Adaptive Tracking Control Research Articles

Predefined Time Fuzzy Adaptive Control of Switched Fractional-Order Nonlinear Systems with Input Saturation

Article Predefined Time Fuzzy Adaptive Control of Switched Fractional-Order Nonlinear Systems with Input Saturation Lusong Ding, and Weiwei Sun * 1 Institute of Automation, Qufu Normal University, Qufu 273165, China * Correspondence: wwsun@hotmail.com Received: 31 August 2023 Accepted: 31 October 2023 Published: 21 December 2023 Abstract: This article investigates the predefined-time fuzzy adaptive tracking control problem for a class of nonlinear switched fractional-order systems with input saturation and external disturbances under a nonstrict feedback structure. By combining the backstepping technique and the common Lyapunov function method, a predefined-time switching control method is constructed based on a novel fractional-order auxiliary function. The fuzzy logic system and the adaptive method are introduced to identify unknown compounded continuous functions. Moreover, the issue of calculating explosion and the problem of singularity are tackled through the newly proposed predefined-time and filter-based dynamic surface control. Especially, the construction of a continuous term in the controller eliminates possible chattering. The developed control strategy achieves that the closed-loop system is practically predefined-time stable under arbitrary switchings, where the upper bound of the settling-time can be defined by users in advance. Finally, two simulation examples are illustrated to prove the feasibility and effectiveness of the presented scheme.

Adaptive radial basis function neural network sliding mode control of robot manipulator based on improved genetic algorithm

ABSTRACT Since the trajectory-tracking control performance of multi-joint robot manipulator may be degraded due to modeling errors and external disturbances, this paper designs a new adaptive robot manipulator trajectory tracking control method through improved genetic algorithm and radial basis function neural network sliding mode control (IGA-RBFNNSMC). Firstly, the genetic algorithm (GA) is improved by establishing superior populations centered on individuals with high fitness values and selecting individuals in the superior populations for crossover and variation. Secondly, the improved genetic algorithm (IGA) is used for the optimization of the center vector and width vector of the Gaussian basis function in radial basis function (RBF) neural network. Then, based on the dynamics model of the robot manipulator, the modeling errors are approximated by RBF neural network and eliminated by sliding mode control (SMC), and the Lyapunov theorem is used to prove the stability and convergence of the control system. Finally, a two-joint robot manipulator is taken as the research objective and the simulation results show that IGA can significantly reduce the solution time on the basis of guaranteed accuracy and IGA-RBFNNSMC can make the trajectory tracking control accurate and more efficient, which proves the effectiveness of the proposed control method.

Resilient adaptive trajectory tracking control for uncalibrated visual servoing systems with unknown actuator failures

A resilient adaptive tracking control scheme for uncalibrated visual servoing system with unknown actuator failures is proposed, where the camera parameters, the robotic physical parameters, and the position information of end-effector cannot be measured accurately. For our scheme, the nonlinear composite Jacobian matrix involving unknown parameters is estimated by an adaptive algorithm based on the depth-independent interaction matrix frame so that the image feature with time-varying depth can be tackled effectively. With the use of projection technique in the adaptive algorithm, the possible singularity of the estimated composite Jacobian matrix can be well circumvented without any stringent assumption, which is critical for establishing the closed-loop stability. Moreover, a novel adaptive resilient control scheme based on dynamic decoupling is developed to separate the design of visual servoing controller and fault compensation, improving the visual servoing system resilience against unknown actuator failures in uncalibrated environment. Through a rigorous Lyapunov argument, the asymptotic convergence of image tracking error to zero is established successfully regardless of the occurrence of unknown actuator failures. The effectiveness of the proposed visual tracking control scheme is confirmed by simulation results.

