Event-triggered finite-time resilient control for switched systems: an observer-based approach and its applications to a boost converter circuit system model

Under an event-triggered communication scheme (ETCS), this note focuses on the observer-based finite-time resilient control problem for a class of switched systems. Different from the existing finite-time problems, not only the problem of finite-time boundedness (FTBs) but also the problem of input-output finite-time stability (IO-FTSy) are considered in this paper. To effectively use the network resources, an ETCS is formulated for switched systems. Considering that not all the states could be measured, thus an event-triggered observer is constructed, and then, an observer-based resilient controller is devised, which robustly stabilizes the given systems in the meaning of finite-time control. Based on time-delay method and Lyapunov functional approach, interesting results are derived to verify the properties of the FTBs and the IO-FTSy of the event-triggered (ET) closed-loop error switched systems. All the matrix inequalities can be converted to linear matrix inequalities (LMIs) so as to simultaneously obtain the controller gain and observer gain. Finally, the applicability of the proposed control scheme is verified via a boost converter circuit system.     

Finite-time stability analysis of fractional-order complex-valued memristor-based neural networks with time delays

In this paper, the problem of finite-time stability of fractional-order complex-valued memristor-based neural networks (NNs) with time delays is extensively investigated. We first initiate the fractional-order complex-valued memristor-based NNs with the Caputo fractional derivatives. Using the theory of fractional-order differential equations with discontinuous right-hand sides, Laplace transforms, Mittag-Leffler functions and generalized Gronwall inequality, some new sufficient conditions are derived to guarantee the finite-time stability of the considered fractional-order complex-valued memristor-based NNs. In addition, some sufficient conditions are also obtained for the asymptotical stability of fractional-order complex-valued memristor-based NNs. Finally, a numerical example is presented to demonstrate the effectiveness of our theoretical results.     

A DIRECT METHOD FOR EVALUATING LINE INTEGRALS WITH ARBITRARY HIGH ORDER OF SINGULARITIES

提出了一种精确计算任意高阶奇异曲线积分的直接计算法.首先将曲线单元上的各种几何量用投影线上的几何量来表示,然后通过幂级数展开和解析的方法显式地消除了积分的奇异性.还导出了计算等参坐标对局部直角坐标偏导数的表达式.由于这种方法涉及到的是总体尺度间的坐标变换,操作起来直观明了,可以处理二维问题边界元分析中出现的任意高阶奇异边界积分.最后用具体算例验证该方法的正确性.     

边界元中计算任意高阶奇异线积分的直接法

提出了一种精确计算任意高阶奇异曲线积分的直接计算法.首先将曲线单元上的各种几何量用投影线上的几何量来表示,然后通过幂级数展开和解析的方法显式地消除了积分的奇异性.还导出了计算等参坐标对局部直角坐标偏导数的表达式.由于这种方法涉及到的是总体尺度间的坐标变换,操作起来直观明了,可以处理二维问题边界元分析中出现的任意高阶奇异边界积分.最后用具体算例验证该方法的正确性.      

Finite-time output feedback control for a class of second-order nonlinear systems with application to DC–DC buck converters

The problem of output feedback control for a class of second-order nonlinear systems is investigated in this paper. Using the techniques of finite-time control and finite-time convergent observer, an observer-based finite-time output feedback controller is proposed which can guarantee that the system’s state converges to the equilibrium in a finite time. As an application of the proposed theoretical results, the problem of finite-time control without current signal for the DC–DC buck converters is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Velocity-based tuning of degree of homogeneity for finite-time stabilization and fault tolerant control of an ROV in the presence of thruster saturation and rate limits

This paper introduces a homogeneous controller along a fixed-time state and fault observer for finite-time stabilization and fault accommodation of a remotely-operated vehicle in the presence of actuator saturation and rate limits. For this, a novel tuning algorithm is improvised for manipulating the degree of homogeneity in homogeneous controllers to effectively acquire different properties from the overall control system. The tuning of degree of homogeneity is based on vehicle’s velocity. The proposed algorithm results in a switching-type controller, which undergoes three different stages during the operation, to eliminate the sensitivity of conventional finite-time and fixed-time controllers to large initial errors in the presence of thruster constraints. In addition, a new fixed-time fault and state observer is designed for the realization of output feedback control and fault tolerance by combining a fixed-time state observer with a fault estimation unit. In contrast to conventional extended-state observers, this observer considers the dynamics of the thruster system in its formulation so that better performance can be provided for the control system upon thruster failures. Control allocation is utilized to accommodate thruster failures and faults and to take account of thruster saturation and rate limits. Stability analyses are carried out for the overall control system and the proposed observer. It is shown that the closed-loop control system would be globally finite-time stable. The state estimation subsystem is fixed-time stable and the fault estimation unit is input-to-state stable. Simulations are carried out and comparisons are made with several finite-time and fixed-time controllers to outline the advantages of the proposed homogeneous controller and the benefits of the overall fault-tolerant control system.

