Distributed fault-tolerant tracking control for heterogeneous nonlinear multi-agent systems under sampled intermittent communications

This paper studies the distributed fault-tolerant control (FTC) problem for heterogeneous nonlinear multi-agent systems (MASs) under sampled intermittent communications. First, in order to estimate the state of leader under sampled intermittent communications, the distributed intermittent observer for each follower is constructed. By using the tool from switching system theory, the estimation error converges to zero exponentially if the communication rate is larger than a threshold value even under the impact of sampled intermittent communications. Then, by applying model reference adaptive tracking technique, a robust FTC protocol is developed to track the distributed intermittent observer. Two algorithms are presented to choose the feedback gain of the distributed intermittent observer and the tracking feedback gain of the fault-tolerant tracking controller. It is proved that the global consensus tracking error is bounded under the developed distributed control protocol. Finally, an example with the coupled pendulums is provided to verify the efficiency of the designed method.     

Sliding mode consistency tracking control of multiple heavy haul trains under input saturation and safety distance constraints

In order to ensure that under the influence of input saturation, a safe distance between adjacent locomotives and adjacent trains in multiple heavy haul trains (HHTS) is main-tained, an anti-saturation sliding mode consistency (ASMC) control algorithm is proposed. First, a multitrain and multiparticle dynamic model (MMDM) based on multitrain single particle that considers nonlinear coupling force and external disturbance effect is established. Next, a dynamic auxiliary compensation (DAC) system combined with sliding mode surface that can rapidly reduce the saturation deviation is designed and consistency algorithm of the simplified control structure is introduced to construct the ASMC control algorithm. Then, theoretical derivation proved that the algorithm can ensure the convergence of the tracking distance between adjacent locomotives and between adjacent trains to a bounded safe range whilst overcoming the influence of input saturation on each train. Lastly, the simulink and RT-LAB simulation results are used to verify the effectiveness of the design algorithm.     

Hermite neural network-based second-order sliding-mode control of synchronous reluctance motor drive systems

This paper proposes a novel Hermite neural network-based second-order sliding-mode (HNN-SOSM) control strategy for the synchronous reluctance motor (SynRM) drive system. The proposed HNN-SOSM control strategy is a nonlinear vector control strategy consisting of the speed control loop and the current control loop. The speed control loop adopts a composite speed controller, which is composed of three components: 1) a standard super-twisting algorithm-based SOSM (STA-SOSM) controller for achieving the rotor angular speed tracking control, 2) a HNN-based disturbance estimator (HNN-DE) for compensating the lumped disturbance, which is composed of external disturbances and parametric uncertainties, and 3) an error compensator for compensating the approximation error of the HNN-DE. The learning laws for the HNN-DE and the error compensator are derived by the Lyapunov synthesis approach. In the current control loop, considering the magnetic saturation effect, two composite current controllers, each of which comprises two standard STA-SOSM controllers, are designed to make direct and quadrature axes stator current components in the rotor reference frame track their references, respectively. Comparative hardware-in-the-loop (HIL) tests between the proposed HNN-SOSM control strategy and the conventional STA-SOSM control strategy for the SynRM drive system are performed. The results of the HIL tests validate the feasibility and the superiority of the proposed HNN-SOSM control strategy.     

Intermittent control strategy for synchronization of fractional-order neural networks via piecewise Lyapunov function method

In this paper, the synchronization problem of fractional-order neural networks (FNNs) with chaotic dynamics is investigated via the intermittent control strategy. Two types of intermittent control methods, the aperiodic one and the periodic one, are applied to achieve the synchronization of the considered systems. Based on the dynamic characteristics of the intermittent control systems, the piecewise Lyapunov function method is employed to derive the synchronization criteria with less conservatism. The results under the aperiodically intermittent control show more generality than the ones via the periodically intermittent control. For each of the aperiodic and periodic cases, a simple controller design process is presented to show how to design the corresponding intermittent controller. Finally, two numerical examples are provided to demonstrate the effectiveness of the obtained theoretical results.     

