Finite-time consensus tracking of second-order multi-agent systems via nonsingular TSM

The finite-time consensus tracking problem for second-order multi-agent system is investigated in this paper. The multi-agent system here is composed of a leader with bounded input signal and n followers with bounded disturbances. A new continuous nonlinear distributed consensus tracking protocol is constructed via nonsingular terminal sliding mode (TSM) scheme. It is proved that the overall system will reach consensus in finite time via Lyapunov theory when appropriately choosing the parameters under directed connected topology. Finally, simulations are performed, and results show that the method is robust and efficient.     

Finite-time consensus of high-order heterogeneous multi-agent systems with mismatched disturbances and nonlinear dynamics

Nonlinear Dynamics - In this study, we investigate the finite-time consensus problem for a general class of high-order nonlinear heterogeneous multi-agent systems, for which not only the unknown...     

Finite-time consensus of multi-agent systems driven by hyperbolic partial differential equations via boundary control

Applied Mathematics and Mechanics - The leaderless and leader-following finite-time consensus problems for multi-agent systems (MASs) described by first-order linear hyperbolic partial differential...     

Thermal stability of a disturbed fluid flow

Stability of periodic solutions of a nonselfsimilar nonlinear problem is studied. The problem describes the thermal state of an axial fluid flow with continuously distributed sources of heat. The flow experiences the action of external lowamplitude perturbations changing in time in accordance with known periodic laws. The spectral problem is solved by the method of parametrix, and the critical conditions of the thermal explosion are determined in the linear approximation. Stability of the periodic solution at the critical point is evaluated using the known theorem of factorization, which takes into account the effect of nonlinear terms of the heatbalance equation. The calculation results show that the periodic solution is stable if the total action of external periodic perturbations at the critical point is directed to reduction of the fluidflow temperature.     

Finite-time stability of nonlinear systems with state-dependent delayed impulses

Nonlinear Dynamics - This paper addresses the issue of finite-time stability (FTS) and finite-time contractive stability (FTCS) of nonlinear systems involving state-dependent delayed impulsive...     

Finite-time stability of Hadamard fractional differential equations in weighted Banach spaces

Nonlinear Dynamics - The main purpose of this paper is to investigate the finite-time stability of Hadamard fractional differential equations (HFDEs). Firstly, the standard definitions of...     

Finite-time consensus of nonlinear multi-agent systems via impulsive time window theory: a two-stage control strategy

This paper concentrates on the finite-time consensus problem faced by nonlinear multi-agent systems (MASs) via impulsive time window theory with a two-stage control (TSC) strategy. The TSC strategy divides the whole control period into two parts: a variable impulsive control stage and a finite-time consensus control stage. Different from general single-stage control, TSC can dynamically adjust the time periods of impulsive control and finite-time control according to practical application requirements. Variable impulsive control is also discussed in this paper. Compared with the sampling based on traditional fixed impulsive theory, impulsive sampling in the TSC strategy occurs randomly within an impulsive time window and provides much more flexibility. In addition, a switching topology scheme is introduced in this paper to strengthen the stability of MASs. Finally, two numerical simulation examples (one leaderless case and one leader-following case) are used for the theoretical analysis.

     

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.     

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.     

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.     

The theory of robot stability in dynamic environment revisited

The problem of stability of a robot in a dynamic environment is solved. Sufficient stability conditions for a given programmed path of the robot are established. The effect of the dynamic environment is illustrated by three examples     

Analytical development of disturbed matrix eigenvalue problem applied to mixed convection stability analysis in Darcy media

This work consists in evaluating algebraically and numerically the influence of a disturbance on the spectral values of a diagonalizable matrix. Thus, two approaches will be possible; to use the theorem of disturbances of a matrix depending on a parameter, due to Lidskii and primarily based on the structure of Jordan of the no disturbed matrix. The second approach consists in factorizing the matrix system, and then carrying out a numerical calculation of the roots of the disturbances matrix characteristic polynomial. This problem can be a standard model in the equations of the continuous media mechanics. During this work, we chose to use the second approach and in order to illustrate the application, we choose the Rayleigh–Bénard problem in Darcy media, disturbed by a filtering through flow. The matrix form of the problem is calculated starting from a linear stability analysis by a finite elements method. We show that it is possible to break up the general phenomenon into other elementary ones described respectively by a disturbed matrix and a disturbance. A good agreement between the two methods was seen. To cite this article: H.B. Hamed, R. Bennacer, C. R. Mecanique 336 (2008).     

