Adaptive Backstepping Control Scheme Research Articles

An adaptive backstepping control strategy based on radial basis function neural networks for the magnetorheological semi-active suspension

Owing to nonlinear issues such as external disturbances and uncertain parameters within the semi-active suspension system (SASS), the vibration amplitude of the suspension system tends to increase, and the time required for the suspension system to reach a steady-state response is prolonged. Hence, this paper proposes an adaptive backstepping control strategy based on radial basis function neural networks (RBF-NNs). Firstly, the damping force characteristics of the magnetorheological (MR) damper are tested, and the experimental data are utilized for parameters identification and fitting of the Bouc-Wen model. To establish a connection between the controller and the forward model of the MR damper, the forward model of the MR damper, the inverse model of the MR damper, and the model of the MR-SASS are constructed. Secondly, the backstepping controller and the adaptive backstepping controller based on RBF-NNs are designed. The stability and reliability of the closed-loop suspension system are verified through stability analysis using Lyapunov function. Finally, the dynamic characteristics of the passive control, backstepping control, and adaptive backstepping control strategies based on RBF-NNs applied to MR-SASS are analyzed under B-Class road excitation and speed bump road excitation. The acceleration, suspension dynamic deflection, and tire dynamic load are selected as the evaluation indices. The results demonstrate that the adaptive backstepping controller based on RBF-NNs significantly enhances the ride comfort of the SASS.

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.

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.

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.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

Saturated adaptive single-parameter backstepping design for underactuated MSVs tracking control with uncertain dynamics

For realizing the trajectory tracking of underactuated marine surface vehicles (MSVs) in the presence of model dynamic uncertainties, actuator saturation constraints, and time-varying uncertain disturbances, a saturated adaptive single-parameter backstepping control (SPBC) scheme is developed, which possesses the properties of being model-parameter free and single-parameter adaptive. A smooth dead-zone operator (SDZO) and dynamic compensation equations are designed to deal with the propulsion system saturation constraints problem. Then, desired velocities and an auxiliary combined velocity variable are introduced to solve the potential singular problem and stabilize the subsystem of kinematics. Following that, a single-parameter adaptive law is designed in surge and yaw channels to compensate compounded uncertainties, which further alleviate computational burdens. Theoretical analysis indicates that the proposed scheme can guarantee the boundedness of all closed-loop signals. Approach efficiency is validated by simulations and experiments.

Adaptive backstepping human-cooperative control of a pediatric gait exoskeleton system with high- and low-level admittance

Post-neurological disorder, passive-assist training disregards human involvement during robot-aided lower-limb rehabilitation. This work presents a novel human-cooperative framework based on the admittance and trajectory control scheme to administer the subject–exoskeleton interaction for pediatric gait rehabilitation. Initially, the mechanical design and dynamic analysis of an existing exoskeleton system are briefly attended. Thereafter, an admittance model is designed in the outer loop, which recasts the desired human trajectory into a reference trajectory. As an inner-loop control scheme, a robust adaptive backstepping controller is designed to trace the reference gait trajectory under parametric uncertainties and external disturbances. Lyapunov stability analysis is solved to guarantee the uniform boundedness of the control signals. Moreover, the well-known problem of “explosion of complexity” and “overparameterization” is avoided through the design of the robust adaptive backstepping control scheme. The performance of the proposed robust adaptive backstepping-based human-cooperative control is studied under the low- and high-level admittance model. Finally, the effectiveness of the proposed control is validated with a variable structure adaptive robust-based human-cooperative control. The co-simulation results show that the proposed control with low-level admittance allows the subject to participate in the training process more frankly. The proposed robust adaptive backstepping-based human-cooperative control tracks the reference gait more promisingly than the variable structure adaptive robust-based human-cooperative control for both admittance levels.

Adaptive Fractional-Order Backstepping Control for a General Class of Nonlinear Uncertain Integer-Order Systems

In this paper, we consider the adaptive fractional-order backstepping control problem for a class of high-order integer-order systems with uncertainties and unknown external disturbance. To obtain enhanced control performance, fractional-order calculus is integrated within the conventional backstepping controller design procedure. Theoretical proof is provided based on the Lyapunov stability theorem to ensure the global stability of the closed-loop system in the sense that all the closed-loop signals are uniformly ultimately bounded and the output tracking error to a reference signal converges to an adjustable arbitrarily small range by tuning certain design parameters. Both numerical simulation and experimental results verify the efficacy of the proposed adaptive fractional-order backstepping control scheme.

