Impulsive effects on weak projective synchronization of parameter mismatched stochastic memristive neural networks

This paper analyses the weak projective synchronization (WPS) of the parameter mismatched memristive neural networks (MNNs) with stochastic disturbance and time delays via impulsive control. Complete synchronization cannot achieve because of the projective factor and mismatched parameters. Therefore, the WPS of practical MNNs under impulsive control strategy is studied. The augmented systems are built to utilize more information of the system and reduce the constraint conditions. Meanwhile, two types of comparison principles are used owing to the impulsive controller with and without time delays. Then, sufficient criteria for the exponential convergence of systems are obtained under the positive and negative effects of impulses. Finally, the validity of the theoretical results is verified by simulations of different conditions.     

Adaptive second order terminal sliding mode controller for robotic manipulators

In this paper an adaptive second order terminal sliding mode (SOTSM) controller is proposed for controlling robotic manipulators. Instead of the normal control input, its time derivative is used in the proposed controller. The discontinuous sign function is contained in the derivative control and the actual control obtained after integration is continuous and hence chatterless. An adaptive tuning method is utilized to deal with the system uncertainties whose upper bounds are not required to be known in advance. The performance of the proposed control strategy is evaluated through the control of a two-link rigid robotic manipulator. Simulation results demonstrate the effectiveness of the proposed control method.     

Fixed-time consensus for stochastic multi-agent systems with discontinuous dynamics via quantized control

In this study, the fixed-time consensus (FDTC) for stochastic multi-agent systems (MASs) with discontinuous inherent dynamics is investigated via quantized control. Firstly, an improved lemma for fixed-time (FDT) stability is derived and several more precise estimations for settling time (SLT) are gained by using certain special functions. Secondly, a more general MAS containing discontinuous inherent dynamics and stochastic perturbations is considered, which is closer to practical life. Thirdly, to overcome the limitation of communication, two kinds of quantized control protocols are designed. Besides, in the light of the graph theory, non-smooth analysis, fixed-time (FDT) stability and stochastic analysis theory, some sufficient conditions are put forward to achieve FDTC of MASs. Finally, the validity of the derived theoretical results is testified by two numerical examples.     

Adaptive fuzzy fixed-time dynamic surface control for stochastic nonstrict nonlinear systems with unknown dead-zones

This paper focuses on an adaptive fuzzy fixed-time control problem for stochastic nonstrict nonlinear systems with unknown dead-zones by using dynamic surface control (DSC) technology. Fuzzy logic systems (FLSs) and DSC technology are used to approximate nonlinear functions and reduce the computational complexity, respectively. At the same time, the influence of the dead-zone disturbance is offset by transforming the dead-zone model into the nonlinear model that can be approximated by the FLSs. Then, based on the fixed-time stability theory, an adaptive fuzzy fixed-time tracking control strategy is proposed, which can ensure semi-global practical fixed-time stability of the system and the tracking error converging to a small neighborhood near the origin. Finally, two simulation examples are given to prove the effectiveness of the proposed control strategy.     

Actuator failure compensation and attitude control for rigid satellite by adaptive control using quaternion feedback

The attitude control problem of a rigid satellite with actuator failure uncertainties and external disturbance is addressed using adaptive control method. A discontinuous adaptive failure compensation controller, using unit quaternion and angular velocities feedback, is designed to accommodate the external disturbance and actuator failures which are uncertain in time instants, values and patterns. A common approximate function is used to avoid system chattering caused by such discontinuous control laws. The parameters of external disturbance and failure uncertainties are estimated directly by adaptive laws, and the desired stability and output tracking properties of the adaptive control system are analyzed. Finally, simulation results of a rigid satellite with six reaction wheels are presented to illustrate the performance of the proposed adaptive actuator failure compensation scheme.     

Barrier Lyapunov function-based decentralized adaptive neural control for uncertain high-order stochastic nonlinear interconnected systems with output constraints

Decentralized adaptive neural backstepping control scheme is developed for uncertain high-order stochastic nonlinear systems with unknown interconnected nonlinearity and output constraints. For the control of high-order nonlinear interconnected systems, it is assumed that nonlinear system functions are unknown. It is for the first time to control stochastic nonlinear high-order systems with output constraints. Firstly, by constructing barrier Lyapunov functions, output constraints are handled. Secondly, at each recursive step, only one adaptive parameter is updated to overcome over-parameterization problems, and RBF neural networks are used to identify unknown nonlinear functions so that the difficulties caused by completely unknown system functions and stochastic disturbances are tackled. Finally, based on the Lyapunov stability method, the decentralized adaptive control scheme via neural networks approximator is proposed, ultimately reducing the number of learning parameters. It is shown that the designed controller can guarantee all the signals of the resulting closed-loop system to be semi-globally uniformly ultimately bounded (SGUUB), and the tracking errors for each subsystem are driven to a small neighborhood of zero. The simulation studies are performed to verify the effectiveness of the proposed control strategy.     

