Adaptive Fuzzy Observer Backstepping Control for a Class of Uncertain Nonlinear Systems with Unknown Time-delay

In this paper, a new adaptive fuzzy backstepping control approach is developed for a class of nonlinear systems with unknown time-delay and unmeasured states. Using fuzzy logic systems to approximate the unknown nonlinear functions, a fuzzy state observer is designed for estimating the unmeasured states. On the basis of the state observer and applying the backstepping technique, an adaptive fuzzy observer control approach is developed. The main features of the proposed adaptive fuzzy control approach not only guarantees that all the signals of the closed-loop system are semiglobally uniformly ultimately bounded, but also contain less adaptation parameters to be updated on-line. Finally, simulation results are provided to show the effectiveness of the proposed approach.

Adaptive Backstepping Sliding Mode Control for Nonlinear Systems with Input Saturation

An adaptive backstepping sliding mode control is proposed for a class of uncertain nonlinear systems with input saturation.A command filtered approach is used to prevent input saturation from destroying the adaptive capabilities of neural networks (NNs).The control law and adaptive updating laws of NNs are derived in the sense of Lyapunov function,so the stability can be guaranteed even under the input saturation.The proposed control law is robust against the disturbance,and it can also eliminate the impact of input saturation.Simulation results indicate that the proposed controller has a good performance.

A new four-dimensional hyperjerk system with stable equilibrium point, circuit implementation, and its synchronization by using an adaptive integrator backstepping control

This paper reports a new simple four-dimensional（4 D） hyperjerk chaotic system. The proposed system has only one stable equilibrium point. Hence, its strange attractor belongs to the category of hidden attractors. The proposed system exhibits various dynamical behaviors including chaotic, periodic, stable nature, and coexistence of various attractors. Numerous theoretical and numerical methods are used for the analyses of this system. The chaotic behavior of the new system is validated using circuit implementation. Further, the synchronization of the proposed systems is shown by designing an adaptive integrator backstepping controller. Numerical simulation validates the synchronization strategy.

Adaptive backstepping control for levitation system with load uncertainties and external disturbances

To explore the precise dynamic response of the levitation system with active controller, a maglev guide way-electromagnet-air spring-cabin coupled model is derived firstly. Based on the mathematical model, it shows that the inherent nonlinearity, inner coupling, misalignments between the sensors and actuators, load uncertainties and external disturbances are the main issues that should be solved in engineering. Under the assumptions that the loads and external disturbance are measurable, the backstepping module controller developed in this work can tackle the above problems effectively. In reality, the load is uncertain due to the additions of luggage and passengers, which will degrade the dynamic performance. A load estimation algorithm is introduced to track the actual load asymptotically and eliminate its influence by tuning the parameters of controller online. Furthermore,considering the external disturbances generated by crosswind, pulling motor and air springs, the extended state observer is employed to estimate and suppress the external disturbance. Finally, results of numerical simulations illustrating closed-loop performance are provided.

Backstepping adaptive control of hydraulic Stewart platform using dynamic surface

Hydraulic Stewart platform is characterized by nonlinearity for driving system in essence,severe load coupling among the legs,which bring a great difficulty for controller design and performance improvement.Afore controller research is either low in tracking performance and movement smoothness when it ignores the nonlinearity and dynamics coupling,or complex in algorithm and has the need of acceleration feedback or observer when the dynamics coupling and nonlinearity is included.To solve the dilemma,a new controller,backstepping adaptive control of hydraulic Stewart platform using dynamic surface is put forward based on the complete dynamics including the upper platform dynamics and hydraulic nonlinearity in driving system.Asymptotic stability of the whole system is proved by Lyapunov method.The proposed algorithm is simple by avoiding the use of acceleration.The simulation results indicate that the control algorithm performs better than the normal PID controller in control precision,dynamic response and depression of the cross coupling.

