Adaptive Law Research Articles

Adaptive Event-Triggered Neural Network Fast Finite-Time Control for Uncertain Robotic Systems

A fast convergence adaptive neural network event-triggered control strategy is proposed for the trajectory tracking issue of uncertain robotic systems with output constraints. To cope with the constraints on the system output in the actual industrial field while reducing the burden on communication resources, an adaptive event-triggered mechanism is designed by using logarithm-type barrier Lyapunov functions and an event-triggered mechanism. Meanwhile, the combination of neural networks and fast finite-time stability theory can not only approximate the unknown nonlinear function of the system, but also construct the control law and adaptive law with a fractional exponential power to accelerate the system’s convergence speed. Furthermore, the tracking errors converge quickly to a bounded and adjustable compact set in finite time. Finally, the effectiveness of the strategy is verified by simulation examples.

Concurrent Learning-Based Neuroadaptive Robust Tracking Control of Wheeled Mobile Robot: An Event-Triggered Design

In this paper, an event-based neuro-adaptive robust tracking controller for a perturbed and networked differential drive mobile robot (DMR) is designed with concurrent learning. A radial basis function neural network, which approximates an unknown perturbation, is used to design an adaptive sliding mode controller (SMC). The RBFNN weights and SMC parameters are estimated online using an adaptive tuning law to ensure performance with reduced chattering. To improve the convergence of RBFNN weight estimation error, a concurrent learning-based adaptive law is derived, which uses measured online and recorded data. Further, a suitable triggering condition is designed to achieve a reduced number of control computations while minimizing network resources without sacrificing the stability of the sampled data closed-loop control system. A finite sampling frequency is guaranteed for the designed triggering condition by establishing a positive lower bound on the inter-event execution time which is equivalent to the Zeno-free behaviour of the system. Finally, the proposed event-based neuro-adaptive robust controller is implemented on a practical system (Q-bot 2e) to show the effectiveness of the proposed design.

Optimized Adaptive Fuzzy Security Control of Nonlinear Systems With Prescribed Tracking Performance.

This article studies the optimized fuzzy prescribed performance control problem for nonlinear nonstrict-feedback systems under denial-of-service (DoS) attacks. A fuzzy estimator is delicately designed to model the immeasurable system states in the presence of DoS attacks. To achieve the preset tracking performance, a simper prescribed performance error transformation is constructed considering the characteristics of DoS attacks, which helps obtain a novel Hamilton-Jacobi-Bellman equation to derive the optimized prescribed performance controller. Furthermore, the fuzzy-logic system, combined with the reinforcement learning (RL) technique, is employed to approximate the unknown nonlinearity existing in the prescribed performance controller design process. An optimized adaptive fuzzy security control law is then proposed for the considered nonlinear nonstrict-feedback systems subject to DoS attacks. Through the Lyapunov stability analysis, the tracking error is proved to approach the predefined region by the preset finite time, even in the presence of DoS attacks. Meanwhile, the consumed control resources are minimized due to the RL-based optimized algorithm. Finally, an actual example with comparisons verifies the effectiveness of the proposed control algorithm.

Adaptive Fixed-Time Control for State-Constrained High-Order Uncertain Nonlinear Cyber-Physical Systems Under Malicious Attacks

A novel fixed-time adaptive fuzzy tracking control strategy is developed to resolve the fixed-time tracking control issue for a category of state-constrained high-order uncertain nonlinear cyber-physical systems (CPSs), which suffer from malicious attacks launched in controller-actuator (C-A) channel. The proposed control strategy is independent of the exact system model and can accommodate external disturbances and malicious attacks. Meanwhile, distinguished from the existing control methods for state-constrained uncertain CPSs under malicious attacks which can only ensure the system performance when time leans towards infinity or in finite time, the presented control strategy can guarantee the system performance in fixed time. It has been substantiated that the developed control strategy can make sure that the output tracking error converges to a predefined small neighborhood of the origin, and all signals of the resulting closed-loop system satisfy the corresponding time-varying state constraints during the total operation. In particular, the settling time and tracking precision are known and can be preconfigured by selecting the design parameters appropriately. More significantly, all the initial states of the system are independent of the developed fixed-time adaptive fuzzy tracking control law and can be arbitrarily chosen in the constrained region specified by the corresponding time-varying state constraints conditions. Ultimately, a representative simulation is supplied to illustrate the effectiveness and superiority of the proposed control scheme.

