Memory Augmented Neural Network-Based Intelligent Adaptive Fault Tolerant Control for a Class of Launch Vehicles Using Second-Order Disturbance Observer

Chen, Haipeng; Chen, Kang; Fu, Wenxing

doi:https://doi.org/10.1155/2021/9961278

Mathematical Problems in Engineering

On this page

Abstract Introduction Conclusions Data Availability Conflicts of Interest References Copyright Related Articles

Research Article | Open Access

Volume 2021 | Article ID 9961278 | https://doi.org/10.1155/2021/9961278

Memory Augmented Neural Network-Based Intelligent Adaptive Fault Tolerant Control for a Class of Launch Vehicles Using Second-Order Disturbance Observer

Haipeng Chen,^1,2,3Kang Chen ,^1,2and Wenxing Fu^1,2

Academic Editor: Jian Zhang

Received14 Mar 2021

Revised26 Apr 2021

Accepted23 Jun 2021

Published02 Jul 2021

Abstract

This paper focuses on the MANN-based intelligent adaptive fault tolerant control for a class of launch vehicles. Firstly, the attitude dynamic model of the launch vehicles suffering from the actuator faults and disturbances has been formulated. Secondly, the second-order disturbance observer has been designed for the launch vehicle to achieve the exact estimation and compensation of the time-varying disturbances. Meanwhile, the MANN has been introduced as online approximator, suppressing the adverse influence of the unknown nonlinearities. Moreover, several adaptive laws have been proposed to achieve the quick response to the actuator faults and the update of the MANN weights. As a result, the MANN-based intelligent adaptive fault tolerant control structure has been constructed for the launch vehicles. It has been proven that all the signals in the closed-loop system are bounded. Simulation results demonstrate the desired performance and the advantages of the proposed control algorithm.

1. Introduction

As an important medium for the development of aerospace technology, launch vehicles require high reliability and low risk. It is inevitable that the control systems of launch vehicles are subjected to the system faults on account of its complex structure and enormous components [1]. Therefore, the capability of fault tolerant in the control system of launch vehicle plays an important role in improving the reliability of aerospace missions [2].

Generally, the fault tolerant control (FTC) method can be categorized into passive fault tolerant control (PFTC) and active fault tolerant control (AFTC) [3]. In PFTC, a controller with fixed structure and parameters is proposed to compensate the anticipated faults, which render the closed-loop system insensitive to the unexpected breakdowns [4]. In [5], a robust tracking controller based on mixed LQ and multiobjective optimization is constructed to solve the problem of actuator failure and control surface impairment. Paper [6] has established an LQ state feedback controller using the algebraic Riccati equation for discrete-time systems with actuator failures, which maintained the reliability of the control system. Paper [7] presents a linear quadratic state feedback control strategy for linear descriptor systems under component faults to guarantee the stability and the desired control performance. Aiming at the actuator faults in a class of nonlinear uncertain systems, an adaptive PFTC method is put forward in [8]. In [9], a Lyapunov-based feedback PFTC method for nonlinear affine systems is proposed considering both additive and loss-of-effectiveness faults. For a class of overactuated nonlinear systems, a PFTC which can automatically distribute control efforts to offset the effect of actuator fault is proposed in [10]. In [11], a PFTC scheme based on nonlinear PID backstepping is proposed for a quadrotor unmanned aerial vehicle to ensure robustness to actuator faults and parameter changes. However, the lack of online feedback for fault information in the controller enables the robustness extremely limited. In terms of AFTC, the impacts of faults are usually compensated either by selecting a precomputed control law or by reconfiguring a controller online [4]. It can cope with not only predetermined faults but also sudden faults. Apparently, this mechanism requires the system to detect and identify unknown faults in real time. In [12], the multiple model adaptive estimation (MMAE) method has been introduced to detect and compensate for sensor and actuator failures in the design of the flight control system. Considering disturbances and partial actuator failures in flexible spacecraft, paper [13] presents a robust fault tolerant control scheme using LMI technique. To achieve attitude control objective, a robust reconfigured controller is designed for a satellite launch vehicle under disturbances in [14]. In [15], an adaptive fault tolerant controller is developed for some particular actuator faults in a class of reusable launch. In [16], a robust adaptive nonlinear fault tolerant control method with norm estimation to deal with actuator fault is proposed. Directing at actuator loss-of-effectiveness fault in hypersonic flight vehicle, an adaptive AFTC strategy based on fault observer and backstepping method is sketched in [17]. In [18], a sliding mode fault tolerant controller based on high-order observer and differentiator is designed to achieve attitude tracking control for reusable launch vehicle. Paper [19] proposes a novel sliding mode-based fault tolerant control scheme for reusable launch vehicle under actuator fault, unknown uncertainty, external disturbances, and input limitation simultaneously. In [20], a model predictive fault tolerant controller against actuator faults is proposed for networked control systems. In [21], a discrete-time fault tolerant control system actuated by a state feedback controller in noisy environment is successfully developed. To tolerate the limited faults for launch vehicles, a neural network fault tolerant control method with high accuracy is proposed in [22]. In [23], a stochastic nonlinear AFTC approach is introduced to realize the insensitiveness to system component failures. So far, AFTC has been widely used in the flight control system as it has stronger robustness to various faults compared with PFTC [4].