Backstepping Adaptive Controller of Electro-Hydraulic Servo System of Continuous Rotary Motor

In order to consider the influence of the continuous rotary motor electro-hydraulic servo system parameters change on its performance,the design method of backstepping adaptive controller is put forward.The mathematical model of electro-hydraulic servo system of continuous rotary motor is established,and the whole system is decomposed into several lower order subsystems,and the virtual control signal is designed for each subsystem from the final subsystem with motor angular displacement to the subsystem with system control input voltage. Based on Lyapunov method and the backstepping theory,an adaptive backstepping controller is designed with the changed parameters adaptive law. It is proved that the system reaches the global asymptotic stability,and the system tracking error asymptotically tends to zero. The simulation results show that the backstepping adaptive controller based on the adaptive law of the changed parameters can improve the performance of continuous rotary motor,and the proposed control strategy is feasible.

Adaptive Backstepping Control for Uncertain Systems with Compound Nonlinear Characteristics

An adaptive backstepping multi-sliding mode approximation variable structure control scheme is proposed for a class of uncertain nonlinear systems.An actuator model with compound nonlinear characteristics is established based on the model decomposition method.The unmodeled dynamic term of the radial basis function neural network approximation system is presented.The Nussbaum gain design technique is utilized to overcome the problem that the control gain is unknown.The adaptive law estimation is used to estimate the upper boundary of neural network approximation and uncertain interference.The adaptive approximate variable structure control effectively weakens the control signal chattering while enhancing the robustness of the controller.Based on the Lyapunov stability theory,the stability of the entire control system is proved.The main advantage of the designed controller is that the compound nonlinear characteristics are considered and solved.Finally,simulation results are given to show the validity of the control scheme.

Adaptive Containment Control for Fractional-Order Nonlinear Multi-Agent Systems With Time-Varying Parameters

This paper investigates adaptive containment control for a class of fractional-order multi-agent systems(FOMASs)with time-varying parameters and disturbances.By using the bounded estimation method,the difficulty generated by the timevarying parameters and disturbances is overcome.The command filter is introduced to solve the complexity problem inherent in adaptive backstepping control.Meanwhile,in order to eliminate the effect of filter errors,a novel distributed error compensating scheme is constructed,in which only the local information from the neighbor agents is utilized.Then,a distributed adaptive containment control scheme for FOMASs is developed based on backstepping to guarantee that the outputs of all the followers are steered to the convex hull spanned by the leaders.Based on the extension of Barbalat's lemma to fractional-order integrals,it can be proven that the containment errors and the compensating signals have asymptotic convergence.Finally,three simulation examples are given to show the feasibility and effectiveness of the proposed control method.

Vibration Control of A Flexible Marine Riser System Subject to Input Dead Zone and Extraneous Disturbances

An observer-based adaptive backstepping boundary control is proposed for vibration control of flexible offshore riser systems with unknown nonlinear input dead zone and uncertain environmental disturbances.The control algorithm can update the control law online through real-time data to make the controller adapt to the environment and improve the control precision.Specifically,based on the adaptive backstepping framework,virtual control laws and Lyapunov functions are designed for each subsystem.Three direction interference observers are designed to track the timevarying boundary disturbance.On this basis,the inverse of the dead zone and linear state transformation are used to compensate for the original system and eliminate the adverse effects of the dead zone.In addition,the stability of the closed-loop system is proven by Lyapunov stability theory.All the system states are bounded,and the vibration offset of the riser converges to a small area of the initial position.Finally,four examples of flexible marine risers are simulated in MATLAB to verify the effectiveness of the proposed controller.

The Impulse Excitation Joint Servo Drive Design and Adaptive Backstepping Control of Humanoid Robots

This study aims to explore the humanoid robot joint servo drive integration design and adaptive backstepping control. To make the humanoid robot have explosive power as the human does, simply increasing the power output of the motor of a lightweight design cannot meet the demand of moving heavy objects and so on. Moreover, the backstepping control algorithm is designed to implement the dual-arm cooperative control. The joint servo drive is redesigned in the present study, which can drive the motor at a limitation state when needed output high-voltage pulse can stimulate the motor so that the motor can produce an instantaneous large torque. A miniature design scheme is presented in this study for the servo drive, explaining the design method of each part module. The ex- perimental data illustrate that the servo drive can produce an output torque greater than the rate of the high-voltage pulse that stimulates the motor. Knowledge of the control of humanoid robot moving a heavy object has important practical significance. The present study provides a complete actual problem and exhibits a real practical use case which can be used to speed up the explosive humanoid robot arms.

