Synchronization of mechanical horizontal platform systems in finite time

The horizontal platform system (HPS) is a mechanical device that exhibits rich and chaotic dynamics. In this paper, the problem of finite-time synchronization of two non-autonomous chaotic HPSs is investigated. It is assumed that both drive and response systems are disturbed by model uncertainties, external disturbances and fully unknown parameters. Appropriate update laws are proposed to undertake the unknown parameters. Using the update laws and finite-time control theory, a robust adaptive controller is derived to synchronize the two uncertain HPSs in a given finite time. Subsequently, the effects of input nonlinearities are taken into account and a robust adaptive controller is introduced to synchronize the two uncertain HPSs within a finite time. The finite-time stability and convergence of the proposed schemes are analytically proved. Two illustrative examples are presented to show the robustness and applicability of the proposed adaptive finite-time control techniques.     

Finite-time synchronization of two different chaotic systems with unknown parameters via sliding mode technique

In this paper, the problem of finite-time chaos synchronization between two different chaotic systems with fully unknown parameters is investigated. First, a new nonsingular terminal sliding surface is introduced and its finite-time convergence to the zero equilibrium is proved. Then, appropriate adaptive laws are derived to tackle the unknown parameters of the systems. Afterwards, based on the adaptive laws and finite-time control idea, an adaptive sliding mode controller is proposed to ensure the occurrence of the sliding motion in a given finite time. It is mathematically proved that the introduced sliding mode technique has finite-time convergence and stability in both reaching and sliding mode phases. Finally, some numerical simulations are presented to demonstrate the applicability and effectiveness of the proposed technique.     

Global finite-time synchronization of different dimensional chaotic systems

This paper addresses the problem of global finite-time synchronization of two different dimensional chaotic systems. Firstly, the definition of global finite-time synchronization of different dimensional chaotic systems are introduced. Based on the finite-time stability methods, the controller is designed such that the chaotic systems are globally synchronized in a finite time. Then, some uncertain parameters are adopted in the chaotic systems, new control law and dynamical parameter estimation are proposed to guarantee that the global finite-time synchronization can be obtained. By considering a dynamical parameter designed in the controller, the adaptive updated controller is also designed to achieve the desired results. At last, the results of two different dimensional chaotic systems are also extended to two different dimensional networked chaotic systems. Finally, three numerical examples are given to verify the validity of the proposed methods.     

Finite-time stabilization for hyper-chaotic Lorenz system families via adaptive control

This paper is concerned with finite-time stabilization of hyper-chaotic Lorenz system families. Based on the finite-time stability theory, a novel adaptive control technique is presented to achieve finite-time stabilization for hyper-chaotic system. The controller is simple and easy to be implemented, and can stabilize almost all well known high-dimensional chaotic systems. Simulation results for hyper-chaotic Lorenz system, Chua’s oscillator, Rössler system are provided to illustrate the effectiveness of the proposed scheme.     

基于自适应模糊控制方法的四翼混沌系统有限时间同步

研究了一类带有未知外部摄动的四翼混沌主从系统的有限时间同步控制问题.首先,基于自适应模糊控制方法,对四翼混沌系统的不确定项进行了处理.其次,基于Lyapunov有限时间稳定性准则,设计了一种有限时间同步控制器,使得主系统与从系统能在有限时间内实现状态同步.最后,通过数值仿真,检验了该方法的有效性和鲁棒性.     

Some criteria for the global finite-time synchronization of two Lorenz–Stenflo systems coupled by a new controller

This paper investigates the global finite-time synchronization of two chaotic Lorenz–Stenflo systems coupled by a new controller called the generalized variable substitution controller. First of all, the generalized variable substitution controller is designed to establish the master–slave finite-time synchronization scheme for the Lorenz–Stenflo systems. And then, based on the finite-time stability theory, a sufficient criterion on the finite-time synchronization of this scheme is rigorously verified in the form of matrix and the corresponding estimation for the synchronization time is analytically given. Applying this criterion, some sufficient finite-time synchronization criteria under various generalized variable substitution controllers are further derived in the algebraic form. Finally, some numerical examples are introduced to compare the results proposed in this paper with those proposed in the existing literature, verifying the effectiveness of the criteria obtained.     