Distributed Fuzzy Containment Control for Stochastic Nonlinear Multiagent Systems Under Denial-of-Service Attacks

The paper investigates distributed fuzzy adaptive containment control problem of stochastic nonlinear multi-agent systems under an directed communication topology suffering Denial-of-Service (DoS) attacks. Firstly, considering unknown stochastic disturbance and nonlinear characteristics for the followers, the mathematical models are modeled as It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\hat{o}$</tex-math></inline-formula> stochastic nonlinearities terms approximated through fuzzy logic systems (FLS). Secondly, the proposed dynamically adjusted event-triggered condition can effectively avoid inefficient transmission behavior. Moreover, an adaptive compensation protocol for input saturation is constructed to eliminate the effects of nonlinearities caused by input saturation. Finally, instead of the previous uniformly ultimately bounded containment control results, stability and asymptotic performance are guaranteed through valid reasonable adaptive control laws acquired through backstepping control approach despite suffers DoS cyber attacks. Moreover, a simulation is given to verify the feasibility of the proposed method.

Adaptive control based neural network sliding mode approach for two links robot

&lt;span lang="EN-US"&gt;In order to improve the control accuracy of the robot manipulator, the sliding mode control combined with the adaptive neural network (ANNSMC) is proposed. Sliding mode control (SMC) is a nonlinear control recognized for its efficiency, easy tuning and implementation, accuracy and robustness. However, higher amplitude of chattering is produced due to the higher switching gain to handle the large uncertainties. For the purpose of reducing this gain, the uncertain parts of the system are estimated using neural network (NN) with on-line training using back propagation (BP) technique. The results of the online interconnection weights between the input and the hidden layers and between the hidden and the output layers are injected offline in order to improve the network performance in term of the convergence speed. In order to reduce the response time caused by the online training, the obtained output and input weights are updated using the adaptive laws derived from the Lyapunov stability approach&lt;/span&gt;&lt;span lang="EN-US"&gt;the proposed control ANNSMC has improved the convergence speed with 41.13% for the first link and 40.15% for the second link comparing to NNSMC. The simulation result illustrates the performance of the proposed approach by using MATLAB and the control action suggested did not manifest any chattering behavior.&lt;/span&gt;

LPVS guidance and adaptive event-triggered control for an underactuated surface vessel with the prevention of obstacle’s vicious maneuvering

This paper investigates the adaptive neural event-triggered control for an underactuated surface vessel (USV), considering constraints of the obstacle’s vicious maneuvering and the limited communication channel. In the algorithm, a novel logical phantom virtual ship (LPVS) guidance principle is developed to generate the global path following reference and the obstacle avoidance order in the simulation results, where the corresponding operation comply to the suggestion in international regulations for prevention collision at sea (COLREGs). The improved design of velocity obstacle (VO) method can guarantee its predictive capability to prevent the obstacle’s vicious maneuvering. As for the control module, the adaptive event-triggered control algorithm is proposed by employing the robust neural damping technique and the input event-triggered mechanism. And the derived adaptive law can effectively solve perturbations from the gain uncertainty and the external disturbances. Through the theoretical analysis, all signals of the closed-loop control system are with the semi-globally uniform ultimate bounded (SGUUB) stability. The simulation experiments have been presented to verify the obstacle avoidance effectiveness and the burden-some superiority of the algorithm.

Visual Servoing Control of Robotics With A Neural Network Estimator Based on Spectral Adaptive Law

In recent years, with the development of machine vision and other relative techniques, visual servoing control of robotics has been wildly applied. A complex calibration process is usually required to get the accurate parameters of the camera and the robot, so that getting the projection relationship between changes of images and movement of robot joints usually takes much effort. In order to solve this problem, a ReLU activating neural network (NN) estimator is proposed to estimate the compound Jacobian matrix of the system in this paper. The weight of the NN is updated online by a project algorithm with a novel spectral adaptive law which can effectively improve the generalization ability of the NN and the robustness of the system. By constructing a new Lyapunov function with the spectral norm of weight of NN, the stability of the proposed adaptive algorithm and the controller can be proved. Simulations and experimental results validate the effectiveness of the proposed controller.

