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Target Tracking Algorithm Using Finite-time Convergence Smooth Second-order Sliding Mode Controller for Mobile Robots 被引量:4
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作者 GE Lianzheng ZHAO Lijun GAO Tong 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2011年第3期414-419,共6页
Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control sy... Target tracking control for wheeled mobile robot (WMR) need resolve the problems of kinematics model and tracking algorithm.High-order sliding mode control is a valid method used in the nonlinear tracking control system,which can eliminate the chattering of sliding mode control.Currently there lacks the research of robustness and uncertain factors for high-order sliding mode control.To address the fast convergence and robustness problems of tracking target,the tracking mathematical model of WMR and the target is derived.Based on the finite-time convergence theory and second order sliding mode method,a nonlinear tracking algorithm is designed which guarantees that WMR can catch the target in finite time.At the same time an observer is applied to substitute the uncertain acceleration of the target,then a smooth nonlinear tracking algorithm is proposed.Based on Lyapunov stability theory and finite-time convergence,a finite time convergent smooth second order sliding mode controller and a target tracking algorithm are designed by using second order sliding mode method.The simulation results verified that WMR can catch up the target quickly and reduce the control discontinuity of the velocity of WMR. 展开更多
关键词 mobile robots second order sliding mode finite-time convergence OBSERVER
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Push-Pull Finite-Time Convergence Distributed Optimization Algorithm 被引量:1
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作者 Xiaobiao Chen Kaixin Yan +3 位作者 Yu Gao Xuefeng Xu Kang Yan Jing Wang 《American Journal of Computational Mathematics》 2020年第1期118-146,共29页
With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution r... With the widespread application of distributed systems, many problems need to be solved urgently. How to design distributed optimization strategies has become a research hotspot. This article focuses on the solution rate of the distributed convex optimization algorithm. Each agent in the network has its own convex cost function. We consider a gradient-based distributed method and use a push-pull gradient algorithm to minimize the total cost function. Inspired by the current multi-agent consensus cooperation protocol for distributed convex optimization algorithm, a distributed convex optimization algorithm with finite time convergence is proposed and studied. In the end, based on a fixed undirected distributed network topology, a fast convergent distributed cooperative learning method based on a linear parameterized neural network is proposed, which is different from the existing distributed convex optimization algorithms that can achieve exponential convergence. The algorithm can achieve finite-time convergence. The convergence of the algorithm can be guaranteed by the Lyapunov method. The corresponding simulation examples also show the effectiveness of the algorithm intuitively. Compared with other algorithms, this algorithm is competitive. 展开更多
关键词 DISTRIBUTED Optimization finite time convergence Linear Parameterized NEURAL Network PUSH-PULL Algorithm Undirected Graph
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Differential geometric guidance command with finite time convergence using extended state observer 被引量:5
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作者 麻毅威 张为华 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第4期859-868,共10页
For improving the performance of differential geometric guidance command(DGGC), a new formation of this guidance law is proposed, which can guarantee the finite time convergence(FTC) of the line of sight(LOS) rate to ... For improving the performance of differential geometric guidance command(DGGC), a new formation of this guidance law is proposed, which can guarantee the finite time convergence(FTC) of the line of sight(LOS) rate to zero or its neighborhood against maneuvering targets in three-dimensional(3D) space. The extended state observer(ESO) is employed to estimate the target acceleration, which makes the new DGGC more applicable to practical interception scenarios. Finally, the effectiveness of this newly proposed guidance command is demonstrated by the numerical simulation results. 展开更多
关键词 missile guidance differential geometric guidance command (DGGC) finite time convergence (FTC) extended state observer (ESO) maneuvering targets
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Convergence and Superconvergence of Fully Discrete Finite Element for Time Fractional Optimal Control Problems 被引量:1
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作者 Yuelong Tang 《American Journal of Computational Mathematics》 2021年第1期53-63,共11页
