the proposed controller which includes the tracking of a threedimensional trajectory by the UAV subject to timevarying wind conditions. The simulation results show the efficiency of the proposed control algorithm, especially in realtime control systems because of its computational efficiency.
Over the past several decades, unmanned aerial vehicles (UAVs) have proved their potential in several applications by using their several capabilities,
UAVs can be classified into two groups: rotary wing and fixed wing. While the former has the capability of having aggressive maneuvers and being able to land and take off in small areas, the latter offers long flight endurance due to its flight characteristics about their gliding capabilities with no power. Among the gigantic number of fixedwing UAVs applications, surveillance seems to be the most common application while benefitting from advanced computer vision techniques [
For having a full autonomy of the aircraft, modelbased controllers require a precise dynamic model of the aircraft. The controller must also be robust to wind and gust disturbances. However, under the timevarying parameters of an aircraft as well as timevarying working conditions and several stochastic disturbances, a learning control strategy is preferred in this paper. The proposed control algorithm does not need an accurate model of the aircraft. Instead, the intelligent structure of the controller learns the system dynamics online throughout the flight and optimizes its performance for any arbitrary trajectory including both straight lines and circular orbits. For this purpose, the fusion of fuzzy logic and artificial neural networks, namely, FNNs, is preferred [
To eliminate all uncertainties in a control system and design a sophisticated modelbased controller based on an accurate model of the system seems to be convincing. The reason is that, in the absence of model uncertainty, nonlinearity, and computational constraints, it is a wellknown fact that linearquadratic regulator (LQR) and linearquadraticGaussian (LQG) control laws give reasonably satisfactory performance. However, eliminating all the uncertainties seems to be neither realistic nor a novel idea. For instance, till the beginning of the 20th century, it had been a big dream to eliminate all the uncertainties and to be able to achieve a fully predictable world. In 1814, P.S. Laplace formulated the predictability of the universe as follows:
On the other hand, quantum mechanics and the theory of relativity, which both appeared in the beginning of the 20th century, showed that our universe is quite random, and it is almost impossible to model or predict everything. In other words, our universe, at least on the level of subatomic particles, is not working like a “giant clock” which was claimed by P. S. Laplace. Even in a deterministic system, that is, a chaotic system, inevitable uncertainties in the initial conditions lead to huge differences in the future states of the system. In a similar manner, estimation and prediction of all changes during a fixedwing UAV flight cannot be foreseen and considered in advance. All the aforementioned facts force us to propose some intelligent control algorithms which have learning capabilities throughout the operation.
Fuzzy logic theory and probability theory are the most widely used approaches to deal with the aforementioned inevitable phenomena: uncertainty. Although the concept of fuzzy logic and the concept of probability seem to be similar, they are quite different. While probability makes guesses about a certain reality, fuzzy logic does not make probability statements but represents membership in vaguely defined sets. For instance, if 0.5 is defined as a probability value for the oldness of a person, it can be said that there is a chance that he/she can be old. It is not known whether he/she is old or young. However in fuzzy logic, if 0.5 is defined as the degree of membership in the set of young and old people, we have some knowledge about his/him and he/she is positioned in the middle of young and old people. Since fuzzy logic contained vagueness, it was not appreciated by researchers when it was proposed for the first time in 1960s. However, since the 1970s, this approach to set theory has been widely applied to control systems.
While the most significant feature of a fuzzy logic controller is its capability to inject expert knowledge into the controller design, the wellknown capability of an artificial neural network is to be able to learn from inputoutput data. The fusion of fuzzy logic controllers and artificial neural networks results in FNNs [
Despite the fact that UAVs are being more and more visible in our daily life, their control is still a challenging task as they are open loop unstable, multiinput multioutput, and highly nonlinear systems in which there are significant intercouplings. What is more, they are always subjected to noise and disturbances because of the uncertainties in their navigation systems as well as wind and gust conditions. One way of controlling them is to use modelbased control techniques. However, they need an accurate model of both the system and disturbances which is a challenging task in real life. A requirement is the use of sophisticated system identification methods to obtain the model of the aerial vehicle which is timeconsuming task. The detailed steps and several methods for system identification and parameter estimation of aerial vehicles are discussed in [
This paper presents a novel SMC theorybased learning algorithm with an adaptive learning rate and the evaluation of the algorithm performance for a UAV flying in changing wind conditions. The paper is organized as follows: Section
This section briefly introduces the translational and rotational equations of motion (EOMs) for a fixedwing UAV in the presence of wind.