Adaptive neural control for nonlinear switched systems with improved MDADT and its applications

In this paper, a new framework of the robust adaptive neural control for nonlinear switched stochastic systems is established in the presence of external disturbances and system uncertainties. In the existing works, the design of robust adaptive control laws for nonlinear switched systems mainly relies on the average dwell time method, while the design and analysis based on the model-dependent average dwell time (MDADT) method remains a challenge. An improved MDADT method is developed for the first time, which greatly relaxes the requirements of Lyapunov functions of any two subsystems. Benefiting from the improved MDADT, a switched disturbance observer for discontinuous disturbances is proposed, which realizes the real-time gain adjustment. For known and unknown piecewise continuous nonlinear functions, a processing method based on the tracking differentiator and the neural network is proposed, which skillfully guarantees the continuity of the control law. The theoretical proof shows that the semiglobal uniform ultimate boundedness of all closed-loop signals can be guaranteed under switching signals with MDADT property, and simulation results of the longitudinal maneuvering control at high angle of attack are given to further illustrate the effectiveness of the proposed framework.     

Dynamic event-triggered optimal tracking control for constrained nonlinear stochastic systems

This paper investigates the optimal tracking control problem (OTCP) for nonlinear stochastic systems with input constraints under the dynamic event-triggered mechanism (DETM). Firstly, the OTCP is converted into the stabilizing optimization control problem by constructing a novel stochastic augmented system. The discounted performance index with nonquadratic utility function is formulated such that the input constraint can be encoded into the optimization problem. Then the adaptive dynamic programming (ADP) method of the critic-only architecture is employed to approximate the solutions of the OTCP. Unlike the conventional ADP methods based on time-driven mechanism or static event-triggered mechanism (SETM), the proposed adaptive control scheme integrates the DETM to further lighten the computing and communication loads. Furthermore, the uniform ultimately boundedness (UUB) of the critic weights and the tracking error are analysed with the Lyapunov theory. Finally, the simulation results are provided to validate the effectiveness of the proposed approach.     

Finite/fixed-time synchronization control of coupled memristive neural networks

Finite-time and fixed-time synchronization (FAFS) of coupled memristive neural networks (CMNNs) with discontinuous feedback functions are explored in this paper. Firstly, a more comprehensive stability theory is systematically established. Secondly, by designing adaptive feedback controller and discontinuous feedback controller, both finite-time and fixed-time synchronization can be realized through regulating the main control parameter. Thirdly, 1-norm and quadratic-norm Lyapunov functions are considered simultaneously in this article, while in estimating the settling time, the former one is more accurate than the latter one under the same synchronization criteria. Finally, in numerical simulation, the analysis and comparison of the proposed controllers are given to show the effectiveness of the corresponding results.     

Event-triggered control for uncertain stochastic systems under triple network attacks

This paper studies the control problem of uncertain stochastic systems, which takes into account the impact of network attacks. The types of network attacks considered are denial-of-service (DoS) attacks, deception attacks and replay attacks. In order to save network resources and improve communication utilization, the static event-triggered mechanism and adaptive event-triggered mechanism are cited respectively. Firstly, a new Lyapunov-Krasovskii functional is constructed, employing improved Wirtinger-based integral inequality and Jensens inequality, the criteria on stochastic stability in the mean square for uncertain stochastic systems are proposed. Secondly, the design methods of static event-triggered controller and adaptive event-triggered controller are given respectively. Finally, a practical example is given to manifest the effectiveness of the theoretical results.     

