Prescribed-time adaptive neural tracking control for a class of uncertain robotic manipulators with dead zone input

This paper solves the prescribed-time control problem for a class of robotic manipulators with system uncertainty and dead zone input. To make the system stable within a given convergence time T, a novel prescribed-time adaptive neural tracking controller is proposed by using the temporal scale transformation method and Lyapunov stability theory. Unlike the finite-time and the fixed-time stability where the convergence time depends on the controller parameters, the convergence time constant T is introduced into the proposed controller so that the closed-loop system will be stable within T. To cope with the system uncertainty, radial basis function neural networks (RBFNNs) are used and only need to update one parameter online. In addition, by choosing the same structure and parameters of RBFNNs, the proposed method can shorten the convergence time of the neural networks. Finally, simulation results are presented to demonstrate the effectiveness of the prescribed-time controller.

     

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.     

On improved passivity criteria of uncertain neural networks with time-varying delays

In this paper, the problem of passivity analysis for uncertain neural networks with time-varying delays is considered. By constructing an augmented Lyapunov–Krasovskii’s functional and some novel analysis techniques, improved delay-dependent criteria for checking the passivity of the neural networks are established. The proposed criteria are represented in terms of LMIs (linear matrix inequalities) which can be easily solved by various convex optimization algorithms. Two numerical examples are included to show the superiority of our results.     

Finite-time tracking control for a class of high-order nonlinear systems and its applications

This study investigates the problem of finite-time tracking control for a class of high-order nonlinear systems. Due to the existence of uncertain time-varying control coefficient and unknown nonlinear perturbations in the nonlinear dynamics, the existing finite-time control results cannot solve the finite-time tracking problem for this kind of nonlinear systems. Based on the technique of adding a power integrator a variable structure control method is proposed. Under the proposed control law, it is shown that the reference signal can be tracked in a finite time. As an application of the proposed theoretic results, the problem of finite-time attitude tracking control for the roll channel of bank-to-turn missile is solved. Simulation results are given to demonstrate the effectiveness of the proposed method.     

Finite-time projective synchronization of memristor-based delay fractional-order neural networks

Nonlinear Dynamics - This paper mainly investigates the finite-time projective synchronization problem of memristor-based delay fractional-order neural networks (MDFNNs). By using the definition of...     

Finite-time stochastic synchronization of time-delay neural networks with noise disturbance

Nonlinear Dynamics - The finite-time stochastic synchronization of time-delay neural networks with noise disturbance is investigated according to finite-time stability theory of stochastic...     

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 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...     

Robust finite-time tracking for a square fully actuated class of nonlinear systems

In this paper, the robust finite-time tracking problem is addressed for a square fully actuated class of nonlinear systems subjected to disturbances and uncertainties. Firstly, two applicable lemmas are derived and novel nonlinear sliding surfaces (manifolds) are defined by applying these lemmas. Secondly, by developing the nonsingular terminal sliding mode control, two different types of robust nonlinear control inputs are designed to meet and accomplish the aforementioned finite-time tracking objective. The global finite-time stability of the closed-loop nonlinear system is evaluated analytically and mathematically. The proposed control inputs are utilized to tackle and solve two interesting issues containing (a): the finite-time tracking problem of the unified chaotic system and (b): the finite-time synchronization of two non-identical hyperchaotic systems. Finally, based on MATLAB software, two numerical simulations are carried out to illustrate and demonstrate the effectiveness and performance of the proposed robust finite-time nonlinear control schemes.

     

Adaptive finite-time stabilization of uncertain non-autonomous chaotic electromechanical gyrostat systems with unknown parameters

This paper deals with the problem of robust finite-time stabilization of non-autonomous chaotic gyrostat systems. It is assumed that the parameters of the gyrostat system are completely unknown in advance and the system is perturbed by unknown uncertainties and disturbances. Some update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and the update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in a finite time. The finite-time stability and convergence of the closed-loop system are analytically proved. A numerical simulation is given to demonstrate the applicability and robustness of the proposed finite-time controller and to verify the theoretical results.     

Robust synchronization of uncertain chaotic neural networks with randomly occurring uncertainties and non-fragile output coupling delayed feedback controllers

This paper deals with the synchronization control problem for the uncertain chaotic neural networks with randomly occurring uncertainties and randomly occurring control gain fluctuations. By introducing an improved Lyapunov–Krasovskii functional and employing reciprocally convex approach, a delay-dependent non-fragile output feedback controller is designed to achieve synchronization with the help of a drive–response system and the linear matrix inequality approach. Finally, numerical results and its simulations are given to show the effectiveness of the derived results.     

