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Three-dimensional finite-time optimal cooperative guidance with integrated information fusion observer
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作者 Yiao Zhan Linwei Wang Di Zhou 《Defence Technology(防务技术)》 2025年第4期12-28,共17页
Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an inte... Intercepting high-maneuverability hypersonic targets in near-space environments poses significant challenges due to their extreme speeds and evasive capabilities.To address these challenges,this study presents an integrated approach that combines a Three-Dimensional Finite-Time Optimal Cooperative Guidance Law(FTOC)with an Information Fusion Anti-saturation Predefined-time Observer(IFAPO).The proposed FTOC guidance law employs a nonlinear,non-quadratic finite-time optimal control strategy designed for rapid convergence within the limited timeframes of near-space interceptions,avoiding the need for remaining flight time estimation or linear decoupling inherent in traditional methods.To complement the guidance strategy,the IFAPO leverages multi-source information fusion theory and incorporates anti-saturation mechanisms to enhance target maneuver estimation.This method ensures accurate and real-time prediction of target acceleration while maintaining predefined convergence performance,even under complex interception conditions.By integrating the FTOC guidance law and IFAPO,the approach optimizes cooperative missile positioning,improves interception success rates,and minimizes fuel consumption,addressing practical constraints in military applications.Simulation results and comparative analyses confirm the effectiveness of the integrated approach,demonstrating its capability to achieve cooperative interception of highly maneuvering targets with enhanced efficiency and reduced economic costs,aligning with realistic combat scenarios. 展开更多
关键词 Anti-saturation predefined-time observer Nonlinear finite-time optimal control Three-dimensional guidance Information fusion
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Adaptive backstepping finite-time sliding mode control of spacecraft attitude tracking 被引量:9
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作者 Chutiphon Pukdeboon 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第4期826-839,共14页
This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertaint... This paper investigates the finite-time attitude tracking problem for rigid spacecraft. Two backstepping finite-time slid- ing mode control laws are proposed to solve this problem in the presence of inertia uncertainties and external disturbances. The first control scheme is developed by combining sliding mode con- trol with a backstepping technique to achieve fast and accurate tracking responses. To obtain higher tracking precision and relax the requirement of the upper bounds on the uncertainties, a se- cond control law is also designed by combining the second or- der sliding mode control and an adaptive backstepping technique. This control law provides complete compensation of uncertainty and disturbances. Although it assumes that the uncertainty and disturbances are bounded, the proposed control law does not require information about the bounds on the uncertainties and disturbances. Finite-time convergence of attitude tracking errors and the stability of the closed-loop system are ensured by the Lya- punov approach. Numerical simulations on attitude tracking control of spacecraft are provided to demonstrate the performance of the proposed controllers. 展开更多
关键词 attitude tracking control sliding mode control back-stepping design finite-time convergence.
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Finite-time adaptive sliding mode control for heavyweight airdrop operations 被引量:4
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作者 Ri Liu Xiuxia Sun +1 位作者 Wenhan Dong Dong Wang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第2期338-346,共9页
This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior k... This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior knowledge of the bounds. On the basis of feedback linearization of the aircraft-cargo motion system, a novel integral sliding mode flight control law with gains adaptation is proposed. It contains a nominal control law used to achieve finite-time stabilization performance and a compensated control law used to reject the uncertainties. The switching gains of the compensated control law are tuned using adaptation algorithms, and the knowledge of the bounds of the uncertainties is not required to be known in advance. Meanwhile, the severe chattering of the sliding mode control that caused by high switching gains is effectively reduced. The controller and its performance are evaluated on a transport aircraft performing a maximum load airdrop task in a number of simulation scenarios. 展开更多
关键词 flight control nonlinear system sliding mode control adaptive control finite-time stability
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Finite-time coordination control for formation flying spacecraft 被引量:2
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作者 Yong Guo Shenmin Song Liwei Deng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第5期859-867,共9页
This paper investigates a distributed coordination control scheme using an adaptive terminal sliding mode for formation flying spacecraft with coupled attitude and translational dynamics. In order to overcome the sing... This paper investigates a distributed coordination control scheme using an adaptive terminal sliding mode for formation flying spacecraft with coupled attitude and translational dynamics. In order to overcome the singularity of the traditional fast terminal sliding manifold, a novel fast terminal sliding manifold is given. And then, based on the adaptive control method, a continuous robust coordinated controller is designed to compensate external disturbances and to alleviate the chattering phenomenon. The theoretical analysis shows that the coordinated controller can guarantee the finite-time stability of the overall closed-loop system through local information exchange, and numerical simulations also demonstrate its effectiveness. 展开更多
关键词 formation flying coordinated control attitude and translational coupling finite-time stability adaptive control.