Reduced-order K-filters-based event-triggered adaptive command filtered tracking control for stochastic constrained nonlinear systems

To ensure better performance and simultaneously save resources, an event-triggered adaptive command filtered dynamic surface control (ACFDSC) method for uncertain stochastic nonstrict-feedback nonlinear systems with dynamic output constraints and prescribed performance is designed in this article. Firstly, with the help of reduced-order K-filters, linearly parameterized neural networks and specific coordinate transformation technique, the unmeasurable states, nonlinearities, two types of unmodeled dynamics and output constraints are dealt with respectively. Then, an event-triggered ACFDSC strategy is proposed to ensure that the tracking error reaches a specific bound within a finite time. By introducing the compensated signal into the complete Lyapunov function, and with the assistance of the compact set defined in the stability analysis, all signals are strictly demonstrated to be semi-globally uniformly ultimately bounded. The simulation results verify the effectiveness of the proposed method.     

Finite-time and fixed-time synchronization of discontinuous complex networks: A unified control framework design

This paper is concerned with the finite-time and fixed-time synchronization of complex networks with discontinuous nodes dynamics. Firstly, under the framework of Filippov solution, a new theorem of finite-time and fixed-time stability is established for nonlinear systems with discontinuous right-hand sides by using mainly reduction to absurdity. Furthermore, for a class of discontinuous complex networks, a general control law is firstly designed. Under the unified control framework and the same conditions, the considered networks are ensured to achieve finite-time or fixed-time synchronization by only adjusting the value of a key control parameter. Based on the similar discussion, a unified control strategy is also provided to realize respectively asymptotical, exponential and finite-time synchronization of the addressed networks. Finally, the derived theoretical results are supported by an example with numerical simulations.     

Event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems

This paper is concerned with event-triggered adaptive fuzzy tracking control for high-order stochastic nonlinear systems. The approach of fuzzy logic systems (FLSs) approximation is extended to high-order stochastic nonlinear systems to deal with the unknown nonlinear uncertainties. A novel high-order adaptive fuzzy tracking controller is firstly presented via a backstepping approach and event-triggering mechanism which can mitigate the unnecessary waste of computation and communication resources. Based on the above techniques, frequently-used growth assumptions imposed on unknown system nonlinearities are removed and the influence for the high order is handled. The proposed high-order adaptive fuzzy tracking control method not only deals with the influence of high order, but also ensures that the tracking error converges to a small neighborhood of the origin in probability. Finally, the effectiveness of the proposed control method is illustrated by a numerical example.     

Adaptive fault-tolerant shape control for nonlinear Lipschitz stochastic distribution systems

This paper addresses the problem of adaptive fault estimation and fault-tolerant control for a class of nonlinear non-Gaussian stochastic systems subject to time-varying loss of control effectiveness faults. In this work, time-varying faults, Lipschitz nonlinear property and general stochastic characteristics are taken into consideration in a unified framework. Instead of using the system output signal, the output distribution is adopted for shape control. Both the states and faults are simultaneously estimated by an adaptive observer. Then, a fault tolerant shape controller is designed to compensate for the faults and realize stochastic output distribution tracking. Both the fault estimation and the fault tolerant control schemes are designed based on linear matrix inequality (LMI) technique. Satisfactory performance has been obtained for a numerical simulation example. Furthermore the proposed scheme is successfully tested in a case study of particle size distribution control for an emulsion polymerization reactor.     

随机非线性系统的控制器设计和闭环性能分析

针对几类重要的随机非线性系统, 提出了一些新的概念,发展了一些基本分析工具, 研究了几类控制器的设计问题. 主要成果包括:(1) 针对一类部分动态不可量测的非线性随机系统,引入了随机输入状态稳定(SISS)的概念, 借助于分析概率理论,发展了随机系统改变能量函数方法, 成功地处理了随机微分中的伊藤项,给出了随机非线性串联系统SISS的小增益类条件. (2) 对一类具有SISS随机逆动态的大规模随机非线性系统,给出了分散自适应输出反馈镇定控制器的构造性设计方法. 既解决了实用镇定问题也解决了渐近镇定问题. 在分散控制框架内,给出了处理随机非线性逆动 态的方法. (3) 对一类具有不稳定零动态的随机非线性系统,引入了随机输入状态可镇定的概念,给出了全局输出反馈镇定控制器构造性设计方法. (4) 对一类具有线性增长的不可量测状态的随机非线性系统,针对方差未知的噪声和一般随机输入,引入了广义随机输入状态稳定(GSISS)的概念,分别给出了随机干扰抑制和渐近镇定的输出反馈控制器的构造性设计方法.(5) 对一般的时滞随机非线性系统, 给出了解存在唯一的判定条件,引入了依概率全局(渐近)稳定的概念及相应的判定准则,丰富了随机时滞非线性系统的控制器设计理论. 对一类不确定随机时变时滞系统,构造性地设计出了自适应输出反馈镇定控制器.     