Bivariate grid-connection speed control of hydraulic wind turbines

The requirement for An electrical grid-connected wind turbine is that the synchronous generator speed is stable within a required speed range for the electrical grid. In this paper, a hydraulic wind turbine (HWT) system is considered, and the working principle and working conditions of the HWT are introduced. A novel speed control method is proposed in this paper, using both a proportional flow control valve and a variable displacement motor, which are adjusted in combination to control the speed of the HWT. By establishing a state space model of the HWT and solving the nonlinear system with a feedback linearization method, a bivariate tracking controller is constructed to realize accurate speed control under fluctuating wind speed and the load disturbance conditions. The effectiveness of the control method is verified by simulation, but experimental results highlight problems with the method. The theoretical controller is simplified to reduce sensitivity to measurement noise and modeling error. The control effect has been improved to some extent, but it is limited. Based on these results, combined with the sliding mode variable structure control method and the feedback linearization method to solve the problem of measurement noise and modeling error, and the effectiveness of the control law is finally verified experimentally. It lays a theoretical foundation for the practical application of HWT.     

Gray-fuzzy control of a nonlinear two-mass system

This study presents application of a fuzzy controller to a nonlinear two-mass system control. The proposed controller structure is strengthened with a gray estimator. Firstly, a complete state-space mathematical model for a nonlinear two-mass system is developed and numerically simulated. Then, a fuzzy controller is designed to regulate the speed of the system. In order to perform a dynamic and powerful control action, future error values are estimated by gray modeling technique. The gray estimators of the torsional torque and the load machine speed are tested with open-loop and closed-loop control structures to test the robustness of the proposed method for step changes in input parameters. It is observed that the tracking ability of the gray estimators is not influenced for different operation modes. The performances of the control structures, which are supported with gray estimators, are given and no additional feedbacks are required for robust control action. The simulation results are confirmed by experimental results and conclusions are given.     

Finite-time cooperative circumnavigation control of multiple second-order agents with desired formations

This paper investigates the finite-time cooperative circumnavigation control of multiple second-order agents, in which the agents should surround a moving target with desired formation and circular velocity based on local information. Firstly, the controller design is transformed into design control parameters such that the error system, including distance error, speed error and angle error, is finite-time consensus. The error system is viewed as a cascaded system containing two second-order subsystems, and then a distributed finite-time controller composed of two parts is delivered. The finite-time stability of the entire system is given by employing cascaded control theory. One significant advantage of the proposed controller is that it allows the agents to converge to desired trajectory in a finite time instead of asymptotically. Another merit is that the desired formation is an extensive case and unlimited, including different tracking radii and angular spacing. Furthermore, the proposed controller can be implemented by each agent in its local frame, utilizing only local information. These properties significantly extend the application scope of cooperative circumnavigation. Finally, simulations are carried out to validate the effectiveness of the proposed method.     

Predictor-based optimal robust guaranteed cost control for uncertain nonlinear systems with completely tracking errors constraint

In this paper, a novel composite controller is proposed to achieve the prescribed performance of completely tracking errors for a class of uncertain nonlinear systems. The proposed controller contains a feedforward controller and a feedback controller. The feedforward controller is constructed by incorporating the prescribed performance function (PPF) and a state predictor into the neural dynamic surface approach to guarantee the transient and steady-state responses of completely tracking errors within prescribed boundaries. Different from the traditional adaptive laws which are commonly updated by the system tracking error, the state predictor uses the prediction error to update the neural network (NN) weights such that a smooth and fast approximation for the unknown nonlinearity can be obtained without incurring high-frequency oscillations. Since the uncertainties existing in the system may influence the prescribed performance of tracking error and the estimation accuracy of NN, an optimal robust guaranteed cost control (ORGCC) is designed as the feedback controller to make the closed-loop system robustly stable and further guarantee that the system cost function is not more than a specified upper bound. The stabilities of the whole closed-loop control system is certified by the Lyapunov theory. Simulation and experimental results based on a servomechanism are conducted to demonstrate the effectiveness of the proposed method.     

