Adaptive Trajectory Tracking Control for Nonholonomic Wheeled Mobile Robots:A Barrier Function Sliding Mode Approach

The trajectory tracking control performance of nonholonomic wheeled mobile robots(NWMRs)is subject to nonholonomic constraints,system uncertainties,and external disturbances.This paper proposes a barrier function-based adaptive sliding mode control(BFASMC)method to provide high-precision,fast-response performance and robustness for NWMRs.Compared with the conventional adaptive sliding mode control,the proposed control strategy can guarantee that the sliding mode variables converge to a predefined neighborhood of origin with a predefined reaching time independent of the prior knowledge of the uncertainties and disturbances bounds.Another advantage of the proposed algorithm is that the control gains can be adaptively adjusted to follow the disturbances amplitudes thanks to the barrier function.The benefit is that the overestimation of control gain can be eliminated,resulting in chattering reduction.Moreover,a modified barrier function-like control gain is employed to prevent the input saturation problem due to the physical limit of the actuator.The stability analysis and comparative experiments demonstrate that the proposed BFASMC can ensure the prespecified convergence performance of the NWMR system output variables and strong robustness against uncertainties/disturbances.

Modified grey wolf optimised adaptive super-twisting sliding mode control of rotary inverted pendulum system

This paper proposes a modified grey wolf optimiser-based adaptive super-twisting sliding mode control algorithm for the trajectory tracking and balancing of the rotary inverted pendulum system.The super-twisting sliding mode algorithm severely alleviates the chattering present in the classical sliding mode control.It provides robustness against model uncertainties and external disturbances with the knowledge of the upper bounds of the uncertainties and disturbances.The gains of the super-twisting sliding mode algorithm are selected through adaptive law.Parameters of the adaption law are tuned using a modified grey wolf optimisation algorithm,a meta-heuristic optimisation technique.Lyapunov stability analysis is carried out to analyse the overall control system stability.The performance of the proposed control algorithm is compared with two other sliding mode control strategies present in the literature,therein showing better performance of the proposed control scheme.

An Energy Efficient Control Strategy for Electric Vehicle Driven by In-Wheel-Motors Based on Discrete Adaptive Sliding Mode Control

This paper presents an energy-efficient control strategy for electric vehicles(EVs)driven by in-wheel-motors(IWMs)based on discrete adaptive sliding mode control(DASMC).The nonlinear vehicle model,tire model and IWM model are established at first to represent the operation mechanism of the whole system.Based on the modeling,two virtual control variables are used to represent the longitudinal and yaw control efforts to coordinate the vehicle motion control.Then DASMC method is applied to calculate the required total driving torque and yaw moment,which can improve the tracking performance as well as the system robustness.According to the vehicle nonlinear model,the additional yaw moment can be expressed as a function of longitudinal and lateral tire forces.For further control scheme development,a tire force estimator using an unscented Kalman filter is designed to estimate real-time tire forces.On these bases,energy efficient torque allocation method is developed to distribute the total driving torque and differential torque to each IWM,considering the motor energy consumption,the tire slip energy consumption,and the brake energy~?recovery.Simulation results of the proposed control strategy using the co-platform of Matlab/Simulink and CarSim way.

Revised barrier function-based adaptive finite-and fixed-time convergence super-twisting control

This paper presents an adaptive gain,finite-and fixedtime convergence super-twisting-like algorithm based on a revised barrier function,which is robust to perturbations with unknown bounds.It is shown that this algorithm can ensure a finite-and fixed-time convergence of the sliding variable to the equilibrium,no matter what the initial conditions of the system states are,and maintain it there in a predefined vicinity of the origin without violation.Also,the proposed method avoids the problem of overestimation of the control gain that exists in the current fixed-time adaptive control.Moreover,it shows that the revised barrier function can effectively reduce the computation load by obviating the need of increasing the magnitude of sampling step compared with the conventional barrier function.This feature will be beneficial when the algorithm is implemented in practice.After that,the estimation of the fixed convergence time of the proposed method is derived and the impractical requirement of the preceding fixed-time adaptive control that the adaptive gains must be large enough to engender the sliding mode at time t=0 is discarded.Finally,the outperformance of the proposed method over the existing counterpart method is demonstrated with a numerical simulation.

