Adaptive Backstepping Control Research Articles

Adaptive fault-tolerant control for attitude maneuvering under attitude constraints and finite sequential actuator faults

The problem of retargeting rigid body attitude with attitude constraints has been extensively investigated, whereas the challenge persists in maneuvering rigid-body attitude with multiple concurrent attitude constraints and finite sequential actuator faults. Finite sequential actuator faults, which can reduce controllability or destabilize the system, necessitate the implementation of fault-tolerant control strategies. Therefore, this paper aims to address the issue of redirecting spacecraft attitude subject to multiple attitude constraints and finite sequential actuator faults comprehensively. Firstly, we represent spacecraft attitude using unit quaternions and employ an artificial potential function to effectively handle multi-attitude constraints. The negative gradient direction guides the rigid-body spacecraft towards seamless convergence with the desired attitude. Our proposed unwinding strategy effectively avoids unwinding phenomena during large-angle spacecraft reorientation as well. Additionally, we design an adaptive compensation strategy for finite sequential actuator faults that enables real-time calculation of the fault compensation matrix under such actuator faults. Importantly, we propose an improved adaptive fault-tolerant back-stepping controller integrated with a potential function that effectively addresses both attitude constraints and finite sequential actuator faults simultaneously. Subsequently, stability analysis is conducted on the proposed controller to ensure its stability in practical applications rigorously. Finally, numerical simulations are performed meticulously to demonstrate the effectiveness and robustness of our proposed controller.

Neural-Network-Based Adaptive Fault-Tolerant Cooperative Control of Heterogeneous Multiagent Systems With Multiple Faults and DoS Attacks.

In this article, the issue of adaptive fault-tolerant cooperative control is addressed for heterogeneous multiple unmanned aerial vehicles (UAVs) and unmanned ground vehicles (UGVs) with actuator faults and sensor faults under denial-of-service (DoS) attacks. First, a unified control model with actuator faults and sensor faults is developed based on the dynamic models of the UAVs and UGVs. To handle the difficulty introduced by the nonlinear term, a neural-network-based switching-type observer is established to obtain the unmeasured state variables when DoS attacks are active. Then, the fault-tolerant cooperative control scheme is presented by utilizing an adaptive backstepping control algorithm under DoS attacks. According to Lyapunov stability theory and improved average dwell time method by integrating the duration and frequency characteristics of DoS attacks, the stability of the closed-loop system is proved. In addition, all vehicles can track their individual references, while the synchronized tracking errors among vehicles are uniformly ultimately bounded. Finally, simulation studies are given to demonstrate the effectiveness of the proposed method.

Adaptive finite‐time recoil control of deepwater drilling riser systems with nonlinear forces and saturation input using switched event‐triggered scheme

AbstractThis article investigates the finite‐time recoil control problem of deepwater drilling riser systems with nonlinear friction force, tension force and saturation input. For the friction force, a new approximation model based on radial basis function neural networks is presented, which not only can ensure a better approximation effect than the sine‐function type and exponential‐polynomial‐function type computational models, but also can be easily used for control design. Different from the existing linear optimal control methods, a neural‐network‐based adaptive backstepping control method is proposed to deal with the nonlinear friction and tension forces, which can achieve better recoil control responses. An auxiliary system combining with the change of coordinates is employed to compensate the saturation input effect. To prolong the average release interval of control input while preserving satisfied control performance, a new switched event‐triggered control (ETC) scheme is developed, in which the triggering conditions are switched between the fixed and relative thresholds based on the strength of control signal. With the event‐triggered controller, the practical finite‐time stability condition of recoil control system is derived and the Zeno behavior is avoided. Numerical results are given to show the advantages of the proposed methods in handling the model nonlinearities, finite‐time stability and ETC performance of riser‐tension systems.