With the development of control theory, more and more control methods are applied to the design of the launch vehicle control system. In [24], an adaptive augmented controller based on the PID and augmented control is designed with the performance of antidisturbance and load-relief. Paper [25] proposes a PID-based adaptive augmented fault tolerant controller to realize online controller reconstruction with the pseudo-inverse method for the heavy lift launch vehicle control system. In [26], a Lyapunov-based model reference adaptive PD and PID controllers to cope with time-varying characteristics in satellite launch vehicle (SLV) systems are proposed. To improve robustness and achieve stability in extreme failure situations, a classical adaptive augmentation controller is designed for launch vehicle in [27]. Paper [28] has developed an adaptive controller based on gain scheduling and model reference filter approach for flexible launch vehicles which is simpler and faster than other methods. In [29], a robust adaptive backstepping control method is proposed to realize the desired attitude tracking in the presence of unknown disturbances and uncertainties. In [30], a nonlinear robust adaptive controller augmented by barrier Lyapunov function is constructed to assure robust tracking of the guidance commands for launch vehicles. Paper [31] explores a neural network (NN)-based adaptive control method with stable online weight-tuning algorithms to conquer the disturbances and uncertainties in flight systems. To improve the robustness and accuracy of the flight control systems for launch vehicle, paper [32] proposes higher order sliding mode (HOSM) control scheme driven by sliding mode disturbance observer (SMDO). Paper [33] has developed a dynamic integral sliding mode control scheme aiming at various perturbations and uncertainties during the fight process. In [34], an integral sliding mode controller based on extended states observer (ESO) is structured to compensate uncertainties and disturbances in the flight process. For a vertical take-off and vertical landing (VTVL) reusable launch vehicle, a nonsingular fast terminal sliding mode control strategy is illustrated in [35]. In [36], a second-order sliding mode controller based on nonlinear disturbance observer is constructed which enhances the robustness of launch vehicles. Paper [37] develops an adaptive-gain multivariable super-twisting sliding mode controller with the unknown bounds of uncertainty and perturbation for reusable launch vehicle. The problem of attitude control is settled by combining sliding mode control and adaptive method in [38]. In [39], a novel active disturbance rejection controller of attitude is designed to attenuate effect of parameter variation and disturbances of launch vehicle. Paper [40] presents a robust active disturbance rejection control approach driven by linear extended state observer so that the launch vehicle system is well decoupled and quite robust. An active disturbance rejection-based trajectory linearization control approach is proposed in [41] to guarantee the ability of anti-interference and low-energy consumption. In [42], a new robust disturbance rejection controller scheme using dynamic inversion technique and extended state observer is designed for launch vehicle attitude control.