Distributed Adaptive Inverse Differential Game Approach to Leader's Behavior Learning for Multiple Autonomous Followers

In this study, the leader's behavior learning problem is investigated for a class of leader-follower systems, where the leader's behavior is assumed not a priori known to all followers that are autonomous. A multi-player nonzero-sum differential game is introduced to indicate the control interaction between agents, where the leader's behavior is modelled by an unknown cost function. The autonomous followers aim to retrieve the weighting matrix in the leader's cost function collaboratively. A distributed online adaptive inverse differential game (IDG) approach to the leader's behavior learning is proposed for the autonomous followers. Specifically, a concurrent learning (CL) based adaptive law and an interactive game controller are first developed for each autonomous follower to learn the leader's feedback gain matrix online, while the feedback Nash equilibrium of the game can be achieved. Then, a linear matrix inequality (LMI) optimization problem is formulated to determine the weighting matrix of the leader's cost function for each autonomous follower. The proposed method simply requires that all followers share their interactive feedback gain matrices, not their private intents, and use only the system state data, not both the system state data and the leader's control input data. The main advantages of the proposed method are that it can be implemented online without requiring the persistent excitation condition and needs less computational power for all followers. Finally, numerical simulations are provided to demonstrate the effectiveness and feasibility of the developed method.

Adaptive neural network fixed‐time control for an uncertain robot with input nonlinearity

AbstractThe article introduces an innovative adaptive fixed‐time control strategy designed for a robot system grappling with challenges like actuator saturation and model uncertainty. Two strategies are explored: model‐based control and neural networks control. In instances of model uncertainty, neural networks are leveraged to contend with the unknown dynamics of the robot system. These networks undergo training to approximate the elusive model parameters. Through this neural network approach, we establish adaptive laws grounded in fixed‐time convergence, ensuring that system tracking errors converge to a confined range near zero within a predetermined time frame. To tackle the issue of actuator saturation, an enhanced auxiliary system is introduced. This auxiliary system is tailored to counterbalance the adverse impacts of actuator saturation, thereby augmenting the tracking performance of the robot system. The proposed control policy is rigorously analyzed using Lyapunov theory, demonstrating that the system's tracking errors converge within a fixed time frame. To validate the efficacy of the proposed methodology, both numerical simulations and practical experiments are conducted, affirming the effectiveness of the approach.

Adaptive robust control for unmanned combat platform: Obstacles avoiding and dynamic trajectory tracking

AbstractThis paper proposes an adaptive robust control scheme to deal with the uncertainty problem of unmanned combat platform. Under the constraint of the controller, the rescue vehicle aims to follow the trajectory of the reconnaissance vehicle and avoid obstacles (e.g., craters and destroyed tanks), while they eventually reach the defined target location (an accident area). First, for the control objective, the original constraints are innovatively separated into two parts: arrival constraint and tracking‐avoidance constraint. An approximate constraint‐following control substitutes for the triple problem, and the constraint‐following error is subsequently established. Second, for the control strategy, a ‐measure is introduced to measure the constraint‐following error. To ensure the tracking‐avoidance constraint and the arrival constraint can be fully satisfied by the system, an adaptive robust control is designed. Finally, for the fast time‐varying uncertainty with unknown boundary, an adaptive law is introduced to evaluate the triple tracking‐avoidance‐arrival performance. In conclusion, the main contribution of this paper is to achieve triple tracking‐avoidance arrival for unmanned combat platform, and the problem of military detection and rescue on complex battlefields can be eliminated.

Adaptive fuzzy extended state observer for a class of nonlinear systems with output constraint

Abstract In this study, an adaptive fuzzy extended state observer (AFESO) for single-input–single-output nonlinear affine systems in the presence of external disturbances and output constraints is proposed. In this regard, an extended state observer (ESO) was employed to estimate the unmeasured states and external disturbances simultaneously. To improve the estimation accuracy, the observer gains were adjusted using an adaptation law. To obtain a more comprehensive mathematical analysis and an accurate model for the ESO and to increase the degree of freedom, a Takagi–Sugeno fuzzy system was employed. The proposed AFESO relaxes the limitations of the ESO and improves the system performance as compared with the classical methods in the presence of time-varying disturbances. Next, a command-filtered backstepping controller is designed based on the barrier Lyapunov function method, which guarantees fast convergence of the tracking error as well as satisfying the output constraints of the system. The stability analysis showed that both the estimation error of the AFESO and the tracking error of the controller are bounded, and the tracking error converges to a small neighborhood of the origin. A simulating example of a flexible-joint manipulator shows the effectiveness of the proposed method as compared with the recently proposed method in the literature.