Adaptive tracking control of a unicycle subject to uncertainties and perturbations

An adaptive trajectory tracking control scheme is proposed for the command of a unicycle robot which is subject to dynamic uncertainties (inertia, mass, viscous parameter, etc), unmodeled dynamics, unknown disturbances, slipping effects, and loss of effectiveness (LOE). The latter are adaptively estimated and compensated in control laws. Moreover, projection algorithms are added to bound estimators, preventing them from drifting. The control objective is developed in two steps. First, a kinematic control law is designed to compute the necessary velocities (linear and angular velocities) that allow the robot to reach the desired trajectory. Afterward, sliding mode based adaptive control torques are developed in order to track velocities computed in the first step. The proposed control strategy guarantees the stability of the closed-loop system by ensuring the asymptotic convergence to both desired trajectory and necessary velocities. Finally, simulation results illustrate the applicability and effectiveness of the proposed control scheme.

Tracking controller of extended chained nonholonomic systems with matched disturbance and input saturation

AbstractThis paper addresses the tracking control for an extended chained nonholonomic system under input saturation and matched disturbances. Specifically, the tracking error dynamic system is split into two subsystems in a cascade form. An integral sliding mode saturated controller is designed in combination with a finite‐time observer (FTDO) to ensure the finite‐time stability of the first subsystem, thereby simplifying the design of the second subsystem. A backstepping‐based adaptive saturated tracking control method is proposed for the second subsystem by incorporating the filter technology. The stability of the resulting closed‐loop system is demonstrated, and the tracking errors can be arbitrarily minimized through the appropriate design parameter selection. The effectiveness of the proposed scheme is validated through simulation and experimental results.

Non‐singular fixed‐time fuzzy adaptive control for nonlinear systems subject to actuator faults

AbstractThis paper proposes a non‐singular fixed‐time fault‐tolerant adaptive tracking control method for a kind of multi‐input and multi‐output nonlinear system, which is in form of non‐strict feedback and is subject to actuator faults. The major contribution, compared to other practical fixed‐time fault‐tolerant control methods, is that the fixed time can be calculated precisely. By applying fuzzy logic systems, the identification of unknown nonlinearities is achieved, and by the boundness of fuzzy basis functions, the algebraic loop problem is avoided. Based on the fixed‐time stability theory, the practical fixed‐time fault‐tolerant adaptive tracking control method is proposed with adaptive back‐stepping control technology, in which the control singular problem is overcome by applying the adding power integration method. By the Lyapunov function theory, the practical fixed‐time stability of the closed‐loop system is theoretically proved. And even in the case of unknown actuator faults, the tracking error of the controlled system for the given command signal can still converge to a small neighbourhood of zero within a fixed time, regardless of the system initial state. Finally, the proposed control method is successfully implemented on a multi‐motor control platform, proving its effectiveness, and multiple comparative simulations are carried out, demonstrating its superiority.

A dynamic-event approach to adaptive asymptotic tracking control of [formula omitted]-normal nonlinear systems under full state constraints

In this paper, we study the problem of asymptotic tracking control for a class of interconnected p-normal nonlinear systems (p-NNS) with full-state constraints (FSCs). An event-triggered mechanism is constructed by introducing a new dynamic variable. It effectively reduces the update frequency of the controller compared to temporal-triggered. By building a new barrier function, the unknown functions of the system are converted into unknown scalars, which will be disposed of by the adaptive technique. To implement the FSCs control, we propose a low-complexity constrained control scheme while removing the condition that the initial value of the output is constrained. According to Barbalat’s lemma, it is proved that the output signal can asymptotically track the predetermined signal, and the system states are kept within the constraint bound, with all signals bounded. Finally, two simulation examples illustrate the effectiveness of the scheme.

Fault-Tolerant Fuzzy Observer-Based Fixed-Time Tracking Control for Nonlinear Switched Systems

This paper focuses on developing an adaptive output feedback fault-tolerant fixed-time tracking control strategy for a class of switched nonlinear systems with non-affine faults. To approximate the unmeasurable states, a mode-dependent state switched fuzzy observer is generated using fuzzy logic systems and a Butterworth low-pass filter. Next, an adaptive fixed-time tracking control strategy is developed by combining dynamic surface technology with the backstepping method. An improved mode-dependent average dwell time switching rule is also introduced to ensure the stability of switched nonlinear systems with unstable subsystems. A stability analysis proves the effectiveness of the proposed control scheme in stabilizing the switched nonlinear system under mode-dependent average dwell time switching, ensuring that the tracking error reaches the residual set within a derived settling time. Finally, a switched resistor-inductor-capacitor circuit example is provided to demon- strate the validity of the proposed strategy.