In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and &l... In this paper, we consider a fully discrete finite element approximation for time fractional optimal control problems. The state and adjoint state are approximated by triangular linear fi nite elements in space and <em>L</em>1 scheme in time. The control is obtained by the variational discretization technique. The main purpose of this work is to derive the convergence and superconvergence. A numerical example is presented to validate our theoretical results. 展开更多
关键词 time Fractional Optimal Control Problems finite Element convergence and Superconvergence
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Mixed time discontinuous space-time finite element method for convection diffusion equations 被引量:1
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作者 刘洋 李宏 何斯日古楞 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2008年第12期1579-1586,共8页
A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order... A mixed time discontinuous space-time finite element scheme for secondorder convection diffusion problems is constructed and analyzed. Order of the equation is lowered by the mixed finite element method. The low order equation is discretized with a space-time finite element method, continuous in space but discontinuous in time. Stability, existence, uniqueness and convergence of the approximate solutions are proved. Numerical results are presented to illustrate efficiency of the proposed method. 展开更多
关键词 convection diffusion equations mixed finite element method time discontinuous space-time finite element method convergence
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Finite time convergent control using terminal sliding mode 被引量:11
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作者 YiguangHONG GuowuYANG +1 位作者 DaizhanCHENG SarahSPURGEON 《控制理论与应用(英文版)》 EI 2004年第1期69-74,共6页
A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under considera... A method for terminal sliding mode control design is discussed. As we know, one of the strong points of terminal sliding mode control is its finite-time convergence to a given equilibrium of the system under consideration, which may be useful in specific applications. The proposed method, different from many existing terminal sliding model control desin methods, is studied, and then feedback laws are designed for a class of nonlinear systems, along with illustrative examples. 展开更多
关键词 Terminal sliding mode control finite-time convergence Nonlinear systems
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A Numerical Algorithm Based on Quadratic Finite Element for Two-Dimensional Nonlinear Time Fractional Thermal Diffusion Model 被引量:3
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作者 Yanlong Zhang Baoli Yin +2 位作者 Yue Cao Yang Liu Hong Li 《Computer Modeling in Engineering & Sciences》 SCIE EI 2020年第3期1081-1098,共18页
In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-d... In this article,a high-order scheme,which is formulated by combining the quadratic finite element method in space with a second-order time discrete scheme,is developed for looking for the numerical solution of a two-dimensional nonlinear time fractional thermal diffusion model.The time Caputo fractional derivative is approximated by using the L2-1formula,the first-order derivative and nonlinear term are discretized by some second-order approximation formulas,and the quadratic finite element is used to approximate the spatial direction.The error accuracy O(h3+t2)is obtained,which is verified by the numerical results. 展开更多
关键词 Quadratic finite element two-dimensional nonlinear time fractional thermal diffusion model L2-1formula.
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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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Dynamics and Long Time Convergence of the Extended Fisher-Kolmogorov Equation under Numerical Discretization
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作者 Wang Jue Ma Fu-ming 《Communications in Mathematical Research》 CSCD 2013年第1期51-60,共10页
We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. I... We present a numerical study of the long time behavior of approxima- tion solution to the Extended Fisher-Kolmogorov equation with periodic boundary conditions. The unique solvability of numerical solution is shown. It is proved that there exists a global attractor of the discrete dynamical system. Furthermore, we obtain the long-time stability and convergence of the difference scheme and the upper semicontinuity d(Ah,τ, .A) → O. Our results show that the difference scheme can effectively simulate the infinite dimensional dynamical systems. 展开更多
关键词 Extended Fisher Kolmogorov equation finite difference method global attractor long time stability and convergence
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Optical simulation of in-plane-switching blue phase liquid crystal display using the finite-difference time-domain method 被引量:1
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作者 窦虎 马红梅 孙玉宝 《Chinese Physics B》 SCIE EI CAS CSCD 2016年第9期117-121,共5页
