Event-triggered Tracking Control Research Articles

Event-triggered adaptive NN tracking control with dynamic gain for a class of unknown nonlinear systems

An event-triggered tracking control problem is investigated for a class of unknown nonlinear systems in this paper. First, to approximate the unknown function, the radial basis function neural network is used. Then, we propose an event-triggered adaptive neural network control scheme with dynamic gain. Both the event-triggered mechanism in the controller-to-actuator channel and the dynamic gain in the sensor-to-controller channel are considered to reduce the communication load between the controller and the actuator and in the meantime to alleviate the burden of parameter adjustment as well. This scheme makes full use of the advantage that the dynamic gain is driven by the tracking error to ensure that the system output signal can track the reference signal within a prespecified accuracy without adjusting the parameters in use. Moreover, a detailed theoretical proof is given to illustrate that Zeno behavior can be excluded under the designed event-triggered controller. Finally, a simulation example is provided to show the effectiveness of our control scheme.

Dynamic Event-Triggered Adaptive Tracking Control for a Class of Unknown Stochastic Nonlinear Strict-Feedback Systems

In this paper, the dynamic event-triggered tracking control issue is studied for a class of unknown stochastic nonlinear systems with strict-feedback form. At first, neural networks (NNs) are used to approximate the unknown nonlinear functions. Then, a dynamic event-triggered controller (DETC) is designed through the adaptive backstepping method. Especially, the triggered threshold is dynamically adjusted. Compared with its corresponding static event-triggered mechanism (SETM), the dynamic event-triggered mechanism (DETM) can generate a larger execution interval and further save resources. Moreover, it is verified by two simulation examples that show that the closed-loop stochastic system signals are ultimately fourth moment semi-globally uniformly bounded (SGUUB).

Observer-based event-triggered tracking control for large-scale high order nonlinear uncertain systems

Observer-based event-triggered tracking control for large-scale high order nonlinear uncertain systems

Event-Triggered Adaptive Fuzzy Fixed-Time Tracking Control for a Class of Nonstrict-Feedback Nonlinear Systems

The problem of fuzzy-based adaptive event-triggered tracking control is investigated for a class of non-strict-feedback nonlinear systems within fixed-time interval in this paper. Fuzzy logic system (FLS) is employed to approximate the packaged unknown nonlinearities. Event-triggered mechanism is employed to schedule the data transmission dependent upon errors exceeding certain threshold. And combining backstepping design algorithm with Lyapunov stability theorem, a fuzzy-based adaptive event-triggered controller is developed. The presented control scheme eliminates the singularity problem that may occur in the design process and guarantees the boundedness of all the closed-loop signals. And the tracking error converges into a small neighborhood of zero in fixed-time. Meanwhile, the Zeno behavior is also avoided. At last, the effectiveness of the proposed approach is demonstrated by simulation results.

A novel fuzzy control with filter-based event-triggered mechanism for nonlinear uncertain stochastic systems suffered input hysteresis

In this paper, an adaptive fuzzy tracking control with filter-based event-triggered mechanism for stochastic nonlinear uncertain system suffered input hysteresis is presented. Considering stochastic disturbances and input hysteresis, Fuzzy Logic Systems (FLSs) are adopted to handle such issues. A time-varying vector contained weight vector and approximation error is established. Then, a class of smooth function is introduced to develop the adaptive control laws. It is aiming to avoid the chattering issue. Further, to achieve the desired tracking performance, this paper considers the discontinuous control input caused by the event-triggered control strategy. And the filter-based event-triggered strategy is presented. With the aid of Lyapunov function and Backstepping technique, the fuzzy event-triggered tracking control method is established for the considered system. It is testified that all signals are bounded under the action of the proposed method. Finally, the theoretical results are verified by the presented simulation examples.

Quantized Static Output Feedback Fuzzy Tracking Control for Discrete-Time Nonlinear Networked Systems With Asynchronous Event-Triggered Constraints

In this article, the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> static output feedback tracking control problem is studied for discrete-time nonlinear networked systems subject to quantization effects and asynchronous event-triggered constraints. The Takagi-Sugeno (T-S) fuzzy model is utilized to represent the investigated nonlinear networked systems. A novel asynchronous event-triggered strategy is given to reduce the network communication burdens in both communication channels from the plant to the controller and from the reference model to the controller. The objective of this article is to design a quantized event-triggered tracking controller such that the resulting system is asymptotically stable and the given <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∞</sub> tracking performance is guaranteed. The sufficient design conditions for the tracking controller are formulated in the form of the linear matrix inequalities (LMIs). Furthermore, a simulation example will be utilized to show the effectiveness of the developed design strategy.