Distributed finite‐time backstepping adaptive containment control for multiple unmanned aerial vehicles with input saturation

AbstractThis paper investigates a distributed adaptive finite‐time containment control scheme for multiple unmanned aerial vehicles subject to external disturbances and input saturation. Combined with a novel indicator of the saturation degree designed by the hyperbolic tangent function, an adaptive method is proposed to deal with the input saturation issue, which considers both symmetry and asymmetry saturation. Moreover, to address the problem of the “explosion of terms” inherent in the traditional backstepping controller design, a fixed‐time sliding mode differentiator is utilized to approximate the derivative of the virtual signal in the command‐filtered backstepping method. Finally, the convergence of the errors and the practicability of the control law are verified by Lyapunov stability analysis and numerical simulations.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

AbstractThis research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

A nonlinear design method of robust PI control by using adaptive backstepping control for web winding system of reversible cold rolling mill

Adaptive Fuzzy Backstepping Control for Itô-Type Nonlinear Switched Systems Subject to Unknown Hysteresis Input

The adaptive fuzzy backstepping control problem is studied for Itô-type nonlinear switched systems subject to unknown hysteresis input. Compared with existing works, the unknown hysteresis and stochastic disturbances are considered in the pure-feedback switched systems. The mean value theorem tackles the non-affine functions. The backstepping technique introduces an auxiliary virtual controller. In addition, the Nussbaum function is employed to solve the difficulty caused by the unknown hysteresis under arbitrary switching. Based on a fuzzy logic system and backstepping technique, a new adaptive control proposal is obtained, which ensures that the system states satisfy semiglobally uniformly ultimately bounded (SGUUB) in probability and that the tracking error converges to a region of the origin. Finally, we provide two examples to show the validity of the presented scheme.

Anti-unwinding adaptive robust backstepping attitude maneuver control for rigid spacecraft

In this paper, an anti-unwinding adaptive robust backstepping control law is proposed to solve the attitude control problem of rigid spacecraft with external disturbances and inertia uncertainties. A new variable based on hyperbolic sine functions is designed to prevent the unwinding phenomenon, and then a novel robust backstepping controller is developed. Initially, a nonlinear tracking law is designed to obtain the desired angular velocity and to ensure that the attitude maneuvering system could have two equilibrium points. Subsequently, an adaptive robust control law is devised, which incorporates the adaptive estimation method to update the inertial parameters in real-time. Moreover, the bounded external disturbances are taken into account in the design of the control law, and thus the robustness of the attitude control system is improved. Furthermore, the global asymptotic stability of the attitude control system is verified by the Lyapunov-Krasovskii theorem. Finally, numerical simulations are carried out to demonstrate the effectiveness and robustness of the proposed control law, as well as the anti-unwinding characteristics are perfectly validated during the attitude maneuver of rigid spacecraft.

Adaptive backstepping control for uncertain semiconductor refrigeration systems considering even-order input

Temperature control technique has received much attention in the field of semiconductor thermal management. This paper presents a novel adaptive backstepping-based temperature control strategy for semiconductor refrigeration systems considering unmodeled dynamics. The inherent non-affine problem caused by the even-order input signal is solved by combining a novel smooth function into the command filtered backstepping method. And then, the adaptive observer is also employed to improve the system performance under unmodeled dynamic deviations. The stability of the closed-loop system is analyzed based on the Lyapunov theory, and simulation experiments are given to verify our control method. The simulation results show that the method can realize the accurate control of temperature under unmodeled dynamics. Under the disturbance of ambient temperature changes and model errors, the steady state error of the system remains below 0.1 °C. In comparison with the traditional control methods, our strategy has a stronger ability to suppress the uncertainty effects.

L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}{}_{1}$$\\end{document} adaptive fault-tolerant control of stratospheric airships

As the utilization of stratospheric airships becomes more prevalent, ensuring their safe operation becomes crucial. This paper explores the ability of an L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}_{1}$$\\end{document} adaptive controller to maintain fault tolerance in the actuators of a stratospheric airship. L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}_{1}$$\\end{document} adaptive control offers fast adaptation while separating adaptation and robustness. This makes the approach a suitable candidate for fault-tolerant control. The performance of the proposed design is compared to the Linear Quadratic Integral and Adaptive Sliding Mode Backstepping controllers. Simulation results show that the robustness of the airship model against faults is improved with the use of the L1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {L}}{}_{1}$$\\end{document} adaptive controller.