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Analysis of finite-time practical stability for time-varying polytopic systems 被引量:1
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作者 Zhong Zhen Duan Guangren 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2009年第1期112-119,共8页
The problem of finite-time practical stability (FTPS) for time-varying polytopic systems is discussed. Three equivalent conditions for FTPS are first proposed. To facilitate the system analysis, a sufficient linear ... The problem of finite-time practical stability (FTPS) for time-varying polytopic systems is discussed. Three equivalent conditions for FTPS are first proposed. To facilitate the system analysis, a sufficient linear matrix inequality (LMI) criterion on the FTPS is further provided. The definition of finite-time practical boundedness and a sufficient LMI criterion are also provided to overcome the exogenous disturbance. A numerical example is used to illustrate the effect of the proposed approach. 展开更多
关键词 polytopic systems linear matrix inequality finite-time control practical stability.
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Finite-time attitude tracking control for spacecraft without angular velocity measurements 被引量:1
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作者 Li Yuan Guangfu Ma +1 位作者 Chuanjiang Li Boyan Jiang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2017年第6期1174-1185,共12页
The output feedback control for spacecraft attitude tracking system is investigated in this study. It is assumed that angular velocity measurements are not available for feedback control.A technique named adding power... The output feedback control for spacecraft attitude tracking system is investigated in this study. It is assumed that angular velocity measurements are not available for feedback control.A technique named adding power integrator(API) is adopted to estimate the pseudo-angular-velocity. Then we design a finite-time attitude control law, which only utilizes the relative attitude information. The stability analyses of the feedback system are proved as well, which shows the attitude tracking errors will converge into a region of zero even the external disturbances exist. The simulation results illustrate the high precision and robust attitude control performance of the proposed control strategy. 展开更多
关键词 output feedback spacecraft attitude stabilization finite-time control
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Finite-time tracking control and vibration suppression based on the concept of virtual control force for flexible two-link space robot 被引量:1
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作者 Rong-Hua Lei Li Chen 《Defence Technology(防务技术)》 SCIE EI CAS CSCD 2021年第3期874-883,共10页
The dynamic modeling, finite-time trajectory tracking control and vibration suppression of a flexible two-link space robot are studied. Firstly, the dynamic model of the system is established by combining Lagrange met... The dynamic modeling, finite-time trajectory tracking control and vibration suppression of a flexible two-link space robot are studied. Firstly, the dynamic model of the system is established by combining Lagrange method with assumed mode method. In order to ensure that the base attitude and the joints of space robot can reach the desired positions within a limited time, a non-singular fast terminal sliding mode(NFTSM) controller is designed, which realizes the finite-time convergence of the trajectory tracking errors. Subsequently, for the sake of suppressing the vibrations of flexible links, a hybrid trajectory based on the concept of the virtual control force is developed, which can reflect the flexible modes and the trajectory tracking errors simultaneously. By modifying the original control scheme, a NFTSM hybrid controller is proposed. The hybrid control scheme can not only realized attitude stabilization and trajectory tracking of joints in finite time, but also provide a new method of vibration suppression. The simulation results verify the effectiveness of the designed hybrid control strategy. 展开更多
关键词 finite-time Terminal sliding mode Flexible links Vibration suppression Virtual control force
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Finite-time control of formation system for multiple flight vehicles subject to actuator saturation 被引量:1