The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the ... The finite-difference time-domain method is used to simulate the optical characteristics of an in-plane switching blue phase liquid crystal display.Compared with the matrix optic methods and the refractive method,the finite-difference timedomain method,which is used to directly solve Maxwell's equations,can consider the lateral variation of the refractive index and obtain an accurate convergence effect.The simulation results show that e-rays and o-rays bend in different directions when the in-plane switching blue phase liquid crystal display is driven by the operating voltage.The finitedifference time-domain method should be used when the distribution of the liquid crystal in the liquid crystal display has a large lateral change. 展开更多
关键词 finite-difference time-domain method blue phase liquid crystal display in-plane switching convergence effect
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A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation
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作者 Baojin Su Yanan Wang +1 位作者 Jingwen Qi Yousen Li 《Journal of Applied Mathematics and Physics》 2022年第10期3156-3174,共19页
In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obt... In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L<sub>∞</sub>-norm. The convergence order is O(τ<sup>2-α</sup> + h<sup>4</sup>). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme. 展开更多
关键词 Multi-Term time Fractional Sub-Diffusion Equation High-Order Compact finite Volume Scheme Stable convergENT
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Analysis of an Implicit Finite Difference Scheme for Time Fractional Diffusion Equation 被引量:1
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作者 MA Yan 《Chinese Quarterly Journal of Mathematics》 2016年第1期69-81,共13页
Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order tim... Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper. 展开更多
关键词 time fractional diffusion equation finite difference approximation implicit scheme STABILITY convergence EFFECTIVENESS
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Redefined Extended Cubic B-Spline Functions for Numerical Solution of Time-Fractional Telegraph Equation
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作者 Muhammad Amin Muhammad Abbas +2 位作者 Dumitru Baleanu Muhammad Kashif Iqbal Muhammad Bilal Riaz 《Computer Modeling in Engineering & Sciences》 SCIE EI 2021年第4期361-384,共24页
This work is concerned with the application of a redefined set of extended uniform cubic B-spline(RECBS)functions for the numerical treatment of time-fractional Telegraph equation.The presented technique engages finit... This work is concerned with the application of a redefined set of extended uniform cubic B-spline(RECBS)functions for the numerical treatment of time-fractional Telegraph equation.The presented technique engages finite difference formulation for discretizing the Caputo time-fractional derivatives and RECBS functions to interpolate the solution curve along the spatial grid.Stability analysis of the scheme is provided to ensure that the errors do not amplify during the execution of the numerical procedure.The derivation of uniform convergence has also been presented.Some computational experiments are executed to verify the theoretical considerations.Numerical results are compared with the existing schemes and it is concluded that the present scheme returns superior outcomes on the topic. 展开更多
关键词 Extended cubic B-spline redefined extended cubic B-spline time fractional telegraph equation caputo fractional derivative finite difference method convergence
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Suppressive Influence of Time- Space White Noise on the Explosion of Solutions of Stochastic Fokker- Planck Delay Differential Equations
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作者 Augustine O. Atonuje Jonathan Tsetimi 《Journal of Mathematics and System Science》 2016年第7期284-290,共7页
It is generally known that the solutions of deterministic and stochastic differential equations (SDEs) usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventual... It is generally known that the solutions of deterministic and stochastic differential equations (SDEs) usually grow linearly at such a rate that they may become unbounded after a small lapse of time and may eventually blow up or explode in finite time. If the drift and diffusion functions are globally Lipschitz, linear growth may still be experienced, as well as a possible blow-up of solutions in finite time. In this paper, a nonlinear scalar delay differential equation with a constant time lag is perturbed by a multiplicative Ito-type time - space white noise to form a stochastic Fokker-Planck delay differential equation. It is established that no explosion is possible in the presence of any intrinsically slow time - space white noise of Ito - type as manifested in the resulting stochastic Fokker- Planck delay differential equation. Time - space white noise has a role to play since the solution of the classical nonlinear equation without it still exhibits explosion. 展开更多
关键词 Explosion non-linear stochastic Fokker Planck delay differential equation time - space white noise finite time.