An adaptive continuous nonsingular fast terminal SMC for permanent magnet synchronous motor fed electric vehicle

This article focuses on the traction control of an electric vehicle (EV) with a permanent magnet synchronous motor (PMSM). A continuous nonsingular fast terminal sliding mode controller (CNFTSMC) with disturbance estimation capability is proposed to enhance the dynamic performance of the system. The CNFTSMC provides high accuracy, robustness against uncertainties, finite-time convergence and non-singularity to a highly uncertain non-linear system. It also has the capability of estimating system velocity without the use of sensors, hence decreasing the total size and cost of EV. However, robustness against uncertainties is only achievable if the uncertainty bounds are available. An adaptive law is introduced to overcome this shortcoming, and an adaptable CNFTSMC (ACNFTSMC) is developed. The proposed controllers (CNFTSMC and ACNFTSMC) are compared to the existing terminal sliding mode controller, and its effectiveness is verified by simulation results. The findings show that, when compared to the former DNFTSMC, the magnitude of chattering in control input (iq) and electromagnetic torque (Te) has been reduced by 65% as a result of the introduction of ACNFTSMC. Also, the initial disturbance in the torque disappears about 40% more quickly in the proposed ACNFTSMC than in the DNFTSMC and CNFTSMC.

Fault-Tolerant Control for Carrier-Based Aircraft Based on Adaptive Fuzzy Sliding-Mode Method

Carrier-based aircraft landing involves complex system engineering characterised by strong nonlinearity, significant coupling and susceptibility to environmental disturbances, and autonomous landing of carrier-based aircraft under fault states is even more challenging and riskier. To address the control-system problems of loss of efficiency and performance due to actuator faults and performance degradation due to various unknown disturbances, presented here is fault-tolerant control for carrier-based aircraft based on adaptive fuzzy sliding-mode fault-tolerant control (AFSMFTC). First, three models are built (the carrier-based aircraft fault model, the carrier air wake model and the deck motion model), and the control framework of the autonomous landing control system is introduced. Next, a longitudinal and lateral flight channel controller comprising an adaptive fuzzy network, adaptive laws and a sliding-mode controller is designed using the AFSMFTC method. The adaptive fuzzy network implements fuzzy approximation for the sliding-mode switching terms to further offset errors induced by unknown disturbances, the adaptive laws compensate for actuator faults, and the sliding-mode controller ensures tracking of the overall flight path. Furthermore, the stability of the fault-tolerant method is demonstrated using the Lyapunov function. Finally, simulation and comparative experiments show that the proposed fault-tolerant method has outstanding control performance and strong fault-tolerant capability, thereby providing an effective and feasible solution for designing an autonomous landing system for carrier-based aircraft under fault states.

Adaptive finite-time output tracker design of uncertain nonlinear systems with sandwich structure and actuator saturation constraint

This paper studies the finite-time output tracking problem for a class of nonlinear sandwich systems with sandwiched dead-zone function and input actuator saturation constraint. To achieve the goal, a systematic adaptive backstepping controller is proposed based on the practical finite-time stability criterion which guarantees the output tracking even if the dead zone and saturation constraints occur, simultaneously. In the control approach to confine the system output to a predefined set, the barrier Lyapunov function is utilised. To cope with the problem of ‘explosion of complexity’, a finite-time command filter is also employed. Furthermore, the values of the unknown parameters are estimated by appropriate adaptive laws. The finite-time stability of the closed-loop system is proved based on the Lyapunov approach which ensures the boundedness of all signals. Finally, the efficiency and applicability of the proposed method are confirmed by providing the simulation results for the hydraulic servo press system.

Event-triggered adaptive control for upper-extremity therapeutic robot in active-assist mode: A simulation study

Upper extremity rehabilitation exercises are essential for individuals recovering from injuries or conditions that affect their arm and hand functionality. Robot-assisted therapy has gained popularity as it offers precise control, objective assessment, and customizable treatment programs. However, several challenges persist, including uncertainties in the patient’s and robot dynamics, limited communication, and the need to maintain a compliant patient-robot interaction. Therefore, an event-triggered adaptive backstepping (ETAB) admittance control strategy is proposed in this work to address these challenges. Initially, the framework of the robot-assisted therapeutic process is briefly explained. The architecture of the proposed control strategy is formulated with two control modules. Thereafter, the adaptive backstepping technique is employed with an online adaptation law to deal with dynamic uncertainties. Moreover, the problem of limited communication is handled using the proposed design of a Lyapunov-based event-triggered mechanism. The admittance controller is integrated to maintain a compliant patient-robot interaction and consider the participation of the patient in the therapeutic sessions. The effectiveness of the proposed control strategy is verified using an end-effector type rehabilitation robot performing two different rehabilitation exercises. Furthermore, a comparative performance analysis is carried out with the proportional-integral-derivative controller (PID) and the adaptive sliding mode controller (ASMC). Based on the simulation runs, the proposed controller has shown promising tracking behavior, appropriate compliant interaction, and considerable reduction in the transmitted signals during the passive and active-assist training exercises.