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 synchronization of complex networks with nonidentical discontinuous nodes

In this paper, we study the finite-time synchronization problem for linearly coupled complex networks with discontinuous nonidentical nodes. Firstly, new conditions for general discontinuous chaotic systems is proposed, which is easy to be verified. Secondly, a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions. Based on a finite-time stability theorem for equations with discontinuous right-hand and inequality techniques, several sufficient conditions are obtained to ensure the synchronization goal. Results of this paper are general, and they extend and improve existing results on both continuous and discontinuous complex networks. Finally, numerical example, in which a BA scale-free network with discontinuous Sprott and Chua circuits is finite-timely synchronized onto discontinuous Chen system, is given to show the effectiveness of our new results.     

A general nonlinear adaptive control scheme for finite-time synchronization of chaotic systems with uncertain parameters and nonlinear inputs

In this paper, the problem of finite-time chaos synchronization between two different uncertain chaotic systems with unknown parameters and input nonlinearities is investigated. It is assumed that both master and slave systems are perturbed by unknown model uncertainties, external disturbances, and fully unknown parameters. Proper update laws are proposed to estimate the systems?? unknown parameters. Based on the update laws and finite-time control technique, a robust adaptive controller is introduced to guarantee the convergence of the slave system trajectories to the trajectories of the master system in a given finite time. Two illustrative examples are presented to illustrate the effectiveness and applicability of the proposed finite-time controller and to validate the theoretical results of the paper.     

Finite-time H ∞ control for a class of Markovian jump delayed systems with input saturation

This work considers the finite-time control problem for a class Markovian jump delayed systems with partially known transition rates subject to saturating actuators. By employing local sector conditions and an appropriate Lyapunov–Krasovkii function, an observer-based state feedback controller is designed to guarantee that the resulted closed-loop constrained system is mean-square locally asymptotically finite-time stabilizable. Some sufficient conditions for the solution to this problem are derived in terms of linear matrix inequalities. Finally, a numerical example is provided to demonstrate the effectiveness of proposed method.     

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.

     

Synchronization of nonlinear chaotic electromechanical gyrostat systems with uncertainties

This paper solves the problem of robust synchronization of nonlinear chaotic gyrostat systems in a given finite time. The parameters of both master and slave chaotic gyrostat systems are assumed to be unknown in advance. In addition, the gyrostat systems are disturbed by unknown model uncertainties and external disturbances. Suitable update laws are proposed to estimate the unknown parameters. Based on the finite-time control idea and update laws, appropriate control laws are designed to ensure the stabilization of the closed-loop system in finite time. The precise value of the convergence time is given. A numerical simulation demonstrates the applicability and efficiency of the proposed finite-time synchronization strategy.     

Direct adaptive neural control for strict-feedback stochastic nonlinear systems

This note considers the problem of direct adaptive neural control for a class of nonlinear single-input/single-output (SISO) strict-feedback stochastic systems. The variable separation technique is introduced to decompose the coefficient functions of the diffusion term. Radical basis function (RBF) neural networks are used to approximate unknown and desired control signals, then a novel direct adaptive neural controller is constructed via backstepping. The proposed adaptive neural controller guarantees that all the signals in the closed-loop system remain bounded in probability. A main advantage of the proposed controller is that it contains only one adaptive parameter needed to be updated online. Simulation results demonstrate the effectiveness of the proposed approach.     

Practical finite-time synchronization of jerk systems: Theory and experiment

This paper addresses the problem of finite-time synchronization of jerk chaotic systems through a simple linear feedback control. The controller is designed such that practical finite-time synchronization could be achieved. As example, we use a new jerk system obtained thanks to the chaotification of the Duffing system using jerk architecture and simplification via a single silicon p-n junction diode. Mathematic proof, numerical and PSpice simulations, and practical results are presented to show the feasibility of the proposed scheme. The proposed method could be applied to all jerk-like systems.     

航天器有限时间饱和姿态跟踪控制

针对刚体航天器系统,对存在模型不确定性、外界干扰力矩和控制器饱和等条件下的姿态跟踪控制问题进行了研究。首先,考虑未知模型不确定性和外界干扰,且总干扰上界为未知常数,结合快速非奇异终端滑模、快速终端滑模趋近律以及辅助系统构造了基本的鲁棒有限时间饱和控制器,并通过辅助系统直接补偿了控制器饱和;其次,针对系统总干扰具有多项式上界的情形,进一步结合自适应控制算法,对其上界函数中的未知参数进行在线估计,并设计了自适应有限时间饱和控制器。同时,基于Lyapunov稳定性理论证明了所提出控制算法的有限时间收敛特性。最后,通过数值仿真验证所提出控制算法的控制效果,在两种控制器作用下姿态的跟踪精度分别为5×10-5和1×10-5,证明了所提出控制算法的有效性。