Most recently, fruitful results have been obtained in the area of intelligent algorithms and can be utilized to address the complex control problem or improve the control performance [43–45]. The MANN is a class of intelligent systems those possess the storage modular and the read/write mechanisms. The conventional neural networks usually neglect the logical flow control or the external memory and cannot obtain the memory ability by utilizing the trainable parameters [46]. The MANN can mimic the memory mechanisms of the human brain, increasing or decreasing the number of neurons to improve the approximation ability [47]. By properly introducing the MANN in the control design of the launch vehicles, the robustness with respect to the unmodeled dynamics or the system nonlinearities can be improved [48, 49]. However, to the best of our knowledge, the MANN-based control law of the launch vehicle control system has never been reported. Furthermore, the issue of applying the MANN to the adaptive fault tolerant control design of the launch vehicle has never been investigated yet [50].

Therefore, in this paper, we investigate the MANN-based intelligent adaptive fault tolerant control for a class of launch vehicles. Firstly, the attitude dynamic model of the launch vehicles subjected to the actuator faults has been formulated. Secondly, to handle the time-varying disturbances, the second-order disturbance observer has been designed for the launch vehicle. In order to suppress the influence of the unknown nonlinearities, the MANN has been introduced as online approximator. Moreover, several adaptive laws have been proposed to achieve the quick response to the actuator faults and the update of the MANN weights. Finally, a novel MANN-based intelligent adaptive fault tolerant control structure has been established for the launch vehicles. Compared with the existing work, the proposed control algorithm possesses the following advantages:(i)By using the SODO and the MANN, the established control method can solve the tracking control problem of the launch vehicles suffering from time-varying actuator faults and disturbances(ii)As far as the authors know, it is also the first attempt to apply the MANN to the control design of the nonlinear systems, providing a canonical form for the MANN-based intelligent control(iii)By using the proposed method, the boundaries of the disturbances and actuator faults are not required to be known in advance

2. Problem Formulation

2.1. The Attitude Dynamic Model of the Launch Vehicle with Actuator Faults

According to [1], by ignoring the elastic vibration, the long period centroid motion, and the shaking of liquid propellant, the small perturbation equation of the attitude dynamic model of the launch vehicle can be formulated bywhere are the pitch, yaw, and roll angle, respectively; are the angle of attack and angle of sideslip caused by the unknown winds; are the dynamic derivatives, whose physical meanings can be found in [2]; represent the uncertainties existing in , respectively; represent the structural disturbance torques; and denote the three-channel equivalent swing angle of the core engine, respectively.

In this paper, the “+” type configuration of the rocket engines is considered, as shown Figure 1. Obviously, the cone engines complete the cross swing, and the swing angles are defined by . Moreover, four booster engines complete tangential swing, and the swing angles are defined as . The relationship between the channel swing angles and the actual swing angles can be formulated by , where denotes the three-channel equivalent swing angle of the core engine, denotes the actual swing angle of the servo mechanism, and is the time varying control distribution matrix. Define . In practical, the thrustors of the launch vehicle may encounter the undesired faults and loss their effectiveness. In this situation, it can be known thatwhere , is the desired effectiveness matrix, and is the uncertainties existing in .

By defining , then from (1) we can get thatwhere

Note that often possess high-dynamic behavior, and the corresponding disturbances are regarded as time-varying disturbances.

The control objective is to develop a dynamic controller such that desired signal can be tracked by the output of system (1) in the presence of the thrust loss of the launch vehicle and the time-varying and unvarying uncertainties.

In this paper, we make the following assumptions.

Assumption 1. The disturbance torques induced by the structural uncertainties are bounded, i.e., there exists a constant such that . The disturbance torques caused by are first-order time varying, which means that .

Assumption 2. In the vicinity of the equilibrium, the uncertain part of remains unchanged and cannot change the positive or negative characteristics of , respectively. In other words, it is assumed that , where .