Command‐filter‐based fast finite‐time composite adaptive neural control for nonlinear systems with input dead‐zone

SummaryIn this paper, a command‐filter‐based fast finite‐time composite adaptive control scheme is proposed for nonlinear systems with input dead‐zone. The neural networks (NNs) are used to approximate the unknown functions of the controlled systems. The series‐parallel nonsmooth estimation models are used to predict the errors. In addition, the tracking error and prediction errors are anastomosed to update the weights of the NNs. To solve the problem of “explosion of complexity,” the command‐filter technology is adopted. Combining the Lyapunov stability theory and the adaptive backstepping algorithm, a composite adaptive backstepping control scheme is proposed. The proposed scheme dissolves the singularity problem which may emerge in the design process and the neural networks approximation performances can be realized as well. Meanwhile, the proposed scheme guarantees the tracking error converges into a small neighborhood of zero in fast finite‐time and the boundedness of all the closed‐loop signals. Finally, the simulation example is provided to verify the effectiveness of the proposed scheme.

A Novel Full Errors Fixed-Time Control for Constraint Nonlinear Systems

In this paper, the issue of adaptive control design with full error constraints for multi-input and multi-output (MIMO) nonlinear systems is investigated. By combining nonlinear filters and an adaptive back-stepping control scheme, a novel dynamic surface control (DSC) scheme is presented. Different from the DSC scheme with the traditional linear filter, the proposed DSC not only solves the inherent problem of computational complexity explosion, but also enhances the control property. In addition, in order to further enhance the tracking performance understructure the fixed-time prescribed performance, a novel barrier Lyapunov function is proposed by considering the transform error constraint based on the fixed-time prescribed performance functions (FTPPF). The design control scheme can ensure that all the dynamic errors can be converged in predefined bounds within a fixed time. By choosing the barrier Lyapunov function, the stability of the closed-loop system is proof. Finally, the validity and innovation of the proposed strategy are verified by numerical practical simulation examples.

Filtering‐based concurrent learning adaptive attitude tracking control of rigid spacecraft with inertia parameter identification

SummaryThis paper investigates the attitude tracking control problem of rigid spacecraft with inertia parameter identification. Based on the relative attitude and angular velocity error dynamics, a basic adaptive backstepping based attitude tracking control scheme is firstly designed such that asymptotic attitude tracking can be achieved. However, the parameter identification error cannot decay to zero if the persistent excitation (PE) condition is not satisfied. To solve this issue, a filtering‐based concurrent learning adaptive backstepping control scheme is then proposed, by incorporating torque filtering technique with concurrent learning technique. A more mild rank condition, which consists of some collectable historical data, is provided to guarantee the convergence of parameter identification error. In addition, a valid data collection algorithm is given. It should be mentioned that a distinctive feature of the proposed filtering‐based concurrent learning adaptive control scheme is that the convergence rate of attitude tracking errors can be improved from asymptotical to exponential. Finally, simulation results are provided to illustrate the effectiveness of the proposed control schemes.

Adaptive Backstepping Axial Position Tracking Control of Autonomous Undersea Vehicles with Deferred Output Constraint

In this paper, an adaptive backstepping control scheme is proposed to solve the the surge motion tracking control problem of an autonomous undersea vehicle (AUV) with system constraint. First, an initial rectification reference signal is constructed for the subsequent implementation of deferred output constraint and making the control input smaller and smoother in the early stage of system operation. Second, a barrier Lyapunov function is adopted for developing an output-constrained state feedback adaptive controller. Then, on the basis of coordinate transformation and estimating the derivative of surge displacement by a linear and nonlinear combined differentiator, we develop an output feedback adaptive backstepping control scheme for AUVs whose velocity signals are unmeasurable. We also carried out a comparative numerical simulation with traditional adaptive control to verify the feasibility of the proposed control strategy.