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作者 ZHAO Enjiao ZHONG Zenan ZHENG Xin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2020年第5期1019-1030,共12页
This paper investigates the problem of formation tracking control for multiple flight vehicle(MFV) system considering actuator saturation constraints. First, the formation tracking control model is established. Then, ... This paper investigates the problem of formation tracking control for multiple flight vehicle(MFV) system considering actuator saturation constraints. First, the formation tracking control model is established. Then, the problem of formation control of the MFV system is converted to the convergence of a dynamical system, which is obtained by using the differential geometry theory.A class of saturation functions is introduced, and on this basis a second-order finite-time formation control protocol is developed.With the help of the homogeneous theory and Lasalle's invariance principle, it is theoretically proved that the designed formation protocol could complete the formation task in finite time, and the control inputs are shown to remain within their available actuating limits. Finally, simulations are performed to verify the effectiveness of the scheme. 展开更多
关键词 formation control multiple flight vehicle(MFV) finite-time actuator saturation
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Finite-time stability and stabilization of Markovian switching stochastic systems with impulsive effects 被引量:1
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作者 Ying Yang Junmin Li Guopei Chen 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第2期254-260,共7页
Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finit... Many practical systems in physics, biology, engineer- ing and information science exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynami- cal processes. The problems of finite-time stab!lity analysis are investigated for a class of Markovian switching stochastic sys- tems, in which exist impulses at the switching instants. Multiple Lyapunov techniques are used to derive sufficient conditions for finite-time stochastic stability of the overall system. Furthermore, a state feedback controller, which stabilizes the closed loop sys- tems in the finite-time sense, is then addressed. Moreover, the controller appears not only in the shift part but also in the diffu- sion part of the underlying stochastic subsystem. The results are reduced to feasibility problems involving linear matrix inequalities (LMIs). A numerical example is presented to illustrate the proposed methodology. 展开更多
关键词 finite-time stability impulsive systems Markovian switching Brownian motion linear matrix inequalities (LMIs) sta- bilization.
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Finite-time fault-tolerant control of teleoperating cyber physical system against faults 被引量:1
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作者 PAN Chengwei LIU Xia +1 位作者 CHEN Yong LI Meng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2023年第2期469-478,共10页
This paper studies a finite-time adaptive fractionalorder fault-tolerant control(FTC)scheme for the slave position tracking of the teleoperating cyber physical system(TCPS)with external disturbances and actuator fault... This paper studies a finite-time adaptive fractionalorder fault-tolerant control(FTC)scheme for the slave position tracking of the teleoperating cyber physical system(TCPS)with external disturbances and actuator faults.Based on the fractional Lyapunov stability theory and the finite-time stability theory,a fractional-order nonsingular fast terminal sliding mode(FONFTSM)control law is proposed to promote the tracking and fault tolerance performance of the considered system.Meanwhile,the adaptive fractional-order update laws are designed to cope with the unknown upper bounds of the unknown actuator faults and external disturbances.Furthermore,the finite-time stability of the closed-loop system is proved.Finally,comparison simulation results are also provided to show the validity and the advantages of the proposed techniques. 展开更多
关键词 teleoperating cyber physical system(TCPS) fractional Lyapunov stability fault-tolerant control(FTC) finite-time stability
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Integrated guidance and control design method based on finite-time state observer 被引量:1
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作者 MA Ping ZHANG Denghui +1 位作者 WANG Songyan CHAO Tao 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第6期1251-1262,共12页
