Tracking control of uncertain switched nonlinear cascade systems: a nonlinear H ∞ sliding mode control method

This paper considers the tracking control problem for a class of uncertain switched nonlinear cascade systems via the multiple Lyapunov functions (MLFs) method. Each subsystem under consideration is composed of two cascade-connected parts: the null space dynamics part and the range space dynamics part. The two main robust control strategies, nonlinear H _∞ control (NHC) and the sliding mode control (SMC), are integrated to function in a complementary manner for tracking control tasks. Furthermore, sufficient conditions for the solvability of the tracking control problem of the switched system and design of both switching laws and controllers are presented. Finally, a simulation example is provided to demonstrate the feasibility of the developed method.     

Noise-to-state finite-time practical stability for random nonlinear systems and its application in random Lagrange systems

The noise-to-state finite-time practical stability for random nonlinear systems and its application is studied in this paper. The definition of noise-to-state finite-time practical stability is firstly introduced in probability sense for random nonlinear systems. Next, the related stability criterion is also given by Lyapunov approach. For random benchmark system, the finite-time adaptive tracking control problem is investigated by the vectorial backstepping method and the obtained stability theorem. Simulation example illustrates that the constructed controller design scheme is effective and feasible.

     

A novel terminal sliding mode controller for a class of non-autonomous fractional-order systems

This paper introduces a finite-time control technique for control of a class of non-autonomous fractional-order nonlinear systems in the presence of system uncertainties and external noises. It is known that finite-time control methods demonstrate better robustness and disturbance rejection properties. Moreover, finite time control methods have optimal settling time. In order to design a robust finite-time controller, a new nonsingular terminal sliding manifold is proposed. The proposed sliding mode dynamics has the property of fast convergence to zero. Afterwards, a novel fractional sliding mode control law is introduced to guarantee the occurrence of the sliding motion in finite time. The convergence times of both reaching and sliding phases are estimated. The main characteristics of the proposed fractional sliding mode technique are (1) finite-time convergence to the origin; (2) the use of only one control input; (3) robustness against system uncertainties and external noises; and (4) the ability of control of non-autonomous fractional-order systems. At the end of this paper, some computer simulations are included to highlight the applicability and efficacy of the proposed fractional control method.     

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.     

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。     

Finite time chaos control for a class of chaotic systems with input nonlinearities via TSM scheme

This paper investigates nonsingular terminal sliding mode control for a class of uncertain systems with nonlinear inputs and its application in chaos control. When some of the system states are finite-time stable, the nonlinear items that coupled with these states may come into zeros in other subsystems. This will simplify the stability analysis of the whole system greatly. Compared with the traditional finite-time stabilization design method, the introduction of the terminal sliding mode can reduce the input dimensions. Only one control input is requested to realize chaos control of the Liu system when unmatched uncertainties and input nonlinearity coexist. The parameter matrices in the TSM can be determined through the solution of LMIS. Simulation results are given to demonstrate the effectiveness of the proposed method.     

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 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 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.

     

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.

     

No-chatter variable structure control for fractional nonlinear complex systems

This paper concerns the problem of robust control of uncertain fractional-order nonlinear complex systems. After establishing a simple linear sliding surface, the sliding mode theory is used to derive a novel robust fractional control law for ensuring the existence of the sliding motion in finite time. We use a nonsmooth positive definitive function to prove the stability of the controlled system based on the fractional version of the Lyapunov stability theorem. In order to avoid the chattering, which is inherent in conventional sliding mode controllers, we transfer the sign function of the control input into the first derivative of the control signal. The proposed sliding mode approach is also applied for control of a class of nonlinear fractional-order systems via a single control input. Simulation results indicate that the proposed fractional variable structure controller works well for stabilization of hyperchaotic and chaotic complex fractional-order nonlinear systems. Moreover, it is revealed that the control inputs are free of chattering and practical.     