Dynamical analysis and accelerated adaptive backstepping funnel control for dual-mass MEMS gyroscope under event trigger

This paper investigates an adaptive backstepping funnel control scheme with an event-triggered mechanism for a chaotic dual-mass Micro-Electro-Mechanical Systems (MEMS) gyroscope. The mathematical model of the dual-mass micro-gyroscope is first developed based on a mutual mechanical coupling. Then, its inherent nonlinear characteristics under different spring and coupling coefficients, all of which have noticeable impacts on the system sensitivity, are fully examined through phase and Lyapunov exponent diagrams. In order to methodically address the control problem involving the uncertainty, the slow convergence, the constraint violation, the “item explosion” and the communication resource waste, an accelerated adaptive backstepping funnel controller is proposed by combining the type-2 sequential fuzzy neural network (T2SFNN), the speed function, the asymmetric funnel boundaries, the accelerated exponential integral tracking differentiator (AEITD) and the event-triggered mechanism. The recommended scheme not only well resolve the above issues, but also guarantee the prescribed performance requirements and the boundedness of all signals in closed-loop system. Finally, the effectiveness of the control scheme is substantiated through several simulated results.

SEMG-based Adaptive Cooperative Multi-mode Control of a Soft Elbow Exoskeleton Using Neural Network Compensation.

Soft rehabilitation exoskeletons have gained much attention in recent years, striving to assist the paralyzed individuals restore motor functions. However, it is a challenge to promote human-robot interaction property and satisfy personalized training requirements. This article proposes a soft elbow rehabilitation exoskeleton for the multi-mode training of disabled patients. An adaptive cooperative admittance backstepping control strategy combined with surface electromyography (sEMG)-based joint torque estimation and neural network compensation is developed, which can induce the active participation of patients and guarantee the accomplishment and safety of training. The proposed control scheme can be transformed into four rehabilitation training modes to optimize the cooperative training performance. Experimental studies involving four healthy subjects and four paralyzed subjects are carried out. The average root mean square error and peak error in trajectory tracking test are 3.18° and 5.68°. The active cooperation level can be adjusted via admittance model, ranging from 4.51 °/Nm to 10.99 °/Nm. In cooperative training test, the average training mode value and effort score of healthy subjects (i.e., 1.58 and 1.50) are lower than those of paralyzed subjects (i.e., 2.42 and 3.38), while the average smoothness score and stability score of healthy subjects (i.e., 3.25 and 3.42) are higher than those of paralyzed subjects (i.e., 1.67 and 1.71). The experimental results verify the superiority of proposed control strategy in improving position control performance and satisfying the training requirements of the patients with different hemiplegia degrees and training objectives.

Adaptive inverse optimal backstepping control strategy for longitudinal vibration of high-speed elevator system based on fuzzy observer

To effectively suppress the longitudinal vibration of the car under the conditions of high-speed operation and emergency braking, and improve the ride comfort of the car system, this paper proposes an adaptive fuzzy inverse optimal output feedback control strategy. Firstly, the dynamic model of the high-speed elevator system is established and the nonlinear dynamic model is approximated by the fuzzy logic system, and the auxiliary system model is established. Fuzzy state observer is designed to estimate the unmeasurable state. Furthermore, an adaptive inverse optimal output feedback controller based on fuzzy observer is designed by using adaptive backstepping technology and inverse optimal control principle. The stability analysis shows that the proposed adaptive fuzzy inverse optimal output feedback control strategy not only ensures the stability of the car attitude of high-speed elevator but also realizes the inverse optimization of the target cost function. Finally, the acceleration time–frequency response analysis of the two typical stages of high-speed elevator uniform running and emergency braking is carried out, and the numerical results are compared with the linear quadratic controller optimized by stepping quantum genetic algorithm (GA-LQR) and controller based on the state-dependent Ricatti equation (SDRE). The analysis verifies the effectiveness of the controller.

Compound Adaptive Fuzzy Synchronization Controller Design for Uncertain Fractional-Order Chaotic Systems

In this paper, the synchronization of two fractional-order chaotic systems with uncertainties and external disturbances is considered. A fuzzy logic system is utilized to estimate uncertain nonlinearity, and its estimation accuracy is improved by constructing a series-parallel model. A disturbance observer is implemented to estimate bounded disturbance. To solve the “explosion of complexity” problem in the backstepping scheme, fractional-order command filters are employed to estimate virtual control inputs and their derivatives, and error compensation signals are devised to reduce filtering errors. Based on the fractional-order Lyapurov criterion, the proposed compound adaptive fuzzy backstepping control strategy can guarantee that the synchronization error converges to a small neighborhood of the origin. At last, the validity of the proposed control strategy is verified via a numerical simulation.