Synchronous control of tri-motor vibration system considering an adaptive back-stepping control strategy

In oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.

Self-Stabilizing Control Strategy of Stabilized Platform for Rotary Steerable Drilling System Based on Adaptive Backstepping Control

To enhance the robustness of the toolface angle control in a fully rotary steerable drilling tool, a backstepping control law and a drilling fluid flow adaptive law are devised based on the dynamic model of the stable platform. The Lyapunov function is constructed, and it is proven that the adaptive backstepping control system of the stabilized platform is stable. Furthermore, in order to address problems such as the friction dead zone and excessive rotational kinetic energy in the stabilized platform system, which could cause toolface angle oscillations and the rapid rotation of the stabilized platform, we additionally propose an online estimation method for the balancing torque and velocity-angle control switching strategy. By combining the backstepping control law, drilling fluid flow adaptive law, and velocity-angle control switching strategy, a self-stabilizing control strategy for the stabilized platform is established. In comparison with the PID control method, the simulation results show the superiority of the proposed scheme under complex disturbances from a downhole environment. And the drilling simulation experiment results indicate that the proposed control method has a good anti-interference capability under various conditions, including drilling fluid flow rate, inclination angle, and drill collar rotational speed. Therefore, the proposed control method can improve the robustness of the stabilized platform control system.

Command filter-based event-triggered fixed-time control for nonlinear systems with prescribed performance and actuator faults

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights’ updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example.

Adaptive neural network backstepping control method for aerial manipulator based on coupling disturbance compensation

The aerial manipulator, designed for complex aerial tasks, encounters multifaceted operational environments influenced by various internal and external disturbances. This paper introduces an adaptive neural network backstepping control technique fortified with coupling disturbance compensation to enhance the resilience of the aerial manipulator against these disturbances. Firstly, we propose a cutting-edge coupling disturbance feedforward compensator based on variable inertia parameters, which offers precise and prompt compensation for significant internal coupling disturbances without needing external sensors or alternative disturbance estimation techniques. Subsequently, radial basis function neural networks with an online adaptive weight updating mechanism are designed to estimate and counteract lumped disturbances stemming from unmodeled dynamics, uncertainties, and external factors in real-time. Utilizing the Lyapunov stability criteria, we validate that the aerial manipulator can reliably track desired trajectories under our proposed controller. Experimental results and simulations further underscore the effectiveness and superiority of our control approach.

An Adaptive Backstepping Control for a Free-Floating Space Manipulator Using a Linearly Parametrized Dynamic Model

An Adaptive Backstepping Control for a Free-Floating Space Manipulator Using a Linearly Parametrized Dynamic Model

Robust adaptive backstepping control of H‐bridge inverter based on type‐2 fuzzy optimization of parameters

AbstractA type‐2 fuzzy logic‐based adaptive backstepping control (T2FABSC) approach is designed for an H‐bridge inverter. This inverter has an LC filter to decrease the level of total harmonic distortion (THD) that can affect the efficiency of the system. Reduction of THD and stability insurance of the filter are challenging trade‐offs, tackled here by a controller design. The performance, however, is not suitable for actual applications under a wider range of disturbances, and the parameters need to be adjusted once more for more dependable operations. Backstepping control is given a Lyapunov definition‐based adaptive mechanism that can improve this scheme's stability and robustness in the face of numerous disturbances. Additionally, the system is viewed as a “Black box” without the need for a precise mathematical model, which might lead to a lighter computing burden and simpler implementation. Moreover, a fuzzy type‐2 structure is adopted that can optimize the gains of the adaptive Backstepping controller (ABSC) in challenging conditions. The antlion optimization algorithm is employed to optimize the parameters of the membership functions in the fuzzy system, hence improving the performance of the controller. In addition, compared with different optimization algorithms, it can more quickly and accurately locate the best solutions. Finally, the findings of both the simulations and the experimental outputs are examined, proving the T2FABSC's significant robustness and faster dynamics in a variety of challenging circumstances.