Non-Negative Adaptive Mechanism-Based Sliding Mode Control for Parallel Manipulators with Uncertainties

In this paper,a non-negative adaptive mechanism based on an adaptive nonsingular fast terminal sliding mode control strategy is proposed to have finite time and high-speed trajectory tracking for parallel manipulators with the existence of unknown bounded complex uncertainties and external disturbances.The proposed approach is a hybrid scheme of the online non-negative adaptive mechanism,tracking differentiator,and nonsingular fast terminal sliding mode control(NFTSMC).Based on the online non-negative adaptive mechanism,the proposed control can remove the assumption that the uncertainties and disturbances must be bounded for the NFTSMC controllers.The proposed controller has several advantages such as simple structure,easy implementation,rapid response,chattering-free,high precision,robustness,singularity avoidance,and finite-time convergence.Since all control parameters are online updated via tracking differentiator and non-negative adaptive law,the tracking control performance at high-speed motions can be better in real-time requirement and disturbance rejection ability.Finally,simulation results validate the effectiveness of the proposed method.

High-speed train cooperativecontrol based on fractional-ordersliding mode adaptive algorithm

Purpose–This study aims to propose an adaptive fractional-order sliding mode controller to solve the problem of train speed tracking control and position interval control under disturbance environment in moving block system,so as to improve the tracking efficiency and collision avoidance performance.Design/methodology/approach–The mathematical model of information interaction between trains is established based on algebraic graph theory,so that the train can obtain the state information of adjacent trains,and then realize the distributed cooperative control of each train.In the controller design,the sliding mode control and fractional calculus are combined to avoid the discontinuous switching phenomenon,so as to suppress the chattering of sliding mode control,and a parameter adaptive law is constructed to approximate the time-varying operating resistance coefficient.Findings–The simulation results show that compared with proportional integral derivative(PID)control and ordinary sliding mode control,the control accuracy of the proposed algorithm in terms of speed is,respectively,improved by 25%and 75%.The error frequency and fluctuation range of the proposed algorithm are reduced in the position error control,the error value tends to 0,and the operation trend tends to be consistent.Therefore,the control method can improve the control accuracy of the system and prove that it has strong immunity.Originality/value–The algorithm can reduce the influence of external interference in the actual operating environment,realize efficient and stable tracking of trains,and ensure the safety of train control.

ROBUST ADAPTIVE SLIDING MODE CONTROL FOR NONLINEAR UNCERTAIN NEUTRAL DELAY SYSTEM

Robust stabilization for a class of nonlinear uncertain neutral system with time-varying delay is investigated. By applying the Lyapunov stability theorem, an adaptive sliding mode controller （ADSMC） is developed.Based on the sliding mode control technique, the controller can drive the system into a pre-specified sliding hyperplane to obtain the desired dynamic performance. Once the system dynamics reaches the sliding plane, the control system is insensitive to uncertainty. The adaptive technique can overcome the unknown upper bound of uncertainty so that the reaching condition can be satisfied. Furthermore, the controller does not include any delayed state,so such an ADSMC is memoryless. Finally, a numerical example is given to verify the validity of the developed memoryless ADSMC and the globally asymptotic stability is guaranteed for the control scheme.

Adaptive Terminal Sliding Mode Control for Rigid Robotic Manipulators

In order to apply the terminal sliding mode control to robot manipulators,prior knowledge of the exact upper bound of parameter uncertainties,and external disturbances is necessary.However,this bound will not be easily determined because of the complexity and unpredictability of the structure of uncertainties in the dynamics of the robot.To resolve this problem in robot control,we propose a new robust adaptive terminal sliding mode control for tracking problems in robotic manipulators.By applying this adaptive controller,prior knowledge is not required because the controller is able to estimate the upper bound of uncertainties and disturbances.Also,the proposed controller can eliminate the chattering effect without losing the robustness property.The stability of the control algorithm can be easily verified by using Lyapunov theory.The proposed controller is tested in simulation on a two-degree-of-freedom robot to prove its effectiveness.

Adaptive Backstepping Slide Mode Control of Pneumatic Position Servo System

With the price decreasing of the pneumatic proportional valve and the high performance micro controller, the simple structure and high tracking performance pneumatic servo system demonstrates more application potential in many fields. However, most existing control methods with high tracking performance need to know the model information and to use pressure sensor. This limits the application of the pneumatic servo system. An adaptive backstepping slide mode control method is proposed for pneumatic position servo system. The proposed method designs adaptive slide mode controller using backstepping design technique. The controller parameter adaptive law is derived from Lyapunov analysis to guarantee the stability of the system. A theorem is testified to show that the state of closed-loop system is uniformly bounded, and the closed-loop system is stable. The advantages of the proposed method include that system dynamic model parameters are not required for the controller design, uncertain parameters bounds are not need, and the bulk and expensive pressure sensor is not needed as well. Experimental performance, as compared with some existing methods. results show that the designed controller can achieve better tracking

Modeling and Robust Backstepping Sliding Mode Control with Adaptive RBFNN for a Novel Coaxial Eight-rotor UAV