不确定非自治混沌陀螺仪在非线性输入下的有限时间稳定性

陀螺仪是一个非常有趣,又是永恒的非线性非自治动力系统课题,它可以显示出非常复杂的动力学行为,如混沌现象.在一个给定的有限时间内,研究非线性非自治陀螺仪鲁棒稳定性问题.假设陀螺仪系统受到模型不确定的外部扰动而摄动,系统参数并不知道,同时考虑了非线性输入的影响.为未知参数提出了适当的自适应律.以自适应律和有限时间控制理论为基础,提出非连续有限时间控制理论,来研究系统的有限时间稳定性.解析证明了闭循环系统的有限时间稳定性及其收敛性.若干数值仿真结果表明,该文的有限时间控制法是有效的,同时验证了该文的理论结果.     

Identifier-based adaptive neural dynamic surface control for uncertain DC-DC buck converter system with input constraint

In this paper, an identifier-based adaptive neural dynamic surface control (IANDSC) is proposed for the uncertain DC-DC buck converter system with input constraint. Based on the analysis of the effect of input constraint in the buck converter, the neural network compensator is employed to ensure the controller output within the permissible range. Subsequently, the constrained adaptive control scheme combined with the neural network compensator is developed for the buck converter with uncertain load current. In this scheme, a newly presented finite-time identifier is utilized to accelerate the parameter tuning process and to heighten the accuracy of parameter estimation. By utilizing the adaptive dynamic surface control (ADSC) technique, the problem of “explosion of complexity” inherently in the traditional adaptive backstepping design can be overcome. The proposed control law can guarantee the uniformly ultimate boundedness of all signals in the closed-loop system via Lyapunov synthesis. Numerical simulations are provided to illustrate the effectiveness of the proposed control method.     

Observer-based finite-time control of time-delayed jump systems

This paper provides the observer-based finite-time control problem of time-delayed Markov jump systems that possess randomly jumping parameters. The transition of the jumping parameters is governed by a finite-state Markov process. The observer-based finite-time H_∞ controller via state feedback is proposed to guarantee the stochastic finite-time boundedness and stochastic finite-time stabilization of the resulting closed-loop system for all admissible disturbances and unknown time-delays. Based on stochastic finite-time stability analysis, sufficient conditions that ensure stochastic robust control performance of time-delay jump systems are derived. The control criterion is formulated in the form of linear matrix inequalities and the designed finite-time stabilization controller is described as an optimization one. The presented results are extended to time-varying delayed MJSs. Simulation results illustrate the effectiveness of the developed approaches.     

一类带有外部扰动的模糊离散非线性系统的有限时间控制问题(英文)

This paper give criterions on finite-time control of fuzzy discrete-time nonlinear system subject to exogenous disturbance.Employing the Lyapunov function theory,several suffcient conditions including relaxed ones are presented for finite-time stability via fuzzy controller laws.An illustrative example is given to demonstrate the effectiveness of the proposed method.     

Finite-Time Synchronization of Coupled Neutral-Type Neural Networks With Stochastic Disturbances and Uncertainties北大核心CSCD

The finite⁃time synchronization problems were solved for coupled neutral⁃type neural networks with stochastic disturbances and uncertainties. Based on the Lyapunov stability theory and the inequality techniques, the finite⁃time synchronization criterion was proposed for this system. Then the finite⁃time synchronization was realized for the master⁃slave system through the construction of an appropriate state feedback controller. At last, a numerical simulation was given to verify the effectiveness of the proposed theory. © 2023 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Finite-time chaos synchronization of unified chaotic system with uncertain parameters

This paper deals with the finite-time chaos synchronization of the unified chaotic system with uncertain parameters. Based on the finite-time stability theory, a control law is proposed to realize finite-time chaos synchronization for the unified chaotic system with uncertain parameters. The controller is simple, robust and only part parameters are required to be bounded. Simulation results for the Lorenz, Lü and Chen chaotic systems are presented to validate the design and the analysis.     

Finite-time stability and stabilization of nonlinear stochastic hybrid systems

This paper deals with the problem of finite-time stability and stabilization of nonlinear Markovian switching stochastic systems which exist impulses at the switching instants. Using multiple Lyapunov function theory, a sufficient condition is established for finite-time stability of the underlying systems. Furthermore, based on the state partition of continuous parts of systems, a feedback controller is designed such that the corresponding impulsive stochastic closed-loop systems are finite-time stochastically stable. A numerical example is presented to illustrate the effectiveness of the proposed method.     

