Adaptive Event-triggered Tracking Control Research Articles

Adaptive event-triggered tracking control for nonlinear systems with prescribed performance: A time-domain mapping approach

This paper proposed an event-triggered adaptive fuzzy prescribed time control strategy for a class of nonlinear systems with uncertain external disturbances and unknown virtual control coefficients under prescribed performance. A novel time-domain mapping technique is proposed to transform the prescribed time tracking control problem into an asymptotic convergence problem. An observer is designed to estimate for the external disturbance and fuzzy approximation error of fuzzy logic systems (FLSs). The problem of “explosion of complexity” is addressed by applying dynamic surface control (DSC) technique to backstepping. An adaptive fuzzy event-triggered strategy is designed using the Lyapunov stability theorem. This strategy ensures that, after time-domain mapping, the tracking error asymptotically converges to zero. Additionally, there is no Zeno behavior and all system signals are bounded. Finally, the effectiveness of the proposed scheme is verified through three simulation examples.

Estimator-based neural adaptive event-triggered control for strict-feedback nonlinear systems with incomplete measurements

This article addresses a neural adaptive event-triggered tracking control for a class of strict-feedback nonlinear dynamics with incomplete measurements, which is novel on the research of Cyber-physical Systems. The incomplete measurement problem caused by packet loss, saturation, and other issues during data transmission can lead to the unavailability of system state variables, which can degrade system performance and even lead to instability. To solve these problems, a state estimator for data-losing case and two controllers for normal and data-losing cases are designed utilising event-triggered strategies which can reduce the burden of calculation and data transmission. Radial basis function neural networks are adopted to approximate the unknown nonlinear system functions. A strict stability analysis in probability shows that the control laws for the considered strict-feedback nonlinear system can guarantee all the closed-loop to be uniformly ultimately bounded in mean square. Two examples are performed to demonstrate the effectiveness of the provided control method.

Observer-based fuzzy adaptive event-triggered control for strictly uncertain nonlinear systems with partial state constraints and output dead-zones

This paper delves into the fuzzy adaptive event-triggered tracking control for a certain class of strictly uncertain nonlinear systems subject to partial state constraints as well as output dead-zones. First of all, fuzzy logic systems (FLSs) are utilised to approximate the unpredictable items, a fuzzy adaptive observer is intended to enable state estimation. Subsequently, a type of smooth approximate model is introduced to settle the nondifferentiable phenomenon of output dead-zones. To reduce the computational overhead of the communication operation effectively, an improved event-triggered control strategy including a decreasing hyperbolic tangent function related to dead-zone, is applied to determine the actual control input. In addition, the barrier Lyapunov function (BLF) is fabricated to address the issue of partial state constraint. By theoretical analysis, the reference signal can be precisely tracked by the system output and all closed-loop signals remain uniformly ultimately bounded (UUB). Finally, the constructed controller's effectiveness is validated with two illustrative examples.

Observer-based event-triggered adaptive neural control for time-delay nonlinear systems with input saturation and external disturbances

In this article, the issue of adaptive event-triggered tracking control is investigated for time-delay nonlinear systems with input saturation and external disturbances. In the whole process of control design, the radial basis function neural networks are utilized to approximate uncertain nonlinearities. To estimate the unknown states, a neural network-based observer is constructed. Pade approximation method is adopted to eliminate the effect of input delay. A smooth non-affine function is introduced to replace input saturation, and an auxiliary variable is employed to obtain the actual control input. An event-triggered strategy is designed to reduce the utilization of communication and computation resources. Moreover, the command filtering technique is applied to handle the issue of “explosion of complexity” in the conventional backstepping method. The designed controller can assure that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded. Therefore, the proposed event-triggered neural control scheme can not only save network resources, but also improve the robustness of the system by dealing with input constraints and external disturbances. Finally, two simulation examples are given to verify the availability and feasibility of the designed controller.

Neural-Network-Based Adaptive Tracking Control for Nonlinear Multiagent Systems: The Observer Case.