Approximate solving method of shock for nonlinear disturbed coupled Schrödinger system

A class of nonlinear disturbed coupled Schrödinger systems is studied. The specific technique is used to relate the exact and approximate solutions. The corresponding typical coupled system is considered. An exact shock travelling solution is obtained by a mapping method. The travelling asymptotic solutions of the disturbed coupled Schrödinger system are then found with an approximate method.     

航天器有限时间自适应容错姿态控制

针对存在执行器故障、转动惯量偏差以及外部扰动等系统不确定性的航天器姿态跟踪问题,提出一种有限时间自适应容错姿态控制方法。建立基于四元数的航天器姿态动力学模型、执行器故障模型和系统不确定性模型,并将执行器故障分为乘性故障和加性故障两大类;利用滑模控制和有限时间控制理论设计有限时间姿态控制器,并通过设计自适应变量及更新方法对执行器故障以及系统不确定性引起的控制偏差上界进行估计和补偿,使姿态控制器对故障和扰动具有良好的适应性和鲁棒性。得到的新型有限时间自适应容错姿态控制器能够保证航天器在执行器故障以及系统不确定性条件下在有限时间内精确收敛到期望值。利用Lyapunov稳定性理论证明了系统的渐进稳定性和有限时间稳定性,数值仿真验证了所提出方法的可行性和有效性。     

Finite-time prescribed performance control of MEMS gyroscopes

This paper addresses the finite-time prescribed performance control of MEMS gyroscopes. From the perspective of practical engineering, this paper arranges the desirable transient and steady-state performances according to the engineering requirements in the controller design procedure. For the tracking performance, prescribed performance control is studied to limited the steady-state error and the maximum overshoot. For the prescribed settling time, super-twisting sliding mode control and nonsingular terminal sliding mode control are employed to achieve finite-time convergence, respectively. The system stability is verified via Lyapunov approach. Through simulation tests, it is demonstrated that prescribed performance and finite-time convergence can be obtained under the proposed control scheme.

     

Finite-time optimal formation tracking control of vehicles in horizontal plane

This paper studies the problem of finite-time optimal formation tracking for planar vehicles which are considered as rigid bodies, under the condition that the tracking time is given according to task requirements in advance. By using Pontryagin’s maximum principle (PMP) on a Lie group, an optimal control law is designed for vehicles with holonomic dynamics to track a desired reference trajectory at the given tracking time in the manner of rigid formation which is also specified by task requirements. Simultaneously, a corresponding cost function is considered and guaranteed to be optimal. Then, the above mentioned result of tracking is extended to the case of multi-vehicle systems with a directed-tree communication topology. Furthermore, some conditions are proposed to ensure the adjoint orbits of vehicles to be non-holonomic. Finally, the numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

Local Existence and Finite-time Blow-up in Multidimensional Radiation Hydrodynamics

We first prove the local existence of smooth solutions to the Cauchy problem for the equations of multidimensional radiation hydrodynamics which are a hyperbolic-Boltzmann coupled system. Then, we show that a smooth solution will blow up in finite time if the initial data are large. Moreover, the property of finite propagation speed is obtained simultaneously. Supported by the NSF of Jiangxi Province, the Special Funds for Major State Basic Research Projects, the NSFC (Grant No. 10225105) and the CAEP (Grant No. 2003-R-02).     

Thermocapillary convection stability in a cylindrically-symmetric two-phase system

Thermocapillary flows in an infinitely long liquid cylinder surrounded by a coaxial gas layer with a controlled flow rate and the stability of such flows are investigated. In the layers a constant axial temperature gradient is maintained. An exact solution of the equations of motion describing the steady-state flow in this two-phase system is derived. Possible flow regimes and their stability in the linear approximation are studied. It is shown that in the liquid phase the thermocapillary flow can be completely stopped by the gas flow at the expense of the interaction between mechanical stresses at the interface. The results obtained indicate the possibility of controlling thermocapillary flows and their stability by means of gas flows.