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.

Practically Predefined-Time Adaptive Fuzzy Tracking Control for Nonlinear Stochastic Systems.

This article addresses the practically predefined-time adaptive fuzzy tracking control problem of strict-feedback nonlinear stochastic systems, where the system under consideration includes stochastic disturbances and uncertain parameters. First, in this study, practically predefined-time stochastic stabilization (PPSS) in the p th moment sense is introduced, and a Lyapunov-type criterion for PPSS is proposed to assure the stabilization of the system considered. With these ideas, based on the backstepping design method, a semiglobally practically predefined-time adaptive fuzzy tracking control algorithm is proposed with a fuzzy system used to approximate the unknown part of the system. Moreover, the settling time of the system response can be arbitrarily adjusted in a mean-value sense, and such freedom can be used to improve the stochastic finite-/fixed-time control results. Finally, a practical example and a numerical example of a comparison are provided to validate the effectiveness of the proposed control strategy.

Robust adaptive tracking control for dynamic positioning ships subject to dynamic safety constraints and actuator saturation

This paper proposed a novel robust adaptive trajectory tracking control scheme for dynamic positioning (DP) ships subjected to unknown time-varying disturbances, unknown model parameters, dynamic safety constraints, and actuator saturation. The dynamic safety constraints were guaranteed based on the tan-type barrier Lyapunov function (BLF) technique, which ensured the position and velocity of the DP vessel within the given constraints. Moreover, the radial basis function neural network (RBFNN) was adopted to approximate the unknown parameters of the dynamics model, and an adaptive neural disturbance observer (ANDO) was designed to compensate for lumped disturbances. An anti-windup system was developed to handle the actuator saturation effect. By combining the above techniques and back-stepping method, the final control law was presented, and the semi-global asymptotic convergence was achieved via rigorous theoretical analysis and Lyapunov proof. The results of simulations demonstrated the superiority and robustness of this approach in resolving the trajectory tracking challenges of DP ships. Moreover, the proposed control scheme is highly effective in optimizing the trajectory tracking of DP ships, as it takes into account the multiple constraints that may arise during the process, which is a valuable contribution to the field of DP ship trajectory tracking, providing a more comprehensive and effective solution to this complex problem.

Finite-Time Model Reference Adaptive Grasping Control With Fuzzy State Observer for Maglev Grasping Robot System

The Maglev grasping robot system (MGRS) with single axial grasping coils is proposed to achieve the reliable transporting, but the grasped body is always subjected to multiple disturbances derived from the robot motion. Hence, the finite-time model reference adaptive control is presented to guarantee the satisfied transient and robustness performance. First, two degree-of-freedom dynamic model is built with consideration of uneven magnetic flux. Second, the prescribed performance reference model (PPRM) is designed by finite-time control (FTC), and its convergence performance is analyzed by FTC Lyapunov function. Then, the adaptive tracking controller is deduced from the model matching and FTC stability, which makes the MGRS to approximate the PPRM in finite time, and fuzzy approximation state observer is used to online get external disturbances and unknown state. It is proved that the proposed strategy can guarantee the closed system semiglobally practical finite-time stability, and the model approximation error and observe error can converge to the desired neighborhood in finite time. Finally, experimental results show that the MGRS with the proposed strategy has faster transient performance, and stronger robustness than the other three strategies.

Adaptive Fixed-Time Neural Control for Uncertain Nonlinear Multiagent Systems.