2.2. Memory Augmented Neural Networks (MANNs)

Memory augmented neural network (MANN) is a kind of width learning neural network with memory augmented cell, possessing the advantages of high efficiency, adjustable, and strong practicality, as shown in Figure 2. Generally speaking, MANN can be divided into two parts: the neural network computing part and the memory augmented (MA) cell. Firstly, the input signal enters the embedding layer, and the embedding layer calculates and outputs the prediction results. Secondly, the error feedback signal is obtained and sent to the MA cell to perform multiple judgments, including choosing which neural network to extend the neurons and how many neurons to increase or decrease. Finally, the memory information is transmitted back to the neural network, and the final prediction result can be obtained. The structure diagram of the MANN is provided in Figure 2. In this paper, the MANN is utilized to achieve the approximation for the unknown nonlinearities.

The output of the MANN can be described bywhere and are the MANN’s input and output. is the weight matrix, and is the basis function which is chosen as the Gaussian function.where is the width of the Gaussian function and are the center shops. It is known that for an arbitrary real continuous function on a compact set , there exist the following MANN and optimal parameter vectors such thatwhere is the reconstruction error, satisfying that is the supremum of reconstruction error.

3. Main Results

3.1. MANN-Based Adaptive Fault Tolerant Control Law Design

The structure of the proposed MANN-based adaptive fault tolerant control law is given in Figure 3. In the inner loop, a virtual control law has to be designed to force the attitude angular tracking error to converge to zero. To force the angular velocity error to track the virtual control input of the inner loop, the outer loop control law is designed. Because of the disturbances and the actuator failure of the launch vehicle, the second-order disturbance observer is designed in the outer loop. The MANN is utilized to approximate and suppress the adverse effects of the unknown nonlinear part.

In view of the dynamic equation,

The tracking error is defined aswhere is the desired signal and is the virtual controller.

To achieve the control of the inner loop, the virtual controller can be designed as follows:where is a design matrix.

Because of the unavailability of , we have to eliminate its influence by using MANN. Hence, we can get that

For the updating law of the weight matrix of MANN, the adaptive law is designed aswhere is the gain of MANN and is the designed constant.

For unknown constant disturbance , define as the estimated value. The following adaptive law is designed to suppress the adverse effect caused by :where is the adaptive gain and is a designed constant which represents the damping factor .

To obtain the estimated value of time-varying disturbance , the following second-order disturbance observer is utilized:where are the estimated values of , are the auxiliary variables, and are the gain of the SODO.

With regard to input uncertainty , the input is divided into two parts as follows:where is the indirect input of the system and is the compensation input to deal with the input uncertainty. To ensure system stability, the indirect controller can be designed aswhere is a design matrix.

To overcome input uncertainty, the compensation input is designed aswhere the estimated value of , , and we use adaptive method to approximatewhere is the gain of the adaptive law and is a designed constant.

3.2. The Adjustment Strategy of the MANN

In this paper, we propose the adjustment strategy of the MANN. The adjustment strategy includes two parts: the first part is used to determine the sub-NN which should change the nodes and the second part is utilized to determine that the sub-NN should increase or decrease its nodes. Part 1. The following index is defined to judge the contribution of the sub-NN for the fitting effect: where represents the number of nodes of the th sub-NN. A larger indicates that this sub-NN has a larger contribution and will be given priority when increasing the number of nodes, while a smaller indicates that this sub-NN has a small contribution and will be reduced first when the number of nodes is reduced. Part 2. The following index is introduced which is obtained by integrating the error within a time span: where represents the start time of the th sampling and represents the time length of the sampling. By comparing the size of and the set constants , we can judge the increase or decrease in the number of nodes. In detail, if , the error is too large and does not reach the predetermined value, and the nodes should be added to ensure the fitting effect; if , the error satisfies the requirement and the nodes can be reduced to save the calculation resource. Moreover, it should be pointed out that when adding nodes, the number of nodes is increased by reducing the distance between nodes and then increasing node density. To reduce nodes, first reduce and remove nodes on both sides.