Event-triggered output-feedback adaptive tracking control of autonomous underwater vehicles using reinforcement learning

This paper investigates the event-triggered tracking control of fully actuated autonomous underwater vehicles (AUVs) in the vertical plane. Specifically, this paper studies the ETC in the sensor-to-controller channel, where the X-Z coordinates and the pitch angle are transmitted in an event-triggered manner. The greater communication saving is ensured. Additionally, the recently-raised problem of “jumps of virtual control laws” is solved by establishing an event-triggered adaptive neural observer. This observer can offer the benefit of state recovery, which conforms to the nautical practice. As the observer is co-located with the controller, a succinct triggering condition is devised to avoid the “Zeno” behavior and co-located with the sensors. To achieve the optimization of the long-term tracking performance, the reinforcement learning (RL) technique is performed by using the critic-actor method with the radial basis function (RBF) neural networks (NNs). The critic NN approximates the performance index and is transferred as the reinforcement signal to the actor NN, which accounts for the uncertainties. The closed-loop stability is analyzed based on the observer-based tracking errors, and all of them are proved to be semi-globally uniformly ultimately bounded (SGUUB). Finally, a numerical experiment substantiates the effectiveness of the proposed scheme.

Single‐network ADP for solving optimal event‐triggered tracking control problem of completely unknown nonlinear systems

In this paper, we propose an optimal event-triggered tracking control scheme for completely unknown nonlinear systems under the adaptive dynamic programming (ADP) framework. A data-driven model based on recurrent neural networks (RNNs) is first constructed to model the system uncertainties including the drift dynamics and the input gain matrix, and the modeling error caused by NN approximation is well eliminated through adding a compensation term in the data-driven model such that the model state can asymptotically track the system state. Apart from the traditional construction of optimal tracking controllers, in this paper, an augmented system is developed and a discounted performance function is considered to achieve the optimality. By employing the Bellman optimal principle, an event-triggered tracking Hamilton–Jacobi–Bellman (HJB) equation is then formulated. The approximate solution of the HJB equation can be obtained by virtue of a critic NN, which significantly simplifies the implementation architecture of ADP. Both the historical state data and the current state data are incorporated into the updating of the weight vector in the critic NN, in this circumstance, the persistence of excitation assumption is not needed anymore. It is strictly proven via Lyapunov stability theory that the tracking error state and the critic NN weight are uniformly ultimately bounded. Simulation results examine the validity of the design scheme.

Event-Triggered Adaptive Fuzzy Tracking Control for Uncertain Nonlinear Systems Preceded by Unknown Prandtl-Ishlinskii Hysteresis.

In this article, the problem of event-triggered tracking control for a class of uncertain nonlinear systems with unknown Prandtl-Ishlinskii (PI) hysteresis is investigated. To solve this problem, two control schemes are proposed via synthesizing the techniques of the event-triggered strategy, fuzzy-logic systems (FLSs), and adaptive backstepping control. The first basic design scheme applies an effective method to keep a balance between communication constraints and system performance under the influence of actuator PI hysteresis, while the Zeno behavior can be avoided. Furthermore, the basic design scheme not only guarantees the tracking error asymptotically converges to zero but also establishes a preserved transient performance. Nevertheless, note that the inclusive sign functions of the basic design scheme will cause possible chattering phenomenon, an alternative event-triggered adaptive control approach is then proposed. Unlike the previous control scheme, the second chattering-avoidance design approach ensures asymptotic convergence of the tracking error within a prescribed boundary δ , and finally the [Formula: see text]-norm transient performance of the tracking error is constructed. Simulations verify the established theoretical results that the proposed schemes successfully overcome the communication constraints and compensate the actuator PI hysteresis, and also present different tracking performances between two control schemes for comparison.

Adaptive Event-Triggered Fuzzy Tracking Control of Uncertain Stochastic Nonlinear Systems With Unmeasurable States

This article is concerned with the problem of adaptive event-triggered tracking control for a class of uncertain stochastic nonlinear systems in strict-feedback form. First, with the help of fuzzy logic systems to approximate the unknown nonlinear functions, a robust fuzzy state observer is constructed to estimate all the unmeasurable states. Next, an adaptive output feedback controller, which can adjust the variables online is designed by using the backstepping scheme. Concomitantly, in order to reduce the computation of communication process, a new event triggering condition involving the decreasing function of tracking errors is introduced. Moreover, the desired closed-loop stability of the resulting systems can be achieved by exploiting Lyapunov function analysis. Finally, simulation results verify the effectiveness of the proposed method.