In this article, we consider the problem of adaptive fixed-time tracking control for a class of multiagent systems (MASs) with mismatched uncertainty. Unlike the existing methodologies that only implement the practical finite-/fixed-time stability for MASs, a newly adaptive consensus control criterion is developed to reach fixed-time stability, where the controller design includes a series of newly Lyavonov functions and modified tuning functions. Radial basis function neural networks are employed to deal with the unknown functions in each agent, and the direct adaptive strategy solves the obstacle of "explosion of complexity." Under the performance-oriented controller, the error of the MASs converges to a predetermined interval within a fixed time. Two simulations illustrate the results obtained.

Adaptive neural tracking control for upper limb rehabilitation robot with output constraints

AbstractThe authors investigate the trajectory tracking control problem of an upper limb rehabilitation robot system with unknown dynamics. To address the system's uncertainties and improve the tracking accuracy of the rehabilitation robot, an adaptive neural full‐state feedback control is proposed. The neural network is utilised to approximate the dynamics that are not fully modelled and adapt to the interaction between the upper limb rehabilitation robot and the patient. By incorporating a high‐gain observer, unmeasurable state information is integrated into the output feedback control. Taking into consideration the issue of joint position constraints during the actual rehabilitation training process, an adaptive neural full‐state and output feedback control scheme with output constraint is further designed. From the perspective of safety in human–robot interaction during rehabilitation training, log‐type barrier Lyapunov function is introduced in the output constraint controller to ensure that the output remains within the predefined constraint region. The stability of the closed‐loop system is proved by Lyapunov stability theory. The effectiveness of the proposed control scheme is validated by applying it to an upper limb rehabilitation robot through simulations.

Finite-Time Adaptive Neural Control for a Class of Nonlinear Systems With Asymmetric Time-Varying Full-State Constraints.

In this article, an adaptive finite-time tracking control scheme is developed for a category of uncertain nonlinear systems with asymmetric time-varying full-state constraints and actuator failures. First, in the control design process, the original constrained nonlinear system is transformed into an equivalent "unconstrained" one by using the uniform barrier function (UBF). Then, by introducing a new coordinate transformation and incorporating it into each recursive step of adaptive finite-time control design based on the backstepping technique, more general state constraints can be handled. In addition, since the nonlinear function in the system is unknown, neural network is employed to approximate it. Considering singularity, the virtual control signal is designed as a piecewise function to guarantee the performance of the system within a finite time. The developed finite-time control method ensures that all signals in the closed-loop system are bounded, and the output tracking error converges to a small neighborhood of the origin. At last, the simulation example illustrates the feasibility and superiority of the presented control method.

Event-Triggered Adaptive Bipartite Asymptotic Tracking Control Using Intelligent Technique for Stochastic Nonlinear Multiagent Systems

The problem of event-triggered based adaptive bipartite asymptotic tracking control for multi-agent stochastic pure-feedback nonlinear systems over sign digraph is considered. The agents classification optimization strategy (ACOS) is presented, which transforms a structurally unbalanced multi-agent topology graph into a structurally balanced multi-agent topology graph. Furthermore, how to deal with the nonaffine structure and unknown control gains for multi-agent stochastic pure-feedback nonlinear systems is a challenging issue for designing controllers. As a result, the mean value theorem is used to transfer the nonaffine systems into the affine systems, and the Nussbaum functions are used to eliminate the influence caused by the unknown control gains. In addition, the intelligent control technique is used to approximate the unknown nonlinearities, the event-triggered control strategy following the switching thresholds is introduced to save unnecessary communication resources, and the computation burden is eliminated by means of the dynamic surface technique. It is proved that all signals of the closed-loop systems are bounded in probability and the tracking errors asymptotically converge to zero in probability. Finally, the simulation results illustrate the validity of the proposed scheme. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Impact Statement</i> —In nature, there are a lot of interesting movements of multi-agents. In this paper, the multi-agent stochastic pure-feedback nonlinear systems over sign digraph is considered. How to handle the nonaffine structure and unknown control gains for the studied systems under interest is a difficult issue. Therefore, the mean value theorem and the Nussbaum functions are used to overcome the difficulty of designing controllers. The bipartition problem with the structurally unbalanced sign digraph is another design difficulty, then we propose the ACOS in the controller design process. In addition, the controllers designed in this paper, which are constructed by applying the backstepping method, event-triggered control strategy, and dynamic surface technique, can save the unnecessary communication resources and alleviate computation burden. Finally, the simulation results illustrate the validity of the proposed scheme.