3.3. Stability Analysis

Theorem 1. Considering system (8), suppose that Assumptions 1 and 2 are satisfied. If the control law is designed as (10), (16), and (17), the adaptive laws are designed as (18), (13), and (12), then the closed-loop control system in the existence of disturbances and is stable, and all the signals are bounded.

Proof. The disturbance estimation error of the SODO is defined as follows:Hence, we can calculate thatwhere . Define . From the definition of the tracking error, we can get the following equations:Consider the Lyapunov function asThe derivative of can be given byFurther, computation shows thatUtilizing Young’s inequalities, we know thatwhere . Moreover, it can be checked thatwhere . Hence, the following inequality can be known:By using Young’s inequalities again, it can be obtained thatCombining (25), (29), and (30) generates thatConsidering the adaptive lawswe can rewrite (31) asBy definingwe know that for any time,Further, derivations yield that ,Therefore, from (36), it can be concluded that the system states , the disturbance estimation errors of the SODO , and the adaptive estimation errors are all stable and bounded. Furthermore, it can be easily known that are also bounded. Therefore, the stability of the closed-loop system and the boundness of all the signals can be verified. The proof is complete.

4. Simulation Study

In order to evaluate the effectiveness and performance of the neural network-based adaptive fault tolerant control (NN-AFTC) law, a simulation experiment was conducted based on the mathematical model described by (8). It is assumed that the launch vehicle rises at a fixed attitude angle in the air. Moreover, the disturbance observer-based NN (DOBNN) control law and the neural network-based adaptive controller are introduced into the simulation to show the distinctions of the control performance.

In the simulation, the constant and changing disturbances are set as

The unknown nonlinearities are , where are unknown parameters. For the proposed method, the control gain matrices are selected as and the adaptive parameters are selected as and . The node number of the neural network is 9, and the approximating area is .

The simulation results are shown in Figures 4–9. Obviously, under the actuator faults and constant or changing external disturbances, the proposed control method can achieve satisfactory results. The tracking errors can converge into a desired value, and all of the signals of the closed-loop control system are bounded during the whole tracking process. However, the DOBNN controller may induce undesired fluctuation, and the NNAC method may generate unacceptable tracking errors. Therefore, it can be concluded that the proposed method can guarantee control performance under the disturbances and actuator faults and can possess advantages with respect to the other two control laws.

5. Conclusions

This paper proposed a novel MANN-based intelligent adaptive fault tolerant control for a class of launch vehicles. The second-order disturbance observer has been introduced to exactly estimate and compensate the time-varying disturbances, the MANN has been introduced to suppress the adverse influence of the unknown nonlinearities, and several adaptive laws have been proposed to quickly handle the actuator faults. The closed-loop stability analysis has been completed, and all the signals are ensured to be bounded. Simulation results show that by using the proposed control algorithm, the tracking errors can converge into a desired value, while the DOBNN controller may induce undesired fluctuation and the NNAC method may generate unacceptable tracking errors. In the future, the MANN-based stochastic adaptive control for the launch vehicles will be considered.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References