This paper focuses on the robust attitude control of a novel coaxial eight-rotor unmanned aerial vehicles (UAV) which has higher drive capability as well as greater robustness against disturbances than quad-rotor UAV. The dynamical and kinematical model for the coaxial eight-rotor UAV is developed, which has never been proposed before. A robust backstepping sliding mode controller (BSMC) with adaptive radial basis function neural network (RBFNN) is proposed to control the attitude of the eightrotor UAV in the presence of model uncertainties and external disturbances. The combinative method of backstepping control and sliding mode control has improved robustness and simplified design procedure benefiting from the advantages of both controllers. The adaptive RBFNN as the uncertainty observer can effectively estimate the lumped uncertainties without the knowledge of their bounds for the eight-rotor UAV. Additionally, the adaptive learning algorithm, which can learn the parameters of RBFNN online and compensate the approximation error, is derived using Lyapunov stability theorem. And then the uniformly ultimate stability of the eight-rotor system is proved. Finally, simulation results demonstrate the validity of the proposed robust control method adopted in the novel coaxial eight-rotor UAV in the case of model uncertainties and external disturbances. © 2014 Chinese Association of Automation.

Robust Adaptive Gain Higher Order Sliding Mode Observer Based Control-constrained Nonlinear Model Predictive Control for Spacecraft Formation Flying

This work deals with the development of a decentralized optimal control algorithm, along with a robust observer,for the relative motion control of spacecraft in leader-follower based formation. An adaptive gain higher order sliding mode observer has been proposed to estimate the velocity as well as unmeasured disturbances from the noisy position measurements.A differentiator structure containing the Lipschitz constant and Lebesgue measurable control input, is utilized for obtaining the estimates. Adaptive tuning algorithms are derived based on Lyapunov stability theory, for updating the observer gains,which will give enough flexibility in the choice of initial estimates.Moreover, it may help to cope with unexpected state jerks. The trajectory tracking problem is formulated as a finite horizon optimal control problem, which is solved online. The control constraints are incorporated by using a nonquadratic performance functional. An adaptive update law has been derived for tuning the step size in the optimization algorithm, which may help to improve the convergence speed. Moreover, it is an attractive alternative to the heuristic choice of step size for diverse operating conditions. The disturbance as well as state estimates from the higher order sliding mode observer are utilized by the plant output prediction model, which will improve the overall performance of the controller. The nonlinear dynamics defined in leader fixed Euler-Hill frame has been considered for the present work and the reference trajectories are generated using Hill-Clohessy-Wiltshire equations of unperturbed motion. The simulation results based on rigorous perturbation analysis are presented to confirm the robustness of the proposed approach.

Adaptive fuzzy sliding mode control for robotic airship with model uncertainty and external disturbance

An adaptive fuzzy sliding mode control （AFSMC） ap- proach is proposed for a robotic airship. First, the mathematical model of an airship is derived in the form of a nonlinear control system. Second, an AFSMC approach is proposed to design the attitude control system of airship, and the global stability of the closed-loop system is proved by using the Lyapunov stability theorem. Finally, simulation results verify the effectiveness and robustness of the proposed control approach in the presence of model uncertainties and external disturbances.

Adaptive Proportional-Derivative Sliding Mode Control Law With Improved Transient Performance for Underactuated Overhead Crane Systems

In this paper, an adaptive proportional-derivative sliding mode control(APD-SMC) law, is proposed for 2D underactuated overhead crane systems. The proposed controller has the advantages of simple structure, easy to implement of PD control, strong robustness of SMC with respect to external disturbances and uncertain system parameters, and adaptation for unknown system dynamics associated with the feedforward parts. In the proposed APD-SMC law, the PD control part is used to stabilize the controlled system, the SMC part is used to compensate the external disturbances and system uncertainties,and the adaptive control part is utilized to estimate the unknown system parameters. The coupling behavior between the trolley movement and the payload swing is enhanced and, therefore, the transient performance of the proposed controller is improved.The Lyapunov techniques and the La Salle's invariance theorem are employed in to support the theoretical derivations. Experimental results are provided to validate the superior performance of the proposed control law.

Adaptive Backstepping Terminal Sliding Mode Control Method Based on Recurrent Neural Networks for Autonomous Underwater Vehicle