This article focuses on the neural-network (NN)-based adaptive tracking control issue for a class of high-order nonlinear multiagent systems both subjected to the immeasurable state variables and unknown external disturbance. Combining with the radial basis function NNs (RBF NNs), the composite disturbance observer and state observer for each follower are established, respectively. The purpose of this work is to develop NN-based adaptive tracking control schemes such that the output of each follower ultimately tracks that of the leader and all the signals of the closed-loop systems are semiglobally uniformly ultimately bounded by utilizing the backstepping technique. Furthermore, so as to cope with the sparsity of the control resources, the proposed method is extended to the event-triggered case and the adaptive event-triggered tracking control protocol is formulated for nonlinear multiagent systems. Finally, the numerical example is performed to verify the efficacy of the proposed approach.

A new event-triggered adaptive tracking controller for nonlinear systems with unknown virtual control coefficients

This paper investigates the adaptive event-triggered tracking control problem for nonlinear systems with virtual control coefficients being unknown nonlinear functions. Firstly, different from approximators using fuzzy logics/neural networks or Nussbaum gain technique, a new transformation with less computation is introduced based on a monotone decreasing positive continuous function to handle uncertain virtual control coefficients (UVCCs). Furthermore, a novel event-triggered threshold scheme is firstly developed, which can switch between the fixed and relative threshold strategies smoothly. Finally, an adaptive event-triggered tracking controller is constructed, whose effectiveness is verified by both theoretical analysis and simulations.

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.

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 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 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.

Fixed-time adaptive event-triggered tracking control of uncertain nonlinear systems

This paper addresses the event-triggered tracking control problem of nonlinear systems with predefined performance in a fixed-time environment. Unlike the existing event-triggered schemes, the developed triggering mechanism only compares the difference between the signal to be transmitted and the holding signal. The proposed control method also considers the response of the triggering mechanism. In order to achieve prescribed control performance under the condition of unmatched uncertainties and uncertain gain functions, a new adaptive fixed-time control strategy is proposed by introducing an error transformation scheme. The proposed control method under the event-triggered framework can reduce the amount of control signals transmitted while ensuring that the system output tracking error converges to a small neighborhood close to zero within a fixed-time frame. The results of two examples, including comparative studies and a practical application, show the effectiveness of the proposed control method.

Adaptive Neural Tracking Control for a Class of Pure-Feedback Systems With Output Constraints Based on Event-Triggered Strategy

In this paper, an adaptive event-triggered tracking control problem is considered for a class of pure-feedback nonlinear systems with output constraints. The mean value theorem is used to transform the pure-feedback system in non-affine form into a system in affine form. In addition, the radial basis function neural network (RBF NN) control is used to approximate the unknown nonlinear function in the system and the tracking error of the controller is limited to a small constant boundary by using the positive obstacle Lyapunov function. An adaptive controller for a class of pure-feedback systems is established, which based on the backstepping control theory and event-triggered control theory, it can ensure all the closed-loop signals are bounded and avoid the Zeno-behavior. The simulation results prove the effectiveness of the controller design.

Asynchronous adaptive event-triggered tracking control for multi-agent systems with stochastic actuator faults

This paper investigates the problem of consensus tracking control for multi-agent systems with stochastic actuator faults, where the asynchronous adaptive event-triggered scheme (AETS) is proposed to reduce communication burden. The failure phenomenon for each actuator is described by an independent and identically distributed (i.i.d) random process. The communication information is divided two groups according to the scenario whether the followers can receive the information from the leader or not. Two adaptive event-triggered communication schemes are introduced based on the above classified information. Considering the stochastic actuator faults and the designed AETS, a new closed-loop fault-tolerant tracking control system model is established. Then, by employing the Lyapunov stability theory and stochastic analysis technique, a new fault-dependent stability criterion is derived, which ensures that the leader-following tracking error system is stochastically mean-square stable. Based on this criterion, the fault-tolerant consensus controller gains and the triggering parameters are obtained simultaneously by solving a linear matrix inequality (LMI). Moreover, the Zeno behavior of the AETS is excluded. Finally, a simulation example is included to illustrate the effectiveness of theoretical results.