J. Yun-Chun, “Fault diagnosis research on the control systems of the launch vehicle based on fault dictionaries,” Journal of Institute of Command and Technology, vol. 23, pp. 1623–1634, 2001.
View at: Google Scholar
L. I. Hong, “The developing roadmap of intelligent launch vehicle,” Astronautical Systems Engineering Technology, 2017.
View at: Google Scholar
Y. Zhang and J. Jiang, “Bibliographical review on reconfigurable fault-tolerant control systems,” Annual Reviews in Control, vol. 32, no. 2, pp. 229–252, 2008.
View at: Publisher Site | Google Scholar
I. Sadeghzadeh and Y. Zhang, A Review on Fault-Tolerant Control for Unmanned Aerial Vehicles (UAVs), Infotech, St. Louis, MO, USA, 2011.
F. Fang Liao, J. L. Jian Liang Wang, and G. H. Guang-Hong Yang, “Reliable robust flight tracking control: an LMI approach,” IEEE Transactions on Control Systems Technology, vol. 10, no. 1, pp. 76–89, 2002.
View at: Publisher Site | Google Scholar
Y. Yang, G. H. Yang, and Y. C. Soh, “Reliable control of discrete-time systems with actuator failure,” IEE Proceedings-Control Theory and Applications, vol. 147, no. 4, pp. 428–432, 2002.
View at: Google Scholar
Y. Bo and Z. Qingling, “Reliable linear quadratic state feedback control for descriptor systems,” Journal of Northeastern University, vol. 24, no. 1, pp. 39–41, 2003.
View at: Google Scholar
A. Nasiri, S. K. Nguang, A. Swain et al., “Passive actuator fault tolerant control for a class of MIMO nonlinear systems with uncertainties,” International Journal of Control, vol. 92, pp. 1–20, 2017.
View at: Google Scholar
M. Benosman and K.-Y. Lum, “Passive actuators’ fault-tolerant control for affine nonlinear systems,” IEEE Transactions on Control Systems Technology, vol. 18, no. 1, pp. 152–163, 2010.
View at: Publisher Site | Google Scholar
R. Wang and J. Wang, “Passive actuator fault-tolerant control for a class of overactuated nonlinear systems and applications to electric vehicles,” IEEE Transactions on Vehicular Technology, vol. 62, no. 3, pp. 972–985, 2013.
View at: Publisher Site | Google Scholar
R. R. Benrezki, M. Tadjine, F. Yacef et al., “Passive fault tolerant control of quadrotor UAV using a nonlinear PID,” in Proceedings of the IEEE International Conference on Robotics & Biomimetics, IEEE, Dali, Yunnan, China, December 2015.
View at: Google Scholar
S. S. Banda, “Multiple model adaptive algorithms for detecting and compensating sensor and actuator/surface failures in aircraft flight control systems,” International Journal of Robust & Nonlinear Control, vol. 9, no. 14, pp. 1051–1070, 2015.
View at: Google Scholar
R. Zhang, J. Qiao, T. Li, and L. Guo, “Robust fault-tolerant control for flexible spacecraft against partial actuator failures,” Nonlinear Dynamics, vol. 76, no. 3, pp. 1753–1760, 2014.
View at: Publisher Site | Google Scholar
R. K. Das, S. Sen, and S. Dasgupta, “Robust and fault tolerant controller for attitude control of a satellite launch vehicle,” IET Control Theory & Applications, vol. 1, no. 1, pp. 304–312, 2007.
View at: Publisher Site | Google Scholar
L. Zhang, C. Wei, R. Wu, and N. Cui, “Adaptive fault-tolerant control for a VTVL reusable launch vehicle,” Acta Astronautica, vol. 159, no. 6, pp. 362–370, 2019.
View at: Publisher Site | Google Scholar
C. Hu, Z. Gao, Y. Ren, and Y. Liu, “A robust adaptive nonlinear fault-tolerant controller via norm estimation for reusable launch vehicles,” Acta Astronautica, vol. 128, pp. 685–695, 2016.
View at: Publisher Site | Google Scholar
Y. Ji, H. Zhou, and Q. Zong, “Adaptive active fault-tolerant control of generic hypersonic flight vehicles,” Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, vol. 229, no. 2, 2014.
View at: Google Scholar