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Cooperative guidance law based on super-twisting observer for target maneuvering
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作者 GAO Mengjing YAN Tian +3 位作者 HAN Bingjie CHENG Haoyu FU Wenxing HAN Bo 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第5期1304-1314,共11页
To solve the problem that multiple missiles should simultaneously attack unmeasurable maneuvering targets,a guidance law with temporal consistency constraint based on the super-twisting observer is proposed.Firstly,th... To solve the problem that multiple missiles should simultaneously attack unmeasurable maneuvering targets,a guidance law with temporal consistency constraint based on the super-twisting observer is proposed.Firstly,the relative motion equations between multiple missiles and targets are established,and the topological model among multiple agents is considered.Secondly,based on the temporal consistency constraint,a cooperative guidance law for simultaneous arrival with finite-time convergence is derived.Finally,the unknown target maneuver-ing is regarded as bounded interference.Based on the second-order sliding mode theory,a super-twisting sliding mode observer is devised to observe and track the bounded interfer-ence,and the stability of the observer is proved.Compared with the existing research,this approach only needs to obtain the sliding mode variable which simplifies the design process.The simulation results show that the designed cooperative guidance law for maneuvering targets achieves the expected effect.It ensures successful cooperative attacks,even when confronted with strong maneuvering targets. 展开更多
关键词 cooperative guidance super-twisting target maneuver finite time convergence.
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大长径比远程制导火箭弹自适应Super-twisting控制方法
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作者 范军芳 闫华杰 +2 位作者 纪毅 唐文桃 赵国宁 《中国惯性技术学报》 EI CSCD 北大核心 2024年第2期196-204,212,共10页
针对具有轻质薄壳结构的大长径比远程制导火箭弹刚体-弹性体耦合动力学控制难题,提出了一种自适应Super-twisting控制方法。首先,将大长径比远程制导火箭弹的弹性模态与外部干扰项视为归一化扰动,建立了考虑参数、模型不确定性的刚体-... 针对具有轻质薄壳结构的大长径比远程制导火箭弹刚体-弹性体耦合动力学控制难题,提出了一种自适应Super-twisting控制方法。首先,将大长径比远程制导火箭弹的弹性模态与外部干扰项视为归一化扰动,建立了考虑参数、模型不确定性的刚体-弹性体耦合动力学模型。针对外部扰动难以实时精准获取的问题,设计了有限时间收敛干扰观测器,能够在大范围气动参数摄动情形下对远程制导火箭弹外部扰动进行实时精准估计。为提高系统鲁棒性,设计了基于Super-twisting算法的自适应有限时间控制方法,使系统能根据状态误差自动调节控制参数,在削弱高频抖振的同时有效提高抗干扰能力。仿真结果表明:所提控制方法在弹体±15%气动参数摄动的条件下,由平飞状态转变为跟踪幅值为10的正弦弹道倾角指令时,实现3.2 s内弹道倾角跟踪误差收敛至0.002°,可实现远程制导火箭弹姿态平稳跟踪控制弹道倾角指令。 展开更多
关键词 远程制导火箭弹 弹性效应 自适应Super-twisting 有限时间收敛 扰动观测器
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Nonlinear robust control of a quadrotor helicopter with finite time convergence 被引量:2
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作者 Guozhou ZHENG Bin XIAN 《Control Theory and Technology》 EI CSCD 2018年第2期133-144,共12页
