Robust Adaptive Tracking Control Research Articles

Robust adaptive backstepping tracking control of stochastic nonlinear systems with unknown input saturation: A command filter approach

SummaryThis paper studies the problem of adaptive observer‐based radial basis function neural network tracking control for a class of strict‐feedback stochastic nonlinear systems comprising an unknown input saturation, uncertainties, and unknown disturbances. To handle the issue of a non‐smooth saturation input signal, a smooth function is chosen to approximate the saturation function and the state observer is used to estimate unmeasured states. By the so‐called command filter method in the controller design procedure, the implementation complexity is reduced in the proposed backstepping method. Moreover, a radial basis function neural network is deployed to reconstruct the unknown nonlinear functions. In addition, the gains of all radial basis function neural networks are updated through one updating law leading to a minimal learning parameter which is independent of the number of neural nodes and the order of the system. Comparing with the existing results, the proposed approach can stabilize a constrained stochastic system more effectively and with less computational burden. Finally, a practical example shows the performance of the proposed controller design.

Robust adaptive dynamic surface back-stepping tracking control of high-order strict-feedback nonlinear systems via disturbance observer approach

In this study, we propose an adaptive tracking dynamic surface back-stepping control based on Nussbaum disturbance observer for uncertain high-order strict-feedback MIMO nonlinear systems with external disturbances, unknown parameters and modelling uncertainties. It is assumed that the control action is affected by input saturation; so to compensate the resulted undesirable effects, the tanh(.) function is used as an approximation to the saturation function. To tackle the unknown external disturbances and uncertainties, a Nussbaum disturbance observer is proposed. Moreover, an appropriate adaptive law is presented to deal with the unknown parameters. Then, the dynamic surface control method is used to overcome the inherent problem ‘explosion of complexity’ that appeared in the conventional back-stepping method. The Lyapunov stability analysis proves that the closed-loop system is semi-globally uniformly bounded. At last, reasonable effectiveness and applicability of the adaptive tracking dynamic surface control are illustrated by simulation results.

Robust Adaptive Finite-Time Tracking Control for Uncertain Euler-Lagrange Systems With Input Saturation

In this paper, a robust adaptive finite-time (FT) tracking control scheme is proposed for Euler-Lagrange systems (ELSs) subject to nonparametric uncertainties, unknown disturbances and input saturation. In the design procedure, a Gaussian error function is utilized to approximate the input saturation nonlinearity. Following that, by employing the natural property that the upper bound of model parameters uncertainties is linear-in-parameters, the lumped uncertain term caused by uncertain model parameters and external disturbances is formulated by a linear-parametric form with a single parameter. And then, a novel robust adaptive tracking control law is designed to resolve the tracking control problem of uncertain ELSs. The proposed control scheme is featured by FT convergence rate, and robustness against uncertainties and unknown disturbances. Furthermore, the robust adaptive FT tracking control scheme is insensitive to the character of the uncertainties, and is with low computational burden and easy to implement in engineering applications. And its rigorous stability is analyzed with the aid of the Lyapunov stability theory, and its effectiveness is verified by simulation results and comparison.

Neural network–based direct adaptive robust control of unknown MIMO nonlinear systems using state observer

SummaryThis paper focuses on the problem of adaptive robust tracking control for a class of uncertain multiple‐input and multiple‐output (MIMO) nonlinear system. Unlike most previous research studies, model dynamics, disturbances, and state variables are unknown in this paper. A novel observer‐based direct adaptive neuro‐sliding mode control approach is proposed of which the only required knowledge is the system output. By incorporating the Adaptive Linear Neuron (ADALINE) neural network (NN) into the conventional sliding mode observer, the proposed observer has favorable performance. In the controller, a radial basis function (RBF) NN is constructed to approximate the unknown equivalent control laws and the estimation of the sliding surface is applied as the input. A gain‐adaptation sliding mode term is designed to enhance the robustness of the control system. Besides, the free parameters of the ADALINE NN and the RBFNN are updated online by adaptive laws to obtain optimal approximation performance. Finally, the comparative simulations are given to show the effectiveness and merits of proposed scheme.