Global finite-time stabilization of a class of nonlinear system based on a dynamic gain approach

In this paper, finite-time control problem of a class of nonlinear systems is considered. By using a dynamic gain-based backstepping approach, a state feedback controller involving the dynamic gains is constructed with the help of appropriate Lyapunov function, which guarantees the closed-loop system to be globally finite-time stabilization. A simulation example is provided to illustrate the effectiveness of the proposed control scheme.     

基于多切换传输的复变量混沌系统的有限时组合同步控制

针对一类复变量混沌系统, 研究了基于多切换传输的有限时同步控制问题.首先,针对网络信号在传输过程中的同步模式,分析了多个混沌系统之间的多切换同步行为.其次,基于预设的切换传输规则,给出了有限时组合同步的定义.进而,依据有限时稳定性理论,设计了一类实现快速同步的控制器,并给出了有限时组合同步的充分条件.最后,通过数值仿真和分析验证了所设计控制方案的有效性.     

Finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay via periodically intermittent control

In this paper, the issue of finite-time lag synchronization of coupled reaction–diffusion systems with time-varying delay (CRDSTD) is considered. A periodically intermittent controller is designed such that drive system and corresponding response system can achieve finite-time lag synchronization. By using graph theory and Lyapunov method, two sufficient criteria are presented to guarantee the finite-time lag synchronization of CRDSTD. Moreover, the time of achieving lag synchronization of CRDSTD is estimated. Finally, a numerical example is given to show the effectiveness of the proposed results.     

Global finite-time stabilization of switched high-order rational power nonlinear systems

This works is concerned with the finite-time optimal stabilization problem for a class of switched non-strict-feedback nonlinear systems whose powers are possibly different positive odd rational numbers in the sense the powers of each subsystem might differ from others. It is well known that high-order nonlinear systems are intrinsically challenging as feedback linearization and backstepping method successfully developed for low-order systems fail to work. To this purpose, the nested saturation homogeneous controller is constructively devised to achieve global finite-time stability. Furthermore, the corresponding design parameters are optimized by minimizing a well-defined cost function, and thus an optimal controller being independent of switching signals is obtained. Simulation results are eventually provided to validate the effectiveness of the proposed control scheme.     

Robust finite-time H∞ control for a class of uncertain switched neutral systems

This paper investigates the robust finite-time H_∞ control problem for a class of uncertain switched neutral systems with unknown time-varying disturbance. The uncertainties under consideration are norm bounded. By using the average dwell time approach, a sufficient condition for finite-time boundedness of switched neutral systems is derived. Then, finite-time H_∞ performance analysis for switched neutral systems is developed, and a robust finite-time H_∞ state feedback controller is proposed to guarantee that the closed-loop system is finite-time bounded with H_∞ disturbance attenuation level γ. All the results are given in terms of linear matrix inequalities (LMIs). Finally, two numerical examples are provided to show the effectiveness of the proposed method.     

Finite-time stabilization of a class of chaotic systems via adaptive control method

This paper investigates the stabilization of three dimensional chaotic systems in a finite time by extending our previous method for chaos stabilization. Based on the finite-time stability theory, a control law is proposed to realize finite-time stabilization of three dimensional chaotic systems. In comparison with the previous methods, the controller obtained by our method is simpler than those. Moreover, the method obtained in this paper is suitable for a class of three dimensional chaotic systems. The efficiency of the control scheme is revealed by some illustrative simulations.     

Input-to-state stability and sliding mode control of the nonlinear singularly perturbed systems via trajectory-based small-gain theorem

This paper presents the trajectory-based input-to-state stability (ISS) and input-to-output stability (IOS) small-gain theorem, and the finite-time ISS (FTISS) and finite-time IOS (FTIOS) of nonlinear singularly perturbed systems. The contribution of this paper is threefold. Firstly, a novel idea is proposed to analyze the stability of the nonlinear singularly perturbed system, which is regarded as an interconnected system by using two-time-scale decomposition. Secondly, the trajectory-based approach is applied to establish ISS and IOS small-gain theorem for singularly perturbed systems and the FTISS and FTIOS properties are proposed. Thirdly, a novel sliding mode controller is developed for a class of nonlinear singularly perturbed systems. Finally, the effectiveness of proposed method is illustrated by using a numerical example, a DC motor simulation and a multi-agent singularly perturbed system.