Q. Dong, Q. Zong, B. Tian et al., “Adaptive disturbance observer-based finite-time continuous fault-tolerant control for reentry RLV,” International Journal of Robust and Nonlinear Control, vol. 27, no. 18, 2017.
View at: Google Scholar
Y. Zhang, A. Li, B. Huang et al., “Sliding-mode based adaptive fault tolerant control for re-entry reusable launch vehicle,” in International Conference on Mechanical, IEEE, Athens, Greece, July 2017.
View at: Google Scholar
X. Luo, J. Zhang, Y. Zhang et al., “Active fault-tolerant control for networked control systems with data packet dropout via predictive control,” in Proceedings of the 30th Chinese Control Conference, Yantai, China, July 2011.
View at: Google Scholar
M. Mahmoud, “Sufficient conditions for the stabilization of feedback delayed discrete time fault tolerant control systems,” International Journal of Innovative Computing, Information and Control, vol. 5, no. 5, pp. 1137–1146, 2009.
View at: Google Scholar
Z. Haiyang, W. Yansheng, C. Yu, Y. Yunfei, and X. Lijie, “A neural network fault- tolerant control method for launch vehicles with thrust decline,” Aerospace Controls, vol. 37, pp. 3–9, 2019.
View at: Publisher Site | Google Scholar
H. Wu and M. Bai, “Stochastic stability analysis and synthesis for nonlinear fault tolerant control systems based on the t-s fuzzy model,” International Journal of Innovative Computing Information & Control Ijicic, vol. 6, no. 9, pp. 3989–4000, 2010.
View at: Google Scholar
C. Nai-Gang, C. Cheng, P. Zhe et al., “Adaptive augmented disturbance rejection and load-relief control for launch vehicle,” Missiles and Space Vehicles, 2017.
View at: Google Scholar
L. Zhang, C. Wei, L. Jing et al., “Heavy lift launch vehicle technology of adaptive augmented fault tolerant control,” in Proceedings of the 2016 IEEE Chinese Guidance, Navigation and Control Conference (CGNCC), IEEE, Nanjing, China, January 2017.
View at: Google Scholar
A. P. Nair, N. Selvaganesan, and V. R. Lalithambika, “Lyapunov based PD/PID in model reference adaptive control for satellite launch vehicle systems,” Aerospace Science and Technology, vol. 51, pp. 70–77, 2016.
View at: Publisher Site | Google Scholar
V. Brinda, A. Narayanan, S. Us, and W. A. Kishore, “Classical adaptive augmentation control for a typical second generation launch vehicle,” IFAC-PapersOnLine, vol. 49, no. 1, pp. 670–675, 2016.
View at: Publisher Site | Google Scholar
A. Khoshnood, J. Roshanian, and A. Khaki-Sedig, “Model reference adaptive control for a flexible launch vehicle,” in Proceedings of the Institution of Mechanical Engineers, Part I: Journal of Systems and Control Engineering, Thousand Oaks, CA, USA, February 2008.
View at: Google Scholar
Z. Wang, Z. Wu, and Y. Du, “Robust adaptive backstepping control for reentry reusable launch vehicles,” Acta Astronautica, vol. 126, pp. 258–264, 2016.
View at: Publisher Site | Google Scholar
S. Mathavaraj and R. Padhi, “Optimally allocated nonlinear robust control of a reusable launch vehicle during re-entry,” Unmanned Systems, vol. 8, no. 1, pp. 33–48, 2020.
View at: Publisher Site | Google Scholar
Y. D. Song, X. H. Liao, M. D. Gheorghiu et al., “Control of reusable launch vehicle using neuro-adaptive approach,” in Proceedings of the International Conference on Advances in Neural Networks, Springer Berlin Heidelberg, Heidelberg, Germany, June 2005.
View at: Google Scholar
J. E. Stott and Y. B. Shtessel, “Launch vehicle attitude control using sliding mode control and observation techniques,” Journal of the Franklin Institute, vol. 349, no. 2, pp. 397–412, 2012.
View at: Publisher Site | Google Scholar
Z. Wang, L. Liu, Y. Wang et al., “Dynamic integral sliding mode for launch vehicle attitude control system,” in Proceedings of the Control & Decision Conference, IEEE, Taiyuan, China, July 2012.
View at: Google Scholar