A composited integrated guidance and control(IGC) algorithm is presented to tackle the problem of the IGC design in the dive phase for the bank-to-turn(BTT) vehicle with the inaccuracy information of the line-of-sight... A composited integrated guidance and control(IGC) algorithm is presented to tackle the problem of the IGC design in the dive phase for the bank-to-turn(BTT) vehicle with the inaccuracy information of the line-of-sight(LOS) rate. For the sake of theoretical derivation, an IGC model in the pitch plane is established. The high-order finite-time state observer(FTSO), with the LOS angle as the single input, is employed to reconstruct the states of the system online. Besides, a composited IGC algorithm is presented via the fusion of back-stepping and dynamic inverse. Compared with the traditional IGC algorithm, the proposed composited IGC method can attenuate effectively the design conservation of the flight control system, while the LOS rate is mixed with noise. Extensive experiments have been performed to demonstrate that the proposed approach is globally finite-time stable and strongly robust against parameter uncertainty. 展开更多
关键词 integrated guidance and control(IGC) finite-time state observer(FTSO) back-to-turn(BTT) vehicle composited control
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Finite-time State Feedback Stabilization Method for a Class of Flexible Manipulators
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作者 王轶卿 李胜 陈庆伟 《Defence Technology(防务技术)》 SCIE EI CAS 2010年第4期284-288,共5页
Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators ... Aimed at the finite-time stabilization problem of a class of flexible manipulators,a finite-time state feedback stabilization controller was proposed in this paper.Firstly,the nonlinear model of flexible manipulators was transformed into linear system through the exact state feedback linearization,and then using the finite time stabilization control method of the linear system,a finite-time state feedback stabilization controller was designed for the flexible manipulators.Furthermore,it was proved that all the states of flexible manipulators could be stabilized to equilibrium in finite-time under the proposed controller.The simulation results show that the performance of the flexible manipulators under the proposed finite-time state feedback controller is better than the traditional state-feedback controller.The proposed finite-time stabilization controller can improve the performance of the flexible manipulators. 展开更多
关键词 automatic control technology flexible manipulators finite-time stabilization exact state feedback linearization
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Group cooperative midcourse guidance law design considering time-to-go
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作者 ZHANG Ruitao FANG Yangwang +2 位作者 CHEN Zhan GUO Hang FU Wenxing 《Journal of Systems Engineering and Electronics》 2025年第3期835-853,共19页
To solve the problem of providing the best initial situation for terminal guidance when multiple missiles intercept multiple targets,a group cooperative midcourse guidance law(GCMGL)considering time-to-go is proposed.... To solve the problem of providing the best initial situation for terminal guidance when multiple missiles intercept multiple targets,a group cooperative midcourse guidance law(GCMGL)considering time-to-go is proposed.Firstly,a threedimensional(3D)guidance model is established and a cooperative trajectory shaping guidance law is given.Secondly,for estimating the unknown target maneuvering acceleration,an adaptive disturbance observer(ADO)is designed,combining finitetime theory with a radial basis function(RBF)neural network,and the convergence of the estimation error is proven using Lyapunov stability theory.Then,to ensure time-to-go cooperation among missiles within the same group and across different groups,the group consensus protocols of virtual collision point mean and the inter-group cooperative consensus protocol are designed respectively.Based on the group consensus protocols,the virtual collision point cooperative guidance law is given,and the finite-time convergence is proved by Lyapunov stability theory.Simultaneously,combined with trajectory shaping guidance law,virtual collision point cooperative guidance law and the intergroup cooperative consensus protocol,the design of GCMGL considering time-to-go is given.Finally,numerical simulation results show the effectiveness and the superiority of the proposed GCMGL. 展开更多