Fractional order sliding mode control for linear maglev synchronous motor based on an adaptive fixed-time extended state observer

In order to improve the tracking accuracy of the linear maglev synchronous motor maglev system with non-linear, strongly coupled, and other uncertainty problems, a fixed-time fractional order terminal sliding mode control (FFTSMC) strategy based on adaptive fixed-time extended state observer (AFxESO) is proposed. Firstly, a fast AFxESO is constructed and an adaptive law is designed to dynamically adjust the gain to reduce the estimation error and measurement noise, which enables the observer to accurately estimate the perturbation of the unknown boundary in a fixed-time. Secondly, a new FFTSM controller is designed by applying the theory of fractional order calculus, which can speed up the system convergence and suppress the chattering problem in SMC. Then, using the Lyapunov stability theory, it is demonstrated that the proposed AFxESO-FFTSM control scheme can guarantee the global fixed-time convergence of the system to equilibrium and the convergence time is dependent on the selection of the controller parameters, which effectively overcomes the drawbacks of finite-time control. Finally, the feasibility and superiority of the proposed strategy are verified on the linear maglev synchronous motor system experiment platform.

Practical Adaptive Fast Terminal Sliding Mode Control for Servo Motors

Position control of servo motor systems is a challenging task because of inevitable factors such as uncertainties, nonlinearities, parametric variations, and external perturbations. In this article, to alleviate the above issues, a practical adaptive fast terminal sliding mode control (PAFTSMC) is proposed for better tracking performance of the servo motor system by using a state observer and bidirectional adaptive law. First, a smooth-tangent-hyperbolic-function-based practical fast terminal sliding mode control (PFTSM) surface is designed to ensure not only fast finite time tracking error convergence but also chattering reduction. Second, the PAFTSMC is proposed for the servo motor, in which a two-way adaptive law is designed to further suppress the chattering and overestimation problems. More importantly, the proposed adaptive technique can update the switching gain according to the system uncertainties, which can provide high gain in the reaching phase and then decrease to the smallest value in the sliding phase to avoid the monotonically increasing gain that exists in most adaptation methods. Third, the finite-time stability of the closed-loop system is proved based on the Lyapunov theorem. Finally, the simulation studies and experimental tests verify the effectiveness of the proposed control in terms of better tracking, strong robustness, and reduced chattering, compared to existing algorithms.

Adaptive fuzzy prescribed settling time consensus control for multi-agent systems with input hysteresis via dynamic event-triggered mechanism

An adaptive fuzzy prescribed settling time consensus control is proposed based on the dynamic event-triggered mechanism for a class of uncertain nonlinear multi-agent systems (UNMASs) subject to input hysteresis. In practical systems, the plant inevitably suffers from input hysteresis and unknown nonlinear characteristics, which dramatically deteriorate its performance. Therefore, to eliminate the effects of those constraints, an adaptive fuzzy prescribed settling time control scheme is constructed by applying backstepping technique and first-order filter. Wherein each agent needs to be equipped with only one adaptive law for fuzzy-logic-system approximation, reducing the computational burden. Simultaneously, the synchronization error is mapped using a transformation function to achieve prescribed settling time consensus control. Moreover, a dynamic event-triggered mechanism is employed to reduce unnecessary communication transmission and save energy. With the presented method, all agents synchronize to the virtual leader within a prescribed settling time. Theoretical analysis and simulation examples verify the presented method.

Practical finite-/fixed-time improved command-filtered backstepping control for nonlinear systems via immersion and invariance

This paper presents a practical finite-/fixed-time adaptive tracking control scheme based on improved command filtered backstepping (ICFBS) and immersion and invariance (I&I) for a class of single-input single-output (SISO) strict-feedback nonlinear systems with uncertainty parameterization. The conventional command-filtered backstepping method (CFBS) is improved by introducing any bounded function such that ICFBS relaxes the boundedness assumption of the control direction function and elevates the tunable space of the design scheme, with almost no increase in computational complexity. The higher-power composite term of a parameter estimation is designed in the parameter update law based on I&I and the inequality constructed by us proves that this form of the adaptive update law can be augmented to suit for not only uniform ultimate bounded (UUB) and practical finite-time stability but also practical fixed-time stability of the whole closed-loop system. The error compensation system is also extended to realize the practical finite-/fixed-time convergence of the error compensation signals. The proposed controller guarantees practical finite-/fixed-time stability of the closed-loop system. Therefore, our work solves two unsolved problems: both practical fixed-time and practical finite-/fixed-time ICFBS and I&I adaptive tracking control. Finally, the proposed control scheme is validated by a practical electromechanical system and a nonlinear system with unbounded control direction functions.