Optimal adaptive reset control with guaranteed transient and steady state tracking error bounds

In this paper, a solution for improvement of transient performance in adaptive control of nonlinear systems is proposed. An optimal adaptive controller based on a reset mechanism and a prescribed performance bound is devised. The suggested controller has the structure of adaptive backstepping controller in which the estimated parameters are reset to an optimal value. The designed controller ensures both the transient bound and the asymptotical convergence of the states. It is shown that the tracking error satisfies the prescribed performance bound all the time, besides the speed of the convergence rate is increased by resetting the estimated parameters. The results have been proved through both the analytical and simulation studies. The proposed method is applied to an Augmented Quarter Car Model as a case study. Simulation results verify the established theoretical consequences that the prescribed performance bound based optimal adaptive reset controller can enhance the transient performance of the adaptive controller.     

Finite-time command filter-based adaptive fuzzy tracking control for stochastic nonlinear induction motors systems with unknown backlash-like hysteresis

In this article, an adaptive fuzzy control method is proposed for induction motors (IMs) drive systems with unknown backlash-like hysteresis. First, the stochastic nonlinear functions existed in the IMs drive systems are resolved by invoking fuzzy logic systems. Then, a finite-time command filter technique is exploited to overcome the obstacle of “explosion of complexity” emerged in the classical backstepping procedure during the controller design process. Meanwhile, the effect of the filter errors generated by command filters is decreased by utilizing corresponding error compensating mechanism. To cope with the influence of backlash-like hysteresis input, an auxiliary system is constructed, in which the output signal is applied to compensate the effect of the hysteresis. The finite-time control technology is adopted to accelerate the response speed of the system and reduce the tracking error, and the stochastic disturbance and backlash-like hysteresis are considered to improve control accuracy. It’s shown that the tracking error can converge to a small neighborhood around the origin in finite-time under the constructed controller. Finally, the availability of the presented approach is validated through simulation results.     

Super-twisting sliding-mode observer-based model reference adaptive speed control for PMSM drives

This paper develops a super-twisting sliding-mode observer-based model reference adaptive speed controller (STSMO-MRA-SC) for the permanent-magnet synchronous motor-based variable speed drive (PMSM-VSD) system. A stable first-order linear model is selected as the reference model to describe the required speed trajectory. To make the actual speed of the PMSM-VSD system follow this trajectory, the proposed STSMO-MRA-SC comprises three terms: (1) the stabilization term dependent on known parameters of the motion dynamics and the selected reference model for stabilizing the speed tracking error dynamics asymptotically; (2) the disturbance compensation term based on the STSMO for compensating the lumped disturbance in the speed tracking error dynamics; and (3) the error compensation term updated online by the adaptive law for confronting the estimation error of the STSMO in practice. Comparative experimental tests among the classic MRA-SC, the radial basis function neural network-based MRA-SC and the proposed STSMO-MRA-SC are performed. Experimental results have verified the effectiveness and the superiority of the proposed STSMO-MRA-SC.     

Finite-time synchronization of drive-response systems via periodically intermittent adaptive control

In this paper, the finite-time synchronization between two complex dynamical networks via the periodically intermittent adaptive control and the periodically intermittent feedback control is studied. The finite-time synchronization criteria are derived based on finite-time stability theory, the differential inequality and the analysis technique. Since the traditional synchronization criteria for some models are improved in the convergence time by using the novel periodically intermittent adaptive control and periodically intermittent feedback control, the results of this paper are important. Numerical examples are finally presented to illustrate the effectiveness and correctness of the theoretical results.     