     

Finite-time stabilization of uncertain non-autonomous chaotic gyroscopes with nonlinear inputs

Gyroscopes are one of the most interesting and everlasting nonlinear nonautonomous dynamical systems that exhibit very complex dynamical behavior such as chaos.In this paper,the problem of robust stabi...     

Finite-time chaos control of unified chaotic systems with uncertain parameters

This paper is concerned with finite-time chaos control of unified chaotic systems with uncertain parameters. Based on the finite-time stability theory in the cascade-connected system, a nonlinear control law is presented to achieve finite-time chaos control. The controller is simple and easy to be constructed. Simulation results for Lorenz, Lü, and Chen chaotic systems are provided to illustrate the effectiveness of the proposed scheme. Supported by the National Natural Science Foundation of China (Grant No. 60674024).     

Finite-time stability with respect to a closed invariant set for a class of discontinuous systems

This paper discusses the problem of finite-time stability with respect to a closed, but not necessarily compact, invariant set for a class of nonlinear systems with discontinuous right-hand sides in the sense of the Filippov solutions. When the Lyapunov function is Lipschitz continuous and regular, the Lyapunov theorem on finite-time stability with respect to a closed invariant set is presented.     

Finite-time non-fragile boundary feedback control for a class of nonlinear parabolic systems

In this paper, the finite-time non-fragile boundary feedback control problem is investigated for a class of nonlinear parabolic systems, where both the multiplicative and additive controller gain variations are considered to describe the actuator parameter perturbation. Non-fragile boundary control strategies are designed with respect to two controller gain variations via collocated or non-collocated boundary measurement, respectively. In light of the finite-time stability and Lyapunov-based techniques, some sufficient conditions are presented in terms of linear matrix inequalities such that the resulting closed-loop system is well-posedness and practically finite-time stable. Finally, numerical examples are given to verify the effectiveness of the proposed design method.

     

航天器终端接近的有限时间输入饱和避碰控制

针对航天器终端接近问题,解决了追踪航天器在跟踪到达期望目标点的过程中不与目标航天器发生碰撞的难题。首先,在目标航天器轨道系下建立了航天器的相对运动和避碰模型。其次,考虑外界扰动上界已知和未知两种情形,均给出了有限时间避碰控制器,且所设计的控制器都具有输入饱和特性。最后,应用Lyapunov稳定性理论证明了在所提出的控制器作用下系统是有限时间收敛的,并且,利用避碰势函数证明了所设计的控制器能够实现避碰。仿真结果表明,所提出的控制器是有效的。     

Finite-time chaos control and synchronization of fractional-order nonautonomous chaotic (hyperchaotic) systems using fractional nonsingular terminal sliding mode technique

In this paper, a novel fractional-order terminal sliding mode control approach is introduced to control/synchronize chaos of fractional-order nonautonomous chaotic/hyperchaotic systems in a given finite time. The effects of model uncertainties and external disturbances are fully taken into account. First, a novel fractional nonsingular terminal sliding surface is proposed and its finite-time convergence to zero is analytically proved. Then an appropriate robust fractional sliding mode control law is proposed to ensure the occurrence of the sliding motion in a given finite time. The fractional version of the Lyapunov stability is used to prove the finite-time existence of the sliding motion. The proposed control scheme is applied to control/synchronize chaos of autonomous/nonautonomous fractional-order chaotic/hyperchaotic systems in the presence of both model uncertainties and external disturbances. Two illustrative examples are presented to show the efficiency and applicability of the proposed finite-time control strategy. It is worth to notice that the proposed fractional nonsingular terminal sliding mode control approach can be applied to control a broad range of nonlinear autonomous/nonautonomous fractional-order dynamical systems in finite time.     