State-Estimator-Integrated Robust Adaptive Tracking Control for Flexible Air-Breathing Hypersonic Vehicle With Noisy Measurements

In this paper, a novel state-estimator-integrated robust adaptive tracking control law is proposed for flexible air-breathing hypersonic vehicle (FAHV), with consideration of noisy measurements, parametric uncertainties, and unknown flexible dynamics. First, to reconstruct the states contaminated by the measurement noises, a continuous-model-based state estimator is designed, which can avoid severe phase lag problem brought by low-pass filter and greatly improve the estimation accuracy in the transition process. Then, based on noise-free measurements, an ideal state feedback robust adaptive tracking controller is formulated to deal with the parametric uncertainties as well as unknown flexible dynamics, where interval type-2 fuzzy logic systems are employed to approximate the unknown dynamics of FAHV online. Lyapunov theorem is utilized to analyze the stability properties of the state estimator and the ideal state feedback tracking controller. By synthesizing the above two parts, the whole state-estimator-integrated robust adaptive tracking control law is finally developed. Comparative numerical simulations of four scenarios demonstrate the effectiveness and superiority of the proposed integrated control law.

Robust Adaptive Tracking Control for Quadrotors by Combining PI and Self-Tuning Regulator

This brief is concerned with the robust adaptive tracking control problem of quadrotors. Considering the practicality of control laws to be designed, the self-tuning regulator (STR) for discrete-time systems is employed as our inner loop adaptive tracking mechanism and the classical proportional–integral (PI) control is designed for the outer loop to guarantee the robustness of the whole system. The main contributions of our work include: 1) we design the control laws for the actuator inputs (pulsewidth modulation signals) directly, which removes the need to measure the motor speeds and 2) the proposed PI-STR method can reduce the large overshoot of a single STR and retain the adaptability of the STR and the robustness of the PI control simultaneously. Furthermore, the outer loop PI controller and inner loop STR can easily be implemented in the digital form. The stability analysis is also provided. Simulations indicate that the PI-STR-based control structure can cope with the situations where vehicles are disturbed or have time-varying parameters. Our preliminary experiments show its practicality.

Robust adaptive trajectory tracking control of underactuated autonomous underwater vehicles with prescribed performance

SummaryIn this paper, a novel robust adaptive trajectory tracking control scheme with prescribed performance is developed for underactuated autonomous underwater vehicles (AUVs) subject to unknown dynamic parameters and disturbances. A simple error mapping function is proposed in order to guarantee that the trajectory tracking error satisfies the prescribed performance. A novel additional control based on Nussbaum function is proposed to handle the underactuation of AUVs. The compounded uncertain item caused by the unknown dynamic parameters and disturbances is transformed into a linear parametric form with only single unknown parameter called virtual parameter. On the basis of the above, a novel robust adaptive trajectory tracking control law is developed using dynamic surface control technique, where the adaptive law online provides the estimation of the virtual parameter. Strict stability analysis indicates that the designed control law ensures uniform ultimate boundedness of the AUV trajectory tracking closed‐loop control system with prescribed tracking performance. Simulation results on an AUV in two different disturbance cases with dynamic parameter perturbation verify the effectiveness of our adaptive trajectory tracking control scheme.

Adaptive disturbance cancellation for a class of MIMO nonlinear Euler–Lagrange systems under input saturation

In this paper, we develop an adaptive disturbance cancellation tracking control strategy with the asymptotically converging output tracking errors for a class of multi-input and multi-output (MIMO) nonlinear Euler–Lagrange systems with unknown time-varying disturbances under input saturation. The unknown time-varying disturbances are firstly described as the outputs of a multivariate linear unknown exosystem with unavailable regressor and regression parameter. To estimate the unavailable regressor, an observer is constructed, such that the disturbance cancellation is converted to an adaptive control problem. An auxiliary dynamic system (ADS) is employed to mitigate the effect of the input saturation. Then, a robust adaptive tracking control law is proposed incorporating the above and a robustifying term into the adaptive vectorial backstepping design tool. It is proven theoretically that the asymptotic convergence of the output tracking errors of Euler–Lagrange systems is achieved, while the uniform ultimate boundedness of the remaining signals of the resulting closed-loop control system is guaranteed. Simulation and comparison results on a two-link rigid manipulator and a scale model ship are presented to illustrate the effectiveness and the superiority of the proposed control scheme.