Improved order-reduction method for cooperative tracking control of time-delayed multi-spacecraft network

This article investigates the order-reduction method for multi-spacecraft cooperative tracking control problems considering non-uniform time delays. The tracking error system is constructed as a linear time-varying (LTV) system since the orbit of the reference point is an ellipse. To facilitate the controller design, a model transformation method is proposed to transform the LTV system into a linear time-invariant (LTI) system with norm-bounded uncertainties. By using the sliding-mode control (SMC) technique, a delay-dependent cooperative tracking controller is designed to guarantee multiple followers to track the leader. Then, an order-reduction method is proposed to reduce the order of sufficient conditions in the form of linear matrix inequalities (LMIs), which make sure that the tracking error system is asymptotically stable. A numerical example is finally provided to illustrate the effectiveness of the designed controller and the improved performance of the order-reduction method.     

Fraction dynamic-surface-based adaptive neural finite-time control for stochastic nonlinear systems subject to unknown control directions,time-varying input delay and state delay

In this paper, an adaptive neural finite-time tracking control is studied for a category of stochastic nonlinearly parameterized systems with multiple unknown control directions, time-varying input delay, and time-varying state delay. To this end, a novel criterion of semi-globally finite-time stability in probability (SGFSP) is proposed, in the sense of Lyapunov, for stochastic nonlinear systems with multiple unknown control directions. Secondly, a novel auxiliary system with finite-time convergence is presented to cope with the time-varying input delay, the appropriate Lyapunov Krasovskii functionals are utilized to compensate for the time-varying state delay, Nussbaum functions are exploited to identify multiple unknown control directions, and the neural networks (NNs) are applied to approximate the unknown functions of nonlinear parameters. Thirdly, the fraction dynamic surface control (FDSC) technique is embedded in the process of designing the controller, which not only the “explosion of complexity” problems are successfully avoided in traditional backstepping methods but also the command filter convergence can be obtained within a finite time to lead greatly improved for the response speed of command filter. Meanwhile, the error compensation mechanism is established to eliminate the errors of the command filter. Then, based on the proposed novel criterion, all closed-loop signals of the considered systems are SGPFS under the designed controller, and the tracking error can drive to a small neighborhood of the origin in a finite time. In the end, three simulation examples are applied to demonstrate the validity of the control method.     

基于位置伺服系统的速度环滑模变结构控制器研究

本文应用状态反馈线性化方法对电枢反应非线性进行线性化处理,通过适当的非线性状态变换和输入变换,将速度非线性控制系统综合问题转化为线性系统的综合问题,并采用对系统参数变化及外界扰动具有较强鲁棒性的滑模变结构控制方法,实现了直流电机速度的跟踪控制。     

Integrated tire slip energy dissipation and lateral stability control of distributed drive electric vehicle with mechanical elastic wheel

Stability and energy consumption have always been important issues in electric vehicle research. Excessive slip energy not only aggravates tire wear, but also consumes energy of electric vehicle. In order to ensure the lateral stability and to reduce the slip energy dissipation of the distributed drive electric vehicle (DDEV) equipped with Mechanical Elastic Wheel (MEW), an integrated framework considering both tire slip energy dissipation and lateral stability control is proposed. The SESC (Slip Energy and Stability Control) is a hierarchical control framework for DDEV with MEW. A PID speed tracking controller and an (Integral Terminal Slide Mode) ITSM controller are designed at the upper-level controller. The ITSM controller can improve the lateral stability of the vehicle by obtaining the desired yaw moment. Speed tracking controller can stabilize the speed of the vehicle and obtain the desired longitudinal force. At the lower-level controller, the brush model of the MEW is proposed to express tire slip energy. In order to reduce the error of the vehicle dynamics and the slip energy dissipation, a mixed objective function including a holistic corner controller (HCC) and a minimum tire slip energy characterization is proposed. The proposed control framework is verified by Carsim and Matlab/Simulink under emergency simulation conditions. The simulation results show that the SESC based method can improve the lateral stability of DDEV with MEW effectively, and has better performance compared with fuzzyPID+AD based method. Meanwhile, the SESC achieves less slip energy than conventional torque distribution method.     