关键词 cooperative midcourse guidance virtual collision point TIME-TO-GO finite-time theory group consensus protocol
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Non-singular fast terminal sliding mode control for roll-pitch seeker based on extended state observers
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作者 XIAO Bowen XIA Qunli 《Journal of Systems Engineering and Electronics》 2025年第2期537-551,共15页
For air-to-air missiles, the terminal guidance’s preci-sion is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode contr... For air-to-air missiles, the terminal guidance’s preci-sion is directly contingent upon the tracking capabilities of the roll-pitch seeker. This paper presents a combined non-singular fast terminal sliding mode control method, aimed at resolving the frame control problem of roll-pitch seeker tracking high maneu-vering target. The sliding mode surface is structured around the principle of segmentation, which enables the control system’s rapid attainment of the zero point and ensure global fast conver-gence. The system’s state is more swiftly converged to the slid-ing mode surface through an improved adaptive fast dual power reaching law. Utilizing an extended state observer, the overall disturbance is both identified and compensated. The validation of the system’s stability and its convergence within a finite-time is grounded in Lyapunov’s stability criteria. The performance of the introduced control method is confirmed through roll-pitch seeker tracking control simulation. Data analysis reveals that newly proposed control technique significantly outperforms existing sliding mode control methods by rapidly converging the frame to the target angle, reduce the tracking error of the detec-tor for the target, and bolster tracking precision of the roll-pitch seeker huring disturbed conditions. 展开更多
关键词 air-to-air missile roll-pitch seeker finite-time con-vergence combined sliding mode control extended state observer
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随机奇异T-S模糊系统的有限时间鲁棒H_∞控制 被引量:2
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作者 邢双云 张庆灵 朱宝彦 《东北大学学报(自然科学版)》 EI CAS CSCD 北大核心 2014年第11期1521-1524,1534,共5页
讨论了一类具有伊藤类型随机奇异T-S模糊系统有限时间鲁棒H∞控制问题.首先,针对含有界干扰的随机奇异系统,采用T-S模糊模型进行系统描述,同时给出了随机奇异T-S模糊系统有限时间随机稳定和有限时间鲁棒H∞控制问题的定义;然后,根据有... 讨论了一类具有伊藤类型随机奇异T-S模糊系统有限时间鲁棒H∞控制问题.首先,针对含有界干扰的随机奇异系统,采用T-S模糊模型进行系统描述,同时给出了随机奇异T-S模糊系统有限时间随机稳定和有限时间鲁棒H∞控制问题的定义;然后,根据有限时间稳定性理论,构造Lyapunov-Krasovskii函数,通过对状态反馈系统的分析,利用线性矩阵不等式方法给出该系统的有限时间鲁棒H∞控制器有解的充分条件;最后,数值算例说明了该设计方法的有效性. 展开更多
关键词 随机奇异T-S模糊系统 鲁棒H∞控制 有限时间随机稳定 伊藤微分 线性矩阵不等式
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考虑连锁故障的多工况电力系统功角稳定性分析 被引量:3
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作者 马静 高翔 +1 位作者 李益楠 王增平 《中国电机工程学报》 EI CSCD 北大核心 2016年第14期3837-3844,共8页
针对连锁故障引发系统大停电等安全稳定问题,提出一种考虑连锁故障的多工况电力系统功角稳定性分析方法。首先,计及保护/断路器不确定动作、系统硬件失效等随机事件,确定基于潮流转移理论的系统运行工况,并计算各工况间转移概率矩阵。然... 针对连锁故障引发系统大停电等安全稳定问题,提出一种考虑连锁故障的多工况电力系统功角稳定性分析方法。首先,计及保护/断路器不确定动作、系统硬件失效等随机事件,确定基于潮流转移理论的系统运行工况,并计算各工况间转移概率矩阵。然后,建立了考虑连锁故障的离散Markov多工况电力系统模型,并构造了含有该模型的李雅普诺夫函数。在此基础上,使用迭代法推导了满足干扰衰减度γ的鲁棒随机稳定性判据,并借助线性矩阵不等式(linear matrix inequalities,LMI)中的可行性问题,分析系统稳定性。IEEE16机68节点系统时域仿真结果表明该方法能够有效判别电力系统多工况变化时的功角稳定性,与时域仿真法相比,无需获取系统运行轨迹,且计算量较小,简单易实现。 展开更多
关键词 多工况电力系统 连锁故障 Markov系统 功角稳定性 鲁棒随机稳定性判据
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Integral terminal sliding mode control for nonlinear systems 被引量:6
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作者 GUO Jianguo LIU Yuchao ZHOU Jun 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2018年第3期571-579,共9页
This paper proposes a fast integral terminal sliding mode(ITSM) control method for a cascaded nonlinear dynamical system with mismatched uncertainties. Firstly, an integral terminal sliding mode surface is presented... This paper proposes a fast integral terminal sliding mode(ITSM) control method for a cascaded nonlinear dynamical system with mismatched uncertainties. Firstly, an integral terminal sliding mode surface is presented, which not only avoids the singularity in the traditional terminal sliding mode, but also addresses the mismatched problems in the nonlinear control system. Secondly, a new ITSM controller with finite convergence time based on the backstepping technique is derived for a cascaded nonlinear dynamical system with mismatched uncertainties. Thirdly, the convergence time of ITSM is analyzed, whose convergence speed is faster than those of two nonsingular terminal sliding modes.Finally, simulation results are presented in order to evaluate the effectiveness of ITSM control strategies for mismatched uncertainties. 展开更多