In this paper, the control problem for a quadrotor helicopter which is subjected to modeling uncertainties and unknown external disturbance is investigated. A new nonlinear robust control strategy is proposed. First, ... In this paper, the control problem for a quadrotor helicopter which is subjected to modeling uncertainties and unknown external disturbance is investigated. A new nonlinear robust control strategy is proposed. First, a nonlinear complementary filter is developed to fuse the raw data from the onboard barometer and the accelerometer to decrease the negative effects from the noise associated with the low-cost onboard sensors Then the adaptive super-twisting methodology is combined with a backstepping method to formulate the nonlinear robust controller for the quadrotor's attitude angles and the altitude position. Lyapunov based stability analysis shows that finite time convergence is ensured for the closed-loop operation of the quadrotor's roll angle, pitch angle, row angle and the altitude position. Real-time flight experimental results, which are performed on a quadrotor flight testbed, are included to demonstrate the good control performance of the proposed control methodology. 展开更多
关键词 QUADROTOR nonlinear control finite time convergence real-time experiment
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领导-跟随多智能体系统有限时间一致性 被引量:4
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作者 陈立军 张玉 夏琳琳 《计算机仿真》 北大核心 2018年第5期274-277,308,共5页
针对领导-跟随一阶多智能体系统在无向网络下的快速一致性问题,提出了一种基于总体代价函数梯度的快速有限时间一致性跟踪算法,并对一致性算法进行了理论分析。利用图论和李雅普诺夫有限时间稳定性理论,证明了当通信拓扑固定连通时,有... 针对领导-跟随一阶多智能体系统在无向网络下的快速一致性问题,提出了一种基于总体代价函数梯度的快速有限时间一致性跟踪算法,并对一致性算法进行了理论分析。利用图论和李雅普诺夫有限时间稳定性理论,证明了当通信拓扑固定连通时,有限时间一致性算法可保证多智能体系统在有限的时间内快速的实现一致性跟踪。最后通过大量的仿真实例和与传统方法的对比分析,验证了改进算法的优越性。 展开更多
关键词 多智能体系统 领导-跟随 有限时间一致性 收敛速度
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速度不可测的领导-跟随MAS一致性跟踪控制 被引量:3
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作者 任彦 解东 +1 位作者 岳美霞 苏楠 《电光与控制》 CSCD 北大核心 2020年第12期36-40,100,共6页
针对带有干扰且速度不可测的领导-跟随二阶MAS,研究了有限时间一致性跟踪控制问题。首先,针对速度不可测和干扰问题,分别设计了有限时间超螺旋观测器和滑模干扰观测器,对干扰进行了快速估计和补偿;其次,结合观测速度,设计了有限时间快... 针对带有干扰且速度不可测的领导-跟随二阶MAS,研究了有限时间一致性跟踪控制问题。首先,针对速度不可测和干扰问题,分别设计了有限时间超螺旋观测器和滑模干扰观测器,对干扰进行了快速估计和补偿;其次,结合观测速度,设计了有限时间快速反正切跟踪微分器,快速估计了领导者的控制输入信息;然后,设计了基于积分滑模的有限时间跟踪控制器,有效地提高了系统的响应速度和跟踪精度,同时提高了系统的抗干扰性能和鲁棒性;最后,通过数值仿真证明了控制算法的有效性。 展开更多
关键词 MAS 有限时间收敛 干扰观测器 跟踪微分器 积分滑模
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三维非线性Sobolev-Galpern方程有限差分逼近的长时间行为(英文) 被引量:1
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作者 张磊 王珏 张法勇 《黑龙江大学自然科学学报》 CAS 北大核心 2010年第4期440-445,共6页
研究三维非线性Sobolev-Galpern方程Dirichlet初值问题的一个全离散有限差分格式。利用离散空间泛函分析和能量估计的方法证明了此数值格式的唯一可解性,同时得到了此差分格式的长时间的稳定性和收敛性。进一步,证明了离散动力系统整体... 研究三维非线性Sobolev-Galpern方程Dirichlet初值问题的一个全离散有限差分格式。利用离散空间泛函分析和能量估计的方法证明了此数值格式的唯一可解性,同时得到了此差分格式的长时间的稳定性和收敛性。进一步,证明了离散动力系统整体吸引子的存在性以及离散动力系统的上半连续性。上述结果说明该数值离散格式可有效地模拟相应的无穷维动力系统。 展开更多
关键词 非线性SOBOLEV-GALPERN方程 有限差分格式 唯一可解性 全局吸引子 长时间收敛性及稳定性
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