Finite-time adaptive event-triggered fault-tolerant control of nonlinear systems based on fuzzy observer

This paper addresses the adaptive event-triggered tracking control problem for a class of uncertain nonlinear systems with actuator failures and disturbances. By designing a fuzzy observer to estimate the unmeasurable states, a novel event-triggered adaptive fuzzy control scheme with a sign function is proposed. Unlike the existing methods, the event-triggered controller with a parameter-updated law containing only one online modulated variable can dynamically compensate for the approximation error caused at each step. The proposed control strategy guarantees that all the signals of the closed-loop systems are bounded, and that the tracking errors can be regulated to a compact set around the origin in finite-time without Zeno behavior. Finally, a numerical example and a practical example validate the effectiveness of the designed scheme.

Observer-based event-triggered control of steer-by-wire systems with prespecified tracking accuracy

This paper addresses the event-triggered tracking control problem of the SbW system subject to unavailable steering angular velocity of front-wheels, time-varying external disturbance, and uncertain dynamics, including friction torque and self-aligning torque. First, an adaptive state observer is proposed to estimate the unavailable steering angular velocity of front-wheels. The uncertain nonlinearity and time-varying disturbance can be estimated by the adaptive interval type-2 fuzzy logic system (IT2 FLS) and the disturbance observer, respectively. An event-triggered control is proposed for SbW systems to guarantee the prespecified control performance and save communication resources in the controller-to-actuator channel. Much importantly, the nested robust terms are incorporated in the control scheme to counteract the observation error and overcome the negative influence of the event-triggering error. Theoretical analysis shows that the prespecified arbitrary tracking accuracy can be guaranteed within finite time, and the Zeno-behavior can be strictly avoided while saving communication resources in the controller-to-actuator channel. Finally, simulation and vehicle experiment results and some comparisons are given to evaluate the effectiveness of the proposed method.

Event-triggered tracking control for multi-agent systems with measurement noises

ABSTRACT This paper considers the mean-square leader-following consensus problem for heterogeneous multi-agent systems (MASs) affected by noises. Because only the output signal of a leader can be measured, a distributed dynamic control driven by an event-triggered mechanism (ETM) is proposed. The proposed ETM can reduce the signal transmission amount from sampler to controller. Using the tine-delay model method, the system under the proposed controller can be modelled as a stochastic time-delay system. Then the time-varying Hanaly inequality is utilised to obtain sufficient conditions that guarantee the consensus of MASs. Further, the quantity-based event-triggered mechanism is proposed to reduce the amount of traffic. Finally, an example is given to illustrate the validity of the obtained results.

Observer-based adaptive event-triggered tracking control for nonlinear MIMO systems based on neural networks technique

In this paper, the issue of adaptive neural networks event-triggered control for nonstrict-feedback nonlinear multi-input-multi-output(MIMO) systems containing unmeasured states is investigated. All unmeasured states are approximated by using neural networks observer. Meanwhile, the neural networks are used to estimate the unknown continuous function at each step of recursion. Then, an observer-based adaptive neural networks event-triggered tracking control strategy is proposed based on backstepping technique. The designed controller enables the outputs of the system to track the target trajectory within a small bounded error range, and all signals in the closed-loop system are bounded.

Adaptive Fuzzy Event-Triggered Command-Filtered Control for Nonlinear Time-Delay Systems

This article focuses on an adaptive fuzzy dynamic event-triggered tracking control for nonlinear time-delay systems with unmodeled dynamics via a command filter method. Fuzzy logic systems are utilized to address the unknown nonlinear functions. The upper bound of the approximation error is allowed to be unknown and can be compensated by skillfully introducing a hyperbolic tangent function to the design of the adaptive laws. Meanwhile, without requiring any assumptions, time delays can be handled by appropriately incorporating the delayed nonlinear functions into the Lyapunov&#x2013;Krasovskii functional. Then, a dynamic event-triggered control mechanism is designed to dynamically adjust the threshold parameter. Finally, a new adaptive controller is constructed such that all states of the closed-loop system are bounded. The system output is demonstrated to follow the desired signal. Two examples are given to illustrate the validity of the presented method.