Robust synchronization of a chaotic mechanical system with nonlinearities in control inputs

Centrifugal flywheel governors are known as chaotic non-autonomous mechanical devices used for automatic control of the speed of engines. The main characteristic of them is avoiding the damage caused by sudden change of the load torques. In this paper, the problem of robust finite-time synchronization of centrifugal flywheel governor systems is studied. The effects of unknown parameters, model uncertainties, external noises, and input nonlinearities are fully taken into account. We propose some adaptive laws to overcome the side effects of the unknown parameters of the system on the synchronization performance. Then, a robust adaptive switching controller is introduced to synchronize centrifugal flywheel governors with nonlinear control inputs in a given finite time. The finite-time fast convergence property of the proposed scheme is analytically proved and numerically illustrated.     

Observer-based adaptive fuzzy finite-time prescribed performance tracking control for strict-feedback systems with input dead-zone and saturation

This paper considers the problems of finite-time prescribed performance tracking control for a class of strict-feedback nonlinear systems with input dead-zone and saturation simultaneously. The unknown nonlinear functions are approximated by fuzzy logic systems and the unmeasurable states are estimated by designing a fuzzy state observer. In addition, a non-affine smooth function is used to approximate the non-smooth input dead-zone and saturated nonlinearity, and it is varied to the affine form via the mean value theorem. An adaptive fuzzy output feedback controller is developed by backstepping control method and Nussbaum gain method. It guarantees that the tracking error falls within a pre-set boundary at finite time and all the signals of the closed-loop system are bounded. The simulation results illustrate the feasibility of the design scheme.

     

Finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties

Nonlinear Dynamics - This paper investigates the problem of finite-time event-triggered sliding mode control for one-sided Lipschitz nonlinear systems with uncertainties. The system is subjected to...     

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.     

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...     

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.     

Efficient targeted energy transfer of bistable nonlinear energy sink: application to optimal design

This paper addresses the tracking control problem of Euler–Lagrange systems with external disturbances in an environment containing obstacles. Based on a novel sliding manifold, a new asymptotic tracking controller is proposed to ensure the tracking errors converge to zero as time goes to infinity. Moreover, based on a modified nonsingular terminal sliding manifold, a finite-time convergent control algorithm is also developed to make sure the tracking errors converge to a small bounded area near the origin in finite time. Through introducing collision avoidance functions into the sliding manifolds, both controllers can guarantee the obstacle avoidance. Moreover, the stability of the closed-loop systems and approaches free of local minima have been rigorously analyzed. Finally, numerical simulations are carried out to demonstrate the effectiveness of the proposed strategies.     

Property and evolution of the running-in attractor in an actual dynamic system

In this paper, the issue of adaptive neural tracking control for uncertain switched multi-input multi-output (MIMO) nonstrict-feedback nonlinear systems with average dwell time is studied. The system under consideration includes unknown dead-zone inputs and output constraints. The uncertain nonlinear functions are identified via neural networks. Also, neural networks-based switched observer is constructed to approximate all unmeasurable states. By means of the information for dead-zone slopes and barrier Lyapunov function (BLF), the problems of dead-zone inputs and output constraints are tackled. Furthermore, dynamic surface control (DSC) scheme is employed to ensure that the computation burden is greatly reduced. Then, an observer-based adaptive neural control strategy is developed on the basis of backstepping technique and multiple Lyapunov functions approach. Under the designed controller, all the signals existing in switched closed-loop system are bounded, and system outputs can track the target trajectories within small bounded errors. Finally, the feasibility of the presented control algorithm is proved via simulation results.

     

Fuzzy observer-based command filtered tracking control for uncertain strict-feedback nonlinear systems with sensor faults and event-triggered technology

For the trajectory tracking problem of nth-order uncertain nonlinear systems with sensor faults, a fuzzy controller based on command filtered and event-triggered technology is designed to improve the tracking error of the system. Concurrently, a fault-tolerant control scheme is introduced to effectively solve the problem of sudden output sensor failure. Additionally, the proposed controller can also greatly avoid complexity explosion problem of derivations of virtual control laws, which makes the design of the controller simpler. Furthermore, an effective observer is designed to solve the problem of system state immeasurability. Therefore, the proposed control scheme makes the design of the controller more convenient and flexible. According to Lyapunov stability theory, it is proved that all closed-loop signals are uniformly and ultimately bounded. Finally, two simulation examples of second-order nonlinear system and single-link robot show the effectiveness of the proposed scheme.