L. Helong, H. E. Yingzi, L. Gaotong et al., “ESO-based integral sliding mode control design for reusable launch vehicle,” Aerospace Control and Application, 2016.
View at: Google Scholar
Z. Liang, W. Changzhu, W. Rong et al., “Fixed-time extended state observer based non-singular fast terminal sliding mode control for a VTVL reusable launch vehicle,” Aerospace Science and Technology, vol. 82–83, pp. 70–79, 2018.
View at: Google Scholar
T. Bailing, Z. Qun, W. Fang et al., “Smooth second order sliding mode control for reusable launch vehicle in reentry phase,” in Proceedings of the Control & Decision Conference, IEEE, Taiyuan, China, June 2012.
View at: Google Scholar
Q. Dong, Q. Zong, B. Tian et al., “Adaptive‐gain multivariable super‐twisting sliding mode control for reentry RLV with torque perturbation,” International Journal of Robust and Nonlinear Control, vol. 7, no. 27, 2017.
View at: Google Scholar
Y. Xia, Z. Zhu, M. Fu, and S. Wang, “Attitude tracking of rigid spacecraft with bounded disturbances,” IEEE Transactions on Industrial Electronics, vol. 58, no. 2, pp. 647–659, 2011.
View at: Publisher Site | Google Scholar
W. Ye and C. Haoyu, “Active disturbance rejection control of attitude for launch vehicle,” Journal of Projectiles, Rockets, Missiles and Guidance, vol. 26, no. 10, pp. 2563–2575, 2015.
View at: Google Scholar
C. Shangshang and H. E. Yingzi, “Robust active disturbance rejection control for a reusable launch vehicle,” Aerospace Control and Application, 2017.
View at: Google Scholar
X. Shao and H. Wang, “Active disturbance rejection based trajectory linearization control for hypersonic reentry vehicle with bounded uncertainties,” ISA Transactions, vol. 54, pp. 27–38, 2015.
View at: Publisher Site | Google Scholar
J. Song, Z. Ren, and X. Song, “New integrated robust disturbance rejection control method for reusable launch vehicle attitude controller design,” in Proceedings of the International Conference on Electrical & Control Engineering, IEEE, Yichang, China, September 2011.
View at: Google Scholar
N. Cingillioglu and A. Russo, “Deep logic: end-to-end logical reasoning,” 2018, https://arxiv.org/abs/1805.07433.
View at: Google Scholar
J. Zeng, J. Li, Y. Song, C. Gao, and M. R. Lyu, “Topic memory networks for short text classification,” in Proceedings of the 2018 Conference on Empirical Methods in Natural Language (EMNLP 2018), Copenhagen, Denmark, September 2018.
View at: Publisher Site | Google Scholar
S. Sukhbaatar, A. Szlam, J. Weston, and R. Fergus, “End-to-end memory networks,” Computer Science, 2015.
View at: Google Scholar
L. Zhao, J. Yu, C. Lin, and Y. Ma, “Adaptive neural consensus tracking for nonlinear multiagent systems using finite-time command filtered backstepping,” IEEE Transactions on Systems, Man, and Cybernetics: Systems, vol. 48, no. 11, pp. 2003–2012, 2018.
View at: Publisher Site | Google Scholar
A. Kumar, O. Irsoy, P. Ondruska et al., “Ask me anything: dynamic memory networks for natural language processing,” 2015, https://arxiv.org/abs/1506.07285.
View at: Google Scholar
T. S. Jayram, Y. Bouhadjar, and R. L. McAvoy, “Learning to remember, forget and ignore using attention control in memory,” 2018, https://arxiv.org/abs/1809.11087.
View at: Google Scholar
D. Yogatama, Y. Miao, and G. Melis, “Memory architectures in recurrent neural network language models,” Computer Science, 2018.
View at: Google Scholar
L. Zhao, J. Yu, and Q.-G. Wang, “Finite-time tracking control for nonlinear systems via adaptive neural output feedback and command filtered backstepping,” IEEE Transactions on Neural Networks and Learning Systems, vol. 32, no. 4, pp. 1474–1485, 2021.
View at: Publisher Site | Google Scholar

Copyright

Copyright © 2021 Haipeng Chen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

PDF Download Citation

Download other formats

Order printed copies