Event-Triggered Tracking Control With Filtered Outputs and Impulsive Observers.

This article studies an event-triggered tracking control problem for linear systems subject to output feedback and disturbances, where a new configuration incorporating filtered outputs and impulsive observers is proposed. The transmissions in the sensor-to-controller and controller-to-actuator channels are scheduled by dynamic event-triggered control (ETC) mechanisms to save communication resources. To eliminate the effects of the derivatives of output noises on the tracking and transmission performance, a low-pass filter is introduced to preprocess the raw output signals. Both the filter state and raw output will be transmitted to the controller node while the latter is only utilized by an impulsive observer at some discrete instants. Then, it is proved that the proposed dynamic ETC schemes can solve the practical tracking control problem with fixed reference points and avoid Zeno behavior in both channels. Meanwhile, when some user-specified parameters in the event-triggering conditions are small enough, the tracking control problem can be solved asymptotically for disturbance-free systems. In addition, to further improve the transient performance, reduced-order impulsive observers and optimization of impulsive gain matrices are studied. Finally, simulation results are provided to illustrate the efficiency and feasibility of the obtained results.

Event‐triggered tracking control for a family of non‐linear systems via output feedback

This study considers the event-triggered tracking control problem for a family of non-linear systems via output feedback. The uncertainty in the parameters is a significant feature, and the growth condition of the non-linear terms is related to an output polynomial function. An observer based on the given tracking signal is constructed, and a dynamic equation is established by the high-gain scaling method. In order to reasonably process the measurement error, an intermediate controller in the form of the hyperbolic tangent function is designed. Based on the relative threshold strategy, an event-triggered controller is naturally given such that all the closed-loop signals are globally bounded and the Zeno-behaviour is favourably avoided. Furthermore, by analysing the constructed dynamic equation, the tracking error converges to a prescribed small residual set. The theoretical results are verified by two numerical examples.

Adaptive event-triggered fuzzy tracking control of nonlinear systems with dead-zones and unmeasurable states

In this paper, the adaptive event-triggered tracking control of uncertain nonlinear systems with dead-zone inputs is developed based on fuzzy approximation technique. Firstly, a robust fuzzy state observer is constructed to effectively estimate all the unmeasurable states. Next, an adaptive output feedback controller with parameter updated law only containing one on-line adjusted variable is designed via the backstepping scheme. Concomitantly, a novel event-triggered condition related to the upper and lower bounds of dead-zone parameters and the decreasing function of tracking errors is given to substantially alleviate the computation load of the communication process. Moreover, the desired closed-loop stability of the resulting systems can be achieved by exploiting Lyapunov function analysis. Finally, simulation results verify the effectiveness of the proposed method.

Designing Event-Triggered Observers for Distributed Tracking Consensus of Higher-Order Multiagent Systems.

In this article, the asymptotic tracking consensus problem of higher-order multiagent systems (MASs) with general directed communication graphs is addressed via designing event-triggered control strategies. One common assumption utilized in most existing results on such tracking consensus problem that the inherent dynamics of the leader are the same as those of the followers is removed in this article. In particular, two cases that the dynamics of the leader are subjected, respectively, to bounded input and unknown nonlinearity are considered. To do this, distributed event-triggered observers are first constructed to estimate the state information of the leader. Then, local event-triggered tracking control protocols are designed for each follower to complete the goal of tracking consensus. One distinguishing feature of the present distributed observers lies in the fact that they could avoid the continuous monitoring for the states of the neighbors' observer states. It is also worth pointing out that the present tracking consensus control strategies are fully distributed as no global information related to the directed communication graph is involved in designing the strategies. Two simulation examples are finally presented to verify the efficiency of the theoretical results.

Event-based tracking control for nonholonomic mobile robots

In this paper, we study the event-triggered control problem for a kind of nonlinear time-varying system. Generally speaking we use the Lyapunov stability theory to solve an event-triggered tracking control problem of non-holonomic mobile robots. Firstly, we propose a continuous tracking control law using nonlinear state feedback. Under some proper assumptions, we use the linearization technique to prove the exponential stability of the tracking system. Then, we propose an event-triggered controller for the robot and prove the uniform boundedness of the solutions by using the Gronwall–Bellman inequality. Moreover, it is shown that the solutions are uniformly ultimately bounded and there is no Zeno behavior in the tracking system. Simulation studies show the effectiveness of the proposed approach.