رگرسیون بردار پشتیبانی تطبیقی ​​برای کنترل پرواز وسیله نقلیه هوایی بدون سرنشین

This paper explores an application of support vector regression for adaptive control of an unmanned aerial vehicle (UAV). Unlike neural networks, support vector regression (SVR) generates global solutions, because SVR basically solves quadratic programming (QP) problems. With this advantage, the input–output feedback-linearized inverse dynamic model and the compensation term for the inversion error are identified off-line, which we call I-SVR (inversion SVR) and C-SVR (compensation SVR), respectively. In order to compensate for the inversion error and the unexpected uncertainty, an online adaptation algorithm for the C-SVR is proposed. Then, the stability of the overall error dynamics is analyzed by the uniformly ultimately bounded property in the nonlinear system theory. In order to validate the effectiveness of the proposed adaptive controller, numerical simulations are performed on the UAV model.

Many dynamic systems to be controlled are affected by various disturbances and uncertain factors. For example, unmanned aerial vehicles (UAVs), which have received a growing interest for various military and civilian applications (Giulietti et al., 2000 and Ryan et al., 2004), are subject to significant wind gusts, vortex effects and time delay from control signal to control servo. Although precise control of UAVs is a basic ingredient for many applications, it is not trivial to obtain an accurate UAV model because of these disturbances and measurement noise. In order to design a controller against the uncertainties that cannot be predicted a priori, black-box identification using artificial neural networks (ANN) has been extensively studied. Sanner and Slotine (1992), a direct adaptive tracking control architecture using Gaussian radial function networks was designed to adaptively compensate for plant nonlinearities. Talebi, Khorasani, and Patel (1998) developed a position controller using four different neural network based schemes and revealed the validation of the proposed controller in the presence of unmodeled dynamics and nonlinearities. Recently, Giulietti et al. (2000) proposed a controller for a hybrid-electric UAV using neural networks to approximate a result of an energy optimization for a propulsion system and spent less energy than a two-stroke gasoline-powered UAV. The performance of ANN’s has been validated in a wide range of applications (Harmon et al., 2005, Kim and Calise, 1997, Polycarpou and Ioannou, 1992, Shin and Kim, 2006 and Yabuta and Yamada, 1991) despite the issues of local minima during gradient descent, and selection of the ANN architecture. On the other hand, kernel-based learning methods such as support vector machine (SVM) or support vector regression (SVR) transform the original problem into a quadratic programming (QP) problem whose global solution can be obtained by QP solvers (Schölkopf et al., 1998 and Smola and Schölkopf, 1998). Thus, pattern classification (by SVM) and regression problems (by SVR) can be solved without the issues of the local minima. Another advantage of the SVM/SVR is that its structure is fixed, so the selection of the design parameters for the SVR is often straightforward. With such advantages, SVM has found various applications including road profile recognition for autonomous navigation (Holzapfel, Sofsky, & Neuschaefer-Rube, 2003) and target recognition from synthetic aperture radar imaging (Zhao & Principe, 2001). Compared with the popularity of SVM in many classification and recognition problems, application of SVR in control systems is still in an early stage. In Wang, Pi, and Sun (2007), an online algorithm for an SVR inverse model has been studied. The online algorithm in Wang et al. (2007) is a training method in the context of incremental or decremental learning (Cauwenberghs & Poggio, 2001), rather than an adaptation algorithm performed in the control loop. In Iplicki (2006) and Xi, Poo, and Chou (2007), SVR-based techniques were used for obtaining a plant model for model predictive control (MPC). An off-line trained SVR plant model is fed to the optimization routine and used for the prediction of the future states over the lookahead horizon. And Suykens, Vandewalle, and Moor (2001) proposed a least-squares SVM-based optimal controller and validated its performance. However, the above studies did not consider the nonlinearity or uncertainties of the plant. Therefore, if the system we want to control changes significantly, overall performance can degrade. Unlike the previous SVR-based control research, this study uses ideas from the input–output feedback linearization in nonlinear control and then, uses the global property of the solution of the SVR. Two SVR machines are trained offline using input–output data from the input–output feedback-linearized system. The first one called the inversion SVR (I-SVR) is designed for training the feedback-linearized inverse dynamic model and the second one called the compensation SVR (C-SVR) is constructed to estimate the output derivative. However, even though the solution of the SVR has the global property in the sense of being offline, there, in practice, exists uncertainty or unknown disturbances that may be unrepresented in the training data set. In order to to handle the unexpected nonlinearities or uncertainties, an online adaptation rule for the C-SVR is designed in an adaptive control framework. This paper is organized as follows. The SVR algorithm is reviewed briefly in Section 2. In Section 3, an approach for combining input–output feedback linearization and C-SVR, and the online adaptation rule for the SVR are addressed. The overall stability under the adaptation rule is analyzed using the ultimately uniformly bounded property in the nonlinear system theory. Section 4 describes an UAV system whose flight test data is used in this study, and presents the results of the UAV flight control using the proposed approach. A conclusion is given in Section 5.

In this study, an SVR-based control approach is proposed using the input–output feedback linearization technique and the adaptive control framework. The inverse transformation of the feeback-linearized system is trained by the I-SVR and the additive term for compensating the inversion error is designed by the C-SVR. Furthermore, in order to handle the error caused by the unexpected nonlinearities and uncertainties, the adaptive rule for the C-SVR is proposed. The stability for the closed-loop error dynamics is analyzed by the uniformly ultimately bounded property of a perturbed system in the nonlinear system theory. In order to validate the effectiveness of the proposed algorithm, numerical simulations have been performed on the UAV model obtained by the flight test data. The adaptive SVR approach showed better performance than the offline trained SVR only. Finally, the proposed adaptive control using the SVR algorithm has been compared with that using the NN algorithm in order to show the superiority of the proposed SVR-based adaptive control.