Synchronization of multiplex networks with stochastic perturbations via pinning adaptive control

This paper investigates the synchronization problems for the multiplex networks with both inter-layer and intra-layer couplings subject to the stochastic perturbations. In particular, the topologies of all layers are not the same, so the model can represent a class of multiplex networks. To synchronize the multiplex networks onto the trajectory of a virtual leader, a pinning adaptive protocol is proposed and some pinning criteria are derived for guaranteeing complete synchronization. Furthermore, when the results are extended to the systems with time delays, the pinning adaptive strategy is still proved to be effective. Finally, a two-layer network and a three-layer network are selected for numerical simulations to illustrate the theoretical results.     

Passivity-based resilient adaptive control for fuzzy stochastic delay systems with Markovian switching

The resilient adaptive controller design problem of a class of Itô-type Takagi–Sugeno (T–S) fuzzy stochastic systems with time-varying delay and Markovian switching is investigated. By utilizing improved matrix decoupling technique, passivity theory and stochastic Lyapunov–Krasovskii functional, LMIs-based sufficient conditions for the existence of resilient adaptive controller are provided such that the corresponding closed-loop system is almost surely asymptotically stable and robustly passive in the sense of expectation. The derived conditions can be easily solved with the help of LMI toolbox in Matlab. A simulation example is presented to illustrate the effectiveness of the proposed resilient adaptive control schemes.     

Adaptive finite-time control for stochastic nonlinear systems subject to unknown covariance noise

This paper is devoted to the adaptive finite-time control for a class of stochastic nonlinear systems driven by the noise of covariance. The traditional growth conditions assumed on the drift and diffusion terms are removed through a technical lemma, and the negative effect generated by unknown covariance noise is compensated by combining adaptive control technique with backstepping recursive design. Then, without imposing any growth assumptions, a smooth adaptive state-feedback controller is skillfully designed and analyzed with the help of the adding a power integrator method and stochastic backstepping technique. Distinctive from the global stability in probability or asymptotic stability in probability obtained in related work, the proposed design algorithm can guarantee the solution of the closed-loop system to be finite-time stable in probability. Finally, a stochastic simple pendulum system is skillfully constructed to demonstrate the effectiveness of the proposed control scheme.     

Fuzzy adaptive fault-tolerant tracking control of MIMO stochastic pure-feedback nonlinear systems with actuator failures

This paper studies the adaptive fuzzy fault-tolerant control design problem for a class of stochastic multi-input and multi-output (MIMO) nonlinear systems in pure-feedback form. The nonlinear systems under study contain unknown functions, unmeasured states and actuator faults, which are described by the loss of effectiveness and lock-in-place modes. With the help of fuzzy logic systems identifying uncertain stochastic nonlinear systems, a fuzzy state observer is established for estimating the unmeasured states. Based on the backstepping design technique with the nonlinear tolerant-fault control theory, an adaptive fuzzy output feedback faults-tolerant control approach is developed. It is proved that the proposed fault-tolerant control approach can guarantee that all the signals of the resulting closed-loop system are bounded in probability. Moreover, the observer errors and tracking errors can be regulated to a small neighborhood of the origin by choosing design parameters appropriately. A simulation example is provided to show the effectiveness of the proposed approach.     

An integrated data-driven Markov parameters sequence identification and adaptive dynamic programming method to design fault-tolerant optimal tracking control for completely unknown model systems

In this paper, an integrated design of data-driven fault-tolerant tracking control is addressed relying on the Markov parameters sequence identification and adaptive dynamic programming techniques. For the unknown model systems, the sequence of Markov parameters together with the covariance of innovation signal is firstly estimated by least square method. After a transformation of value function from stochastic to deterministic, a policy iteration adaptive dynamic programming algorithm is then formulated to find the optimal tracking control law. In order to eliminate the influence of unpredicted faults, an active fault-tolerant supervisory control strategy is further constructed by synthesizing fault detection, isolation, estimation and compensation. All these involved designs are performed in the data-driven manner, and thus avoid the information requirement about system drift dynamics. From the perspective of system operation management, the above integrated control scheme provides a framework to achieve the tracking performance optimization, monitoring and maintaining simultaneously. The effectiveness of these conclusions is finally verified via two case studies.