Probability-constrained tracking control for a class of time-varying nonlinear stochastic systems

This paper is concerned with the probability-constrained tracking control problem for a class of time-varying systems with stochastic nonlinearities, stochastic noises and successively packet loss. The main purpose of this paper is to design a time-varying observer and tracking controller such that (1) the probabilities of both the estimation error and tracking error confined to given ellipsoidal sets are larger than prescribed constants, and (2) the ellipsoids are minimized in the sense of matrix norm at each time point. By using a stochastic analysis method, the probability constrained tracking control problem is solved and sufficient conditions are obtained in terms of recursive linear matrix inequalities. A recursive optimization algorithm is developed to design the observer and tracking controller such that not only the addressed probability constrained aim is satisfied, but also the ellipsoidal sets are minimized. At last, a simulation example is given to illustrate the effectiveness and applicability of the developed approach.     

Finite-time performance guaranteed event-triggered adaptive control for nonlinear systems with unknown control direction

This paper studies the issue of finite-time performance guaranteed event-triggered (ET) adaptive neural tracking control for strict-feedback nonlinear systems with unknown control direction. A novel finite-time performance function is first constructed to describe the prescribed tracking performance, and then a new lemma is given to show the differentiability and boundedness of the performance function, which is important for the verification of the closed-loop system stability. Furthermore, with the help of the error transformation technique, the origin constrained tracking error is transformed into an equivalent unconstrained one. By utilizing the first-order sliding mode differentiator, the issue of “explosion of complexity” caused by the backstepping design is adequately addressed. Subsequently, an ingenious adaptive updated law is given to co-design the controller and the ET mechanism by the combination of the Nussbaum-type function, thus effectively handling the influences of the measurement error resulted from the ET mechanism and the challenge of the controller design caused by the unknown control direction. The presented event-triggered control scheme can not only guarantee the prescribed tracking performance, but also alleviate the communication burden simultaneously. Finally, numerical and practical examples are provided to demonstrate the validity of the proposed control strategy.     

Output feedback control with performance recovery analysis for a class of time-delay nonlinear systems

A class of nonlinear systems is considered in this paper which contains multiple time-varying delays and additional disturbances. Motivated by a robust model-free state-feedback controller, an observer-based output-feedback controller is designed to achieve uniformly ultimately bounded tracking. A high-gain-like observer is designed to estimate the unmeasurable current states utilizing the delayed output, and the estimated states are further used to facilitate the development of the output-feedback controller. The control input is saturated to avoid the side effects resulting from the high-gain-like observer’s peaking phenomenon. Under some sufficient conditions, it is proved that the saturation of the controller will no longer take place after a specific time, and both the estimation error and the tracking error will be uniformly ultimately bounded. In the stability analysis, Lyapunov–Krasovskii functionals are implemented to alleviate the difficulties resulting from the delays. Relationships among the delays, the desired trajectories, and the maximal tolerable error are identified. Behaviors of the closed-loop system under different observation and control gains are also analyzed. A two-link revolute robotic arm is taken as an example to conduct a series of simulations, and the results show that the output-feedback controller can recover the performance of the corresponding state-feedback controller.     

Robust hierarchical control of a laboratory helicopter

This paper deals with the robust position control problem for a three degree-of-freedom (3DOF) laboratory helicopter. The 3DOF helicopter system is a nonlinear multiple-input multiple-output (MIMO) uncertain system, and has the elevation, pitch, and travel angles. The proposed robust controller is a hierarchical controller including an attitude controller and a position controller. The position controller generates the desired reference of the pitch angle based on the tracking error of the travel angle, while the attitude controller achieves the reference tracking of the pitch and elevation angles. It is proven that the tracking errors of the three angles can converge into the given neighborhoods ultimately. Experimental results on the laboratory helicopter demonstrate the effectiveness of the proposed hierarchical control strategy.