Generalized finite-time synchronization between coupled chaotic systems of different orders with unknown parameters

This letter investigates the adaptive finite-time synchronization of different coupled chaotic (or hyperchaotic) systems with unknown parameters. The sufficient conditions for achieving the generalized finite-time synchronization of two chaotic systems are derived based on the theory of finite-time stability of dynamical systems. By the adaptive control technique, the control laws and the corresponding parameters update laws are proposed such that the generalized finite-time synchronization of nonidentical chaotic (or hyperchaotic) systems is to be obtained. These results obtained are in good agreement with the existing one in open literature and it is shown that the technique introduced here can be further applied to various finite-time synchronizations between dynamical systems. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed scheme.     

Extinction Versus Persistence in Strong Oscillating Flows

In this paper, we give some conditions for finite-time extinction or persistence of the solutions of diffusion–advection equations in strong and oscillating flows under Dirichlet boundary conditions. The enhancement of the diffusion rate depends on the interplay between strong advection and time-homogenization, and in particular on the ratio between the strength of the flow and its frequency parameter. Quantitative estimates of this ratio, which depend on the geometry of the domain, are provided in the case of a uniform flow. In the general time–space dependent case, the finite-time behavior of the solutions is related to the existence of first integrals of the flow.     

Finite-time generalized synchronization of chaotic systems with different order

In this paper, the generalized synchronization of chaotic systems with different order is studied. The definition of finite-time generalized synchronization is put forward for the first time. Based on the finite-time stability theory, two control strategies are proposed to realize the generalized synchronization of chaotic systems with different order in finite time. Besides the relation between the parameter β, the initial states of systems and the convergent time were obtained. The corresponding numerical simulations are presented to demonstrate the effectiveness of proposed schemes.     

Numerical analyses and experimental validations of coexisting multiple attractors in Hopfield neural network

In this paper, a finite-time controller is proposed for the quadrotor aircraft to achieve hovering control in a finite time. The design of controller is mainly divided into two steps. Firstly, a saturated finite-time position controller is designed such that the position of quadrotor aircraft can reach any desired position in a finite time. Secondly, a finite-time attitude tracking controller is designed, which can guarantee that the attitude of quadrotor aircraft converges to the desired attitude in a finite time. By homogenous system theory and Lyapunov theory, the finite-time stability of the closed-loop systems is given through rigorous mathematical proofs. Finally, numerical simulations are given to show that the proposed algorithm has a faster convergence performance and a stronger disturbance rejection performance by comparing to the PD control algorithm.     

Finite-time synchronization of switched stochastic R?ssler systems

This paper presents the finite-time synchronization between switched stochastic R?ssler systems accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, the finite-time synchronization of switched stochastic master-slave R?ssler systems and the finite-time stability for the mean of error states are developed with the proposed feedback controller. Numerical simulations demonstrate the effectiveness of the proposed methods.     

Finite-time convergent guidance law with impact angle constraint based on sliding-mode control

In this paper, a finite-time convergent sliding-mode guidance law with terminal impact angle constraint is presented. The guidance law insures that the line-of-sight angular rate will converge to zero before the final time of the guidance process. Meanwhile the flight-path angle will meet the terminal impact angle requirement. Based on the finite-time convergence stability theory and the variable structure control theory, the finite convergence time is determined. Finally, the simulation results show that the guidance law is effective.     

Fuzzy adaptive output feedback control for robotic systems based on fuzzy adaptive observer

In this paper, a fuzzy adaptive output feedback control scheme based on fuzzy adaptive observer is proposed to control robotic systems with parameter uncertainties and external disturbances. It is supposed that only the joint positions of the robotic system can be measured, whereas the joint velocities are unknown and unmeasured. First, a fuzzy adaptive nonlinear observer is presented to estimate the joint velocities of robotic systems, and the observation errors are analyzed using strictly positive real approach and Lyapunov stability theory. Next, based on the observed joint velocities, a fuzzy adaptive output feedback controller is developed to guarantee stability of closed-loop system and achieve a certain tracking performance. Based on the Lyapunov stability theorem, it is proved that all the signals in closed-loop system are bounded. Finally, simulation examples on a two-link robotic manipulator are presented to show the efficiency of the proposed method.     

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor. The hidden attractor in this system can be localized by analytical/numerical methods based on the continuation and perpetual points. The concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors. A conjecture on the Lyapunov dimension of self-excited attractors and the notion of exact Lyapunov dimension are discussed. A comparative survey on the computation of the finite-time Lyapunov exponents and dimension by different algorithms is presented. An adaptive algorithm for studying the dynamics of the finite-time Lyapunov dimension is suggested. Various estimates of the finite-time Lyapunov dimension for the hidden attractor and hidden transient chaotic set in the case of multistability are given.