关键词 terminal sliding mode(TSM) finite-time convergence mismatched disturbance Lyapunov stability nonlinear systems
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Three-dimensional cooperative guidance law for multiple missiles with impact angle constraint 被引量:3
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作者 YANG Biao JING Wuxing GAO Changsheng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2020年第6期1286-1296,共11页
This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angl... This paper proposes a cooperative guidance law for attacking a ground target with the impact angle constraint based on the motion camouflage strategy in the line-of-sight(LOS)frame.A dynamic model with the impact angle constraint is established according to the relative motion between multiple missiles and the target.The process of cooperative guidance law design is divided into two stages.Firstly,based on the undirected graph theory,a new finite-time consensus protocol on the LOS direction is derived to guarantee relative distances reach consensus.And the value of acceleration command is positive,which is beneficial for engineering realization.Secondly,the acceleration command on the normal direction of the LOS is designed based on motion camouflage and finite-time convergence,which can ensure the missiles reach the target with the desired angle and satisfy the motion camouflage state.The finitetime stability analysis is proved by the Lyapunov theory.Numerical simulations for stationary and maneuver targets have demonstrated the effectiveness of the cooperative guidance law proposed. 展开更多
关键词 cooperative guidance law motion camouflage impact angle constraint finite-time
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Application of hybrid robust three-axis attitude control approach to overactuated spacecraft——A quaternion based model 被引量:2
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作者 A.H.Mazinan 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第7期1740-1753,共14页
A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that th... A novel hybrid robust three-axis attitude control approach, namely HRTAC, is considered along with the well-known developments in the area of space systems, since there is a consensus among the related experts that the new insights may be taken into account as decision points to outperform the available materials. It is to note that the traditional control approaches may generally be upgraded, as long as a number of modifications are made with respect to state-of-the-art, in order to propose high-precision outcomes. Regarding the investigated issues, the robust sliding mode finite-time control approach is first designed to handle three-axis angular rates in the inner control loop, which consists of the pulse width pulse frequency modulations in line with the control allocation scheme and the system dynamics. The main subject to employ these modulations that is realizing in association with the control allocation scheme is to be able to handle a class of overactuated systems, in particular. The proportional derivative based linear quadratic regulator approach is then designed to handle three-axis rotational angles in the outer control loop, which consists of the system kinematics that is correspondingly concentrated to deal with the quaternion based model. The utilization of the linear and its nonlinear terms, simultaneously, are taken into real consideration as the research motivation, while the performance results are of the significance as the improved version in comparison with the recent investigated outcomes. Subsequently, there is a stability analysis to verify and guarantee the closed loop system performance in coping with the whole of nominal referenced commands. At the end, the effectiveness of the approach considered here is highlighted in line with a number of potential recent benchmarks. 展开更多
关键词 three-axis angular rates and rotations sliding mode finite-time control approach proportional derivative based linearquadratic regulator approach dynamics and kinematics of overactuated spacecraft
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