Command filter-based adaptive fuzzy integral backstepping control for quadrotor UAV with input saturation

This paper presents an adaptive fuzzy integral backstepping control strategy combined with command filter to solve trajectory tracking problem of quadrotor unmanned aerial vehicle (UAV). By using Fuzzy logic system to approximate uncertain disturbance. The tracking error integral term is introduced to reduce the steady-state tracking error. The backstepping approach is combined with the command filter to solve the “computational explosion” problem, and the error compensation mechanism is introduced to reduce the influence of filtering error. The hyperbolic tangent function is used to solve the problem of input saturation. By choosing the appropriate Lyapunov function to calculate the adaptive law for tuning the adjustable parameters of the fuzzy logic system. Morever, the stability of the controller is analyzed by using Lyapunov stability theory. Numerical simulation results are provided to illustrate the effectiveness and superiority of the proposed control method.

Improved adaptive backstepping control of MPCVD reactor systems with non-parametric uncertainties

This paper presents an improved adaptive backstepping control strategy for a microwave plasma chemical vapor deposition (MPCVD) reactor system. To describe the dynamics of the reactor system, a non-parametric uncertain nonlinear system model with unknown control direction functions is built up. In order to deal with the non-parametric uncertainties of the system, direct adaptive laws are primarily proposed to estimate such uncertainties, which is superior to traditional adaptive backstepping that can only address parametric uncertainties. Moreover, an equivalence transformation of the system is given to address the system unknown control direction functions. By using Lyapunov stability criterion, it can be proved that the target signals (desired temperature, desired pressure, and desired gas flow rates) are tracked by the reactor system outputs with small errors. Finally, simulation results are given to demonstrate the effectiveness of the proposed control method.

Robust adaptive backstepping control for a lower-limb exoskeleton system with model uncertainties and external disturbances

ABSTRACT The main purpose of this work is to design a robust adaptive backstepping (RABS) control strategy for a pediatric exoskeleton system during passive-assist gait rehabilitation. The nonlinear dynamics of the exoskeleton system have ill-effects of uncertain parameters and external interferences. In this work, the designed robust control strategy is applied on the exoskeleton to assist children of 08–12 years, 25–40 kg weight, and 115–125 cm height. The dynamic model of the coupled human-exoskeleton system is established using the Euler–Lagrange principle. An appropriate Lyapunov function is selected to prove the uniform boundedness of the control signals. The “explosion of terms” is avoided by establishing a virtual control law without the dynamical system parameters. A Microsoft Kinect-LabVIEW experiment is carried out to estimate the desired gait trajectory. The robustness of the proposed control is validated by varying the limb segment masses and inducing the periodic external disturbances. The proposed control strategy is compared with the decentralized modified simple adaptive-PD (DMSA-PD) control strategy. From simulation results and performance improvement index, it is observed that RABS control outperforms the contrast control (DMSA-PD) to track the desired gait during passive-assist rehabilitation under the effect of model uncertainties and external disturbances.

A finite‐time adaptive fuzzy backstepping control for multiple‐input multiple‐output coupled nonlinear systems with tracking error constraints

SUMMARYIn this study, a finite‐time adaptive fuzzy backstepping control strategy with tracking error constraints is designed for a class of multiple‐input multiple‐output (MIMO) coupled nonlinear systems with uncertainties. First, the uncertainty of the system is approximated by adaptive fuzzy logic systems (AFLSs), then, the rapidity of the state tracking of the control system are ensured by backstepping and finite time theory. The problem of error constraints is solved by the combination of performance function and simplified barrier Lyapunov function (SBLF). It is proved that the states of a closed‐loop adaptive control system are semi‐globally practical finite‐time stable (SGPFS) by the finite‐time Lyapunov function, and in a finite time, the tracking error of the system state converges to a narrow block of origin with the prescribed bounded. Finally, the scheme's effectiveness is verified by the simulation.