Adaptive patient-cooperative compliant control of lower limb rehabilitation robot

With the increase in the number of stroke patients,there is a growing demand for rehabilitation training.Robot-assisted training is expected to play a crucial role in meeting this demand.To ensure the safety and comfort of patients during rehabilitation training,it is important to have a patient-cooperative compliant control system for rehabilitation robots.In order to enhance the motion compliance of patients during rehabilitation training,a hierarchical adaptive patient-cooperative compliant control strategy that includes patient-passive exercise and patient-cooperative exercise is proposed.A low-level adaptive backstepping position controller is selected to ensure accurate tracking of the desired trajectory.At the high-level,an adaptive admittance controller is employed to plan the desired trajectory based on the interaction force between the patient and the robot.The results of the patient-robot cooperation experiment on a rehabilitation robot show a significant improvement in tracking trajectory,with a decrease of 76.45%in the dimensionless squared jerk(DSJ)and a decrease of 15.38%in the normalized root mean square deviation(NRMSD)when using the adaptive admittance controller.The proposed adaptive patient-cooperative control strategy effectively enhances the compliance of robot movements,thereby ensuring the safety and comfort of patients during rehabilitation training.

Adaptive backstepping control of tracked robot running trajectory based on real-time slip parameter estimation

To ensure the stable driving of tracked robots in a complex farmland environment,an adaptive backstepping control method for tracked robots was proposed based on real-time slip parameter estimation.According to the kinematics analysis method,the kinematic model of the tracked robot was established,and then,its pose error differential equation was further obtained.On this basis,the trajectory tracking controller of the tracked robot was designed based on the backstepping control theory.Subsequently,according to the trajectory tracking error of the tracked robot,the back propagation neural network(BPNN)was used to adaptively adjust the control parameters in the backstepping controller,and the inputs of the BPNN are the trajectory tracking error xe,ye,θe.After that,the soft-switching sliding mode observer(SSMO)was designed to identify the slip parameters during the running of the tracked robot.And then the parameters were compensated into the adaptive backstepping controller to reduce the trajectory tracking error.The simulation results show that the proposed adaptive backstepping control method with SSMO can improve the accuracy of the trajectory tracking control of the tracked robot.Additionally,the designed SSMO can accurately estimate the slip parameters.

Capture and detumbling control for active debris removal by a dual-arm space robot

Active debris removal(ADR) technology is an effective approach to remediate the proliferation of space debris, which seriously threatens the operational safety of orbital spacecraft. This study aims to design a controller for a dual-arm space robot to capture tumbling debris, including capture control and detumbling control. Typical space debris is considered as a non-cooperative target, which has no specific capture points and unknown dynamic parameters. Compliant clamping control and the adaptive backstepping-based prescribed trajectory tracking control(PTTC)method are proposed in this paper. First, the differential geometry theory is utilized to establish the constraint equations, the dynamic model of the chaser-target system is obtained by applying the Hamilton variational principle, and the compliance clamping controller is further designed to capture the non-cooperative target without contact force feedback. Next, in the post-capture phase,an adaptive backstepping-based PTTC is proposed to detumble the combined spacecraft in the presence of model uncertainties. Finally, numerical simulations are carried out to validate the feasibility of the proposed capture and detumbling control method. Simulation results indicate that the target detumbling achieved by the PTTC method can reduce propellant consumption by up to24.11%.

Robust Adaptive Actuator Failure Compensation for a Class of Uncertain Nonlinear Systems

This paper presents a robust adaptive state feedback control scheme for a class of parametric-strict-feedback nonlinear systems in the presence of time varying actuator failures. The designed adaptive controller compensates a general class of actuator failures without any need for explicit fault detection. The parameters, times, and patterns of the considered failures are completely unknown. The proposed controller is constructed based on a backstepping design method. The global boundedness of all the closed-loop signals is guaranteed and the tracking error is proved to converge to a small neighborhood of the origin. The proposed approach is employed for a two-axis positioning stage system as well as an aircraft wing system. The simulation results show the correctness and effectiveness of the proposed robust adaptive actuator failure compensation approach.