The trajectory tracking control problem is addressed for autonomous underwater vehicle(AUV) in marine environ?ment, with presence of the influence of the uncertain factors including ocean current disturbance, dynamic modeling uncertainty, and thrust model errors. To improve the trajectory tracking accuracy of AUV, an adaptive backstepping terminal sliding mode control based on recurrent neural networks(RNN) is proposed. Firstly, considering the inaccu?rate of thrust model of thruster, a Taylor’s polynomial is used to obtain the thrust model errors. And then, the dynamic modeling uncertainty and thrust model errors are combined into the system model uncertainty(SMU) of AUV; through the RNN, the SMU and ocean current disturbance are classified, approximated online. Finally, the weights of RNN and other control parameters are adjusted online based on the backstepping terminal sliding mode controller. In addition, a chattering?reduction method is proposed based on sigmoid function. In chattering?reduction method, the sigmoid function is used to realize the continuity of the sliding mode switching function, and the sliding mode switching gain is adjusted online based on the exponential form of the sliding mode function. Based on the Lyapu?nov theory and Barbalat’s lemma, it is theoretically proved that the AUV trajectory tracking error can quickly converge to zero in the finite time. This research proposes a trajectory tracking control method of AUV, which can e ectively achieve high?precision trajectory tracking control of AUV under the influence of the uncertain factors. The feasibility and e ectiveness of the proposed method is demonstrated with trajectory tracking simulations and pool?experi?ments of AUV.

Finite-time adaptive sliding mode control for heavyweight airdrop operations

This paper investigates the problem of designing a fast convergent sliding mode flight controller of a transport aircraft for heavyweight airdrop operations in the presence of bounded uncertainties without the prior knowledge of the bounds. On the basis of feedback linearization of the aircraft-cargo motion system, a novel integral sliding mode flight control law with gains adaptation is proposed. It contains a nominal control law used to achieve finite-time stabilization performance and a compensated control law used to reject the uncertainties. The switching gains of the compensated control law are tuned using adaptation algorithms, and the knowledge of the bounds of the uncertainties is not required to be known in advance. Meanwhile, the severe chattering of the sliding mode control that caused by high switching gains is effectively reduced. The controller and its performance are evaluated on a transport aircraft performing a maximum load airdrop task in a number of simulation scenarios.

Decentralized model reference adaptive sliding mode control based on fuzzy model

A new design scheme of decentralized model reference adaptive sliding mode controller for a class of MIMO nonlinear systems with the high-order interconnections is propcsed. The design is based on the universal approximation capability of the Takagi - Seguno （T-S） fuzzy systems. Motivated by the principle of certainty equivalenteontrol, a decentralized adaptive controller is designed to achieve the tracking objective without computafion of the T-S fuzz ymodel. The approach does not require the upper bound of the uncertainty term to be known through some adaptive estimation. By theoretical analysis, the closed-loop fuzzy control system is proven to be globally stable in the sense that all signalsinvolved are bounded, with tracking errors converging to zero. Simulation results demonstrate the effectiveness of the approach.

Neural network based adaptive sliding mode control of uncertain nonlinear systems

The purpose of this paper is the design of neural network-based adaptive sliding mode controller for uncertain unknown nonlinear systems. A special architecture adaptive neural network, with hyperbolic tangent activation functions, is used to emulate the equivalent and switching control terms of the classic sliding mode control （SMC）. Lyapunov stability theory is used to guarantee a uniform ultimate boundedness property for the tracking error, as well as of all other signals in the closed loop. In addition to keeping the stability and robustness properties of the SMC, the neural network-based adaptive sliding mode controller exhibits perfect rejection of faults arising during the system operating. Simulation studies are used to illustrate and clarify the theoretical results.

Adaptive terminal sliding mode control for high-order nonlinear dynamic systems

An adaptive terminal sliding mode control (SMC) technique is proposed to deal with the tracking problem for a class of high-order nonlinear dynamic systems. It is shown that a function augmented sliding hyperplane can be used to develop a new terminal sliding mode for high-order nonlinear systems. A terminal SMC controller based on Lyapunov theory is designed to force the state variables of the closed-loop system to reach and remain on the terminal sliding mode, so that the output tracking error then converges to zero in finite time which can be set arbitrarily. An adaptive mechanism is introduced to estimate the unknown parameters of the upper bounds of system uncertainties. The estimates are then used as controller parameters so that the effects of uncertain dynamics can be eliminated. It is also shown that the stability of the closed-loop system can be guaranteed with the proposed control strategy. The simulation of a numerical example is provided to show the effectiveness of the new method.

Adaptive sliding mode backstepping control for near space vehicles considering engine faults

A fault tolerant control methodology based adaptive sliding mode(ASM) backstepping is proposed for near space vehicle(NSV) attitude control system under engine faults. The proposed scheme combined adaptive backstepping with the sliding mode control strategy could guarantee the system’s stability and track desired signals under external disturbances and engine faults. Firstly, attitude mode description and the engine faulty model are given. Secondly, a nominal control law is designed.Thirdly, a sliding mode observer is given later in order to estimate both the information of engine faults and external disturbances. An adaptive sliding mode technology based on the previous nominal control law is developed via updating faulty parameters. Finally,analyze the system’s fault-tolerant performance and reliability through experiment simulation, which verifies the proposed design of fault-tolerant control can tolerate engine faults, as well as the strong robustness for external disturbance.

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.