Robust adaptive visual tracking control for uncertain robotic systems with unknown dead-zone inputs

This paper is concerned with the image-based visual servoing (IBVS) control for uncalibrated camera-robot system with unknown dead-zone constraint, where the uncertain kinematics and dynamics are also considered. The control implementation is achieved by constructing a smooth inverse model for dead-zone-input to eliminate the nonlinear effect resulting from the actuator constraint. A novel adaptive algorithm, which does not require a priori knowledge of the parameter intervals of dead-zone model, is proposed to update the parameter values online, and the dead-zone slopes are not required the same. Furthermore, to accommodate the uncertainties of uncalibrated camera-robot system, adaptation laws are developed to estimate the uncertain parameters, simultaneously avoiding singularity of the image Jacobian matrix. With the full consideration of unknown dead-zone constraint and system uncertainties, an adaptive robust visual tracking control scheme together with dead-zone compensation is subsequently established such that the image tracking error converges to the origin. Based on a 3-DOF manipulator, simulations are conducted to verify the tracking performance of the proposed controller.

Robust adaptive consensus of nonstrict-feedback multi-agent systems with quantized input and unmodeled dynamics

This paper deals with the distributed robust adaptive neural network tracking control for a class of nonstrict-feedback multi-agent systems (MASs) with unmodeled dynamics and input quantized by the hysteresis quantizer. A decomposition technique is utilized to handle the problem that only finite and discrete control values are available to control system. Meanwhile, the radial basis function neural networks (RBFNNs) are employed for approximation of the packaged unknown nonlinearities induced by recursive design. By introducing the structural characteristic of Gaussian basis function (see Lemma 5), the effects from the nonstrict-feedback are effectively compensated and the backstepping-based method can be successfully implemented. Then, by combining the dynamic signal with adaptive backstepping control technique, a robust adaptive distributed quantized tracking control scheme is developed for each follower. It is proved that all closed-loop signals are semi-globally uniformly ultimately bounded and the asymptotic consensus tracking is guaranteed. Finally, the effectiveness of the control method is illustrated by two simulation examples.

Smart Rotor With Trailing Edge Flap Considering Bend–Twist Coupling and Aerodynamic Damping: Modeling and Control

Aerodynamic damping and bend–twist coupling significantly affect the dynamic response of wind turbines. In this paper, unsteady aerodynamics, aerodynamic damping, and bend–twist coupling (twist-towards-feather) are combined to establish a smart rotor model with trailing edge flaps (TEFs) based on a National Renewable Energy Laboratory (NREL) 5 MW reference horizontal-axis wind turbine. The overall idea is to quantitatively evaluate the influence of aerodynamic damping and bend–twist coupling on the smart rotor and to present the control effect of the TEFs under normal wind turbine operating conditions. An aerodynamic model considering the dynamic stall and aerodynamic damping as well as a structural bend–twist coupling model with the influence of gravity and centrifugal force are incorporated into the coupling analysis. The model verification shows that the present model is relatively stable under highly unsteady wind conditions. Then, a robust adaptive tracking (RAT) controller is designed to suppress fluctuations in both the flapwise tip deflection and output power. The simulations show an average reduction of up to 63.86% in the flapwise tip deflection power spectral density (PSD) of blade 1 at the 1P frequency, with an average reduction in the standard deviation of the output power of up to 34.33%.

Robust adaptive tracking control for servo mechanisms with continuous friction compensation

In this paper, a robust adaptive tracking control scheme is developed for servo mechanisms with nonlinear friction dynamics. A continuously differentiable friction model is used to capture the friction behaviors (e.g. Stribeck effect, Coulombic friction and Viscous friction). The robust integral of the sign of the error (RISE) feedback term is employed to design an innovative adaptive controller to compensate nonlinear friction and bounded disturbances. To reduce the effect of noise pollution, the desired trajectory is employed to replace the output signal in controller design. The developed adaptive controller can guarantee the asymptotic tracking performance for nonlinear servo mechanisms in the presence of nonlinear friction and bounded disturbances. Comparative experimental results are used to validate the effectiveness of the developed control algorithm.