Command filter-based adaptive neural tracking control of nonlinear systems with multiple actuator constraints and disturbances

In this paper, the adaptive practical finite-time tracking control problem for a class of strictly feedback nonlinear systems with multiple actuator constraints is investigated using backstepping techniques and practical finite-time stability theory. The effects of deadband and saturated nonlinear constraints on the controller design of nonlinear systems are addressed by the equivalent transformation method. The problem of complexity explosion due to the derivatives of virtual control signals is solved by using the virtual control signals as inputs to the command filters and using the outputs of the command filters to perform the corresponding control tasks. An adaptive neural network tracking backstepping control strategy based on the command filter technique and the backstepping design algorithm is proposed by approximating an unknown nonlinear function using a neural network. The control strategy ensures the boundedness of all variables in the closed-loop system, and the output tracking error fluctuates in a small region near the origin. Finally, simulations verify the effectiveness of the control strategy designed in this paper.

Trajectory-Tracking Control for Quadrotors Using an Adaptive Integral Terminal Sliding Mode under External Disturbances

In the face of external disturbances affecting the trajectory tracking of quadrotors, a control scheme targeted at accurate position and attitude trajectory tracking was designed. Initially, a quadrotor dynamic model, essential for control design, was derived. Adaptive integral backstepping control (AIBS) was then employed within the position loop, enabling the upper boundaries of disturbances to be estimated through adaptive estimation. Subsequently, a new adaptive backstepping fast nonsingular integral terminal sliding mode control (ABFNITSM) was proposed to enable adherence to the desired Euler angles. Rapid convergence and accurate tracking were facilitated by the incorporation of the nonsingular terminal sliding mode and an integral component. The dead zone technique was deployed to curtail estimation errors, while a saturation function was used to eradicate the phenomenon of chattering. Finally, to validate the proposed control scheme, simulation experiments were conducted in the Simulink environment, and the results were contrasted with those obtained from traditional integral terminal sliding mode control (ITSM) and integral backstepping control (IBS), providing evidence of the effectiveness of the proposed method.

Intermittent monitoring‐based adaptive fault‐tolerant control for uncertain nonlinear systems with actuator switching

AbstractIn this paper, an adaptive fault‐tolerant control (FTC) scheme is proposed for a class of uncertain nonlinear systems with actuator failure, in which a healthy actuator is available as a backup. Instead of monitoring the failure in real‐time, an intermittent monitoring mechanism (IMM) is proposed by designing a set of monitoring functions operating only at discrete time instants, which makes the proposed scheme more applicable for networked control systems for which the actuator status has to be monitored via network. An adaptive backstepping controller is designed with the errors being modified to include shifting functions. Once actuator failure is detected by the monitoring functions, the actuator is switched to its backup and the controller is reconfigured by updating the shifting functions so that the tracking error can be driven into the prescribed performance in a given time.

Adaptive Neural Preassigned-Time Control for Macro–Micro Composite Positioning Stage With Displacement Constraints

This paper considers the rapid vibration reduction problem of macro-micro composite positioning stage (MMCPS) using an adaptive neural preassigned-time control strategy. Based on Newton's second law, the MMCPS is modeled as an interconnected system with unknown perturbations, and for the first time, the vibration reduction problem of MMCPS is transformed into a displacement constraint problem. Through adaptive neural network approximation and backstepping control, a preassigned-time controller with a novel performance function-related term is developed, which not only significantly improves the positioning accuracy and reduces the vibration amplitude but also ensures that the displacements of the voice coil motor axis and the stage are constrained to a predefined region in a finite time. Another distinguished feature of the proposed controller lies in the fact that the settling time of the displacement signals can be set as an arbitrary positive value. Moreover, all signals of the closed-loop system are proved to be semi-globally uniformly ultimately bounded. Finally, the feasibility of the designed control strategy is demonstrated via a simulation experiment.