Let
Let
The following expressions of forces and moments are used in this paper:
The kinematic model is given by (
The following reference value is defined (i.e., coordinated turn conditions):
Defining the trim angle of attack as
The proportional (P) controller can be implemented as follows:
Even if Mamdanitype fuzzy logic controllers were firstly proposed in the literature, a Takagi Sugeno Kang (TSK) fuzzy structure is preferred in this paper benefitting from its capability to be adapted over time. In the proposed method, as shown in Figure
Block diagram of the proposed adaptive FNN control structure.
Figure
Structure of the proposed FNN.
The fuzzy
For the calculation of the firing strength, a product
The Gaussian MFs
Hence, (
The output of the proposed FNN can be calculated as the weighted average of the output of each rule:
The control signal
In order to ease the notation and make some of the equations vectorial, the following definitions are made.
The following assumptions have been used in this paper.
The presence of the classical control system in the control scheme which adopted (Figure
The adaptation laws for the parameters of the MFs are made bounded which guarantees that
It is also assumed that the timevarying parameters of the consequent part of the TSK FNN are bounded; that is,
From (
Constraints (
Using the SMC theory principles [
The sliding surface for the nonlinear system under control
A sliding motion will appear on the sliding manifold
If the adaptation law for the parameters of the considered FNN is chosen, respectively, as
Then, given an arbitrary initial condition
See Appendix.
If the adaptation strategy for the adjustable parameters of the FNN is chosen as in (
See Appendix.
The obtained result means that, assuming the SMC task is achievable, using
The reason behind using continuous time instead of using discrete time is that the stability proof in discrete time is very challenging. That is why we have decided to use the continuous time. This selection does not play a very critical role as we keep the sampling frequency of the system very high. Therefore, the system behaves like a continuous time system in its implementation. The explained framework is preferred by many researchers in literature.
The physical parameters used in the simulations can be found in Table
Parameters for the Lambda UAV landing at sea level [
Parameter  Value 



































































The initial conditions are taken as
The P controller (
After 200 s, the FNNs are turned on. The mean wind velocity has a magnitude of
It can be seen in Figure
Time responses of the air velocity (
Threedimensional representation of the UAV trajectory (blue line) compared with its reference (red line) trajectory.
Time responses of the roll (
The control action (i.e., deflection of the different control surfaces) is shown as the corresponding contribution of the P controller (blue line) and the FNN (red line) in Figure
Time responses of the thrust (
Figure
Time response of the Euclidean error between the actual and reference trajectory for the P controller acting alone (dashed line) and the FNN in parallel with the P controller (solid line).
It is to be noted that although there exist four independent subsystem controllers in the UAV control system, the FNN works in parallel with a P controller only for the control of the thrust, pitch, and yaw, given the good performance of the roll channel being actuated only by the P controller.
In this paper, an SMC theorybased learning algorithm has been introduced for the control of a fixedwing UAV in the presence of wind. The adaptation laws for the parameters of the FNN are proposed and their learning stability conditions are investigated for a structure with two inputs, each being modeled by Gaussian MFs. The proposed control structure consists of a P controller and an FNN which can learn the inverse dynamics of the plant model online rather than a need for an accurate predefined dynamic model of the system. The obtained simulation results illustrate that using the proposed learning laws for the parameters of the FNN makes it possible to reach and maintain the predefined sliding manifold. It is further observed that not only is the proposed method robust but also another prominent feature of it is its ease of implementation. The effectiveness of the proposed algorithm has been demonstrated through computer simulations, which include the tracking of a threedimensional trajectory by the UAV in the presence of timevarying wind conditions. As a future extension to this paper, authors would like to implement state estimation methods for the available on board information.
The time derivatives of (
Considering the adaptation law of
The relation between the sliding function (it is a point in this investigation)
The tracking performance of the feedback control system can be analyzed by introducing the following Lyapunov function candidate:
Evaluating the time derivative of the Lyapunov function in (
The authors declare that there is no conflict of interests regarding the publication of this paper.
This research was supported by Nanyang Technological Internal StartUp Grant and Ministry of Education with the project titles “Learning Control Algorithms for Unmanned Aerial Vehicles” and “Model Predictive ControlMoving Horizon Estimation Framework as Applied to Tilt Rotor UAVs and Its Experimental Evaluation,” respectively.