Adaptive Event-Triggered Fuzzy Control of State-Constrained Stochastic Nonlinear Systems Using IBLFs

In this article, an adaptive tracking control problem is addressed for nonstrict-feedback stochastic nonlinear systems subject to state constraints. Fuzzy logic systems (FLSs) are used to model unknown nonlinearities and avoid the algebraic loop arising from the system structure. Appropriate integral Barrier Lyapunov functions (IBLFs) are chosen so that time-varying full state constraints can be guaranteed directly rather than by transforming the constraint object. In the framework of backstepping technology, the relative threshold strategy is introduced to modify the adaptive control scheme so that the controller can be updated only after the trigger condition has been met, which reduces the update frequency of the controller and the loss of the actuator. Combined with Lyapunov stability theory, it is shown that all closed-loop signals are bounded in probability, in which the states remain within the specified constraints, and there is no Zeno behavior. A series of simulation results are given to reveal the effectiveness of the constructed control scheme.

Adaptive Multi-Dimensional Taylor Network Tracking Control for a Class of Nonlinear Strict Feedback Systems

Nonlinear systems are very common in real life, but because they are not superposed and homogeneous, there are many difficulties in controlling nonlinear systems. Therefore, an adaptive control method based on a multi-dimensional Taylor network (MTN) is proposed for a class of nonlinear systems with strict feedback so that the output of the system can track the given signal. In order to achieve the control effect, we define a new state variable and transform the strict feedback system. After transformation, the original feedback system has a standard form, and two parameters to be identified are obtained. Then, the state observer is designed, and the two parameters are identified via the approximation of the MTN. On this basis, the controller design and a system stability analysis are completed. The lemma is introduced, and the stability condition is established by using this low-pass filter to ensure that all closed-loop signals are semi-globally uniform and finally bounded and the output tracking error converges to the residual set near zero. Finally, a numerical simulation of a hydraulic system is carried out to verify the effectiveness of the proposed method. Under the three indexes, the proposed method has obvious advantages.

Pseudo-partial-derivative information-driven adaptive fault-tolerant tracking control for discrete-time systems

The fault-tolerant tracking control problem is studied for the discrete-time systems with actuator faults. To lessen adverse impacts of actuator fault, a PPD information-driven fault estimation algorithm is established to adaptively estimate actuator fault information online, which avoids the additional construction and training process of neural network. With the aid of the adaptive fault compensation, a model-free adaptive fault-tolerant tracking control algorithm is constructed to ensure that the expected output reference trajectory can be tracked by system output. Moreover, only input and output data are employed throughout the design process, system dynamics are not demanded. Ultimately, the availability of developed strategy is proved through a simulation.

Stable approximate Q-learning under discounted cost for data-based adaptive tracking control

In this paper, the stability of tracking error dynamics under the data-based discounted iterative Q-learning is investigated. First, a novel performance index with a discount factor is introduced into the iterative Q-learning-based tracking control. Then, considering the approximation errors caused by the Q-function approximator, the finite error bound between the iterative and optimal Q-functions is established. Moreover, based on the new stability analysis, the selection rule of the discount factor is developed, which ensures that the corresponding optimal control policy is admissible. Next, to ensure the stability of the tracking error dynamics under iterative control policies, the stability condition about the approximate Q-function is established. It is guaranteed that iterative control policies derived from the critic network drive the tracking error to zero. Additionally, considering the adopted policy function approximator, the upper bound function of the approximation errors is developed. It is ensured that the trained action network stabilizes the tracking error dynamics. Finally, a simulation example is utilized to implement the data-based discounted iterative Q-learning and verify the present theoretical results.