Indirect Adaptive Robust Trajectory Tracking Control of Hard Rock TBM with Load Variation of Tunneling Face

Posture adjustment of open-type hard rock tunnel boring machine (TBM) can be achieved by properly adjusting the hydraulic pressure of gripper cylinder and torque cylinders. However, the time-varying inhomogeneous load acting on tunneling face of TBM and complex stratum working condition can cause the trajectory deviation. In this paper, the position and posture rectification kinematics and dynamics models of TBM have been established in order to track the trajectory. Moreover, there are uncertain parameters and uncertain loads from complex working conditions in the dynamic model. An indirect adaptive robust control strategy is applied to achieve precise position and posture trajectory tracking control. Simulation results show when the position deviation only occurs in Y-axis and the current orientation is parallel with the designed axis, the deviation can be corrected by controlling the pressure of gripper cylinder and the actual trajectory meets the designed axis when TBM is pushed forward 0.14 m in X-axis. If the deviation only occurs in Z-axis, then the deviation can be corrected by controlling torque cylinders. If the position deviation occurs both in Y-axis and Z-axis at the same time, the pressure of gripper cylinder and torque cylinders should be controlled at the same time to rectify the deviation. Simulation results are shown to illustrate the effectiveness and robustness of the proposed controller. This research proposes an indirect adaptive robust controller that can track the planned tracking trajectory smoothly and rapidly.

Prescribed performance fixed-time tracking control for a class of second-order nonlinear systems with disturbances and actuator saturation

This paper investigates the prescribed performance fixed-time tracking control problem for a class of second-order nonlinear systems with bounded disturbance and actuator saturation limit. In order to facilitate the controller development, we introduce the performance function and output error transformation technique to transform the tracking error dynamics with inequality performance constraints to an equivalent unconstrained error one. Different from the existing work on the guaranteeing prescribed performance control, we incorporate the fixed-time sliding mode surface into the control design procedure to cope with the disturbances and actuator saturation limit. Specifically, a robust adaptive fixed-time tracking controller, which requires no upper bound of the disturbance, is designed to solve the prescribed performance fixed-time tracking control problem. The rigorous mathematical stability proof is given. Finally, numerical simulations for the attitude tracking control are presented to demonstrate the effectiveness and robustness of the proposed controller.

A Robust Online Adaptive B-Spline MPPT Control of Three-Phase Grid-Coupled Photovoltaic Systems Under Real Partial Shading Condition

This work contributes to the research on three-phase photovoltaic systems via a new more robust online adaptive neuro-fuzzy maximum power point tracking (MPPT) control technique considering real partial shading and load conditions. The trapping in local minima and high computational cost in the existing neuro-fuzzy structure are addressed by incorporating B-spline function in the proposed control method. The system parameters are adjusted online via an adaptive neuro-fuzzy inference system rules acquired from the MPPT error. The optimization part of the proposed control law is performed through an online learning gradient-descent back-propagation algorithm. The superiority of the proposed control in terms of energy conversion efficiency, MPPT error, and output power is checked under the same operating conditions with well-known used traditional and intelligent MPPT control algorithms. Finally, the robustness of the proposed control is confirmed through a complete day simulation and comparison indexes.

Fuzzy unknown observer-based robust adaptive path following control of underactuated surface vehicles subject to multiple unknowns

In this paper, suffering from multiple unknowns including unmodeled dynamics, uncertainties, and disturbances, a fuzzy unknown observer-based robust adaptive path following control (FUO-RAPFC) scheme for an underactuated surface vehicle (USV) is proposed. Main contributions are as follows: (1) A surge-guided line-of-sight (SGLOS) guidance law is created to guide surge speed and heading angle, simultaneously, and thereby adapting to path following errors to enhance robustness and flexibility; (2) By virtue of combining auxiliary observation dynamics with adaptive approximation error compensation, the FUO is innovatively devised to accurately lumped unknowns rather than bounded observations; (3) FUO-based robust adaptive tracking control laws are eventually synthesized and ensure that the guided signals can be globally asymptotically tracked. Simulation studies are conducted to demonstrate remarkable performance of the FUO-RAPFC scheme.

Adaptive sliding mode enhanced disturbance observer-based control of surgical device

This paper presents an enhanced adaptive robust disturbance observer-based motion tracking control methodology. This control approach is established and investigated for a semi-automated hand-held ear surgical device for the treatment of Otitis Media with Effusion. The proposed control methodology is utilised for tracking a desired motion trajectory in the presence of unknown or uncertain system parameters, nonlinearities including hysteresis, and disturbances in the motion system. The stability of the control approach is analysed. The convergence of position and velocity tracking errors is proven theoretically. A precise tracking performance following desired motion trajectory is demonstrated in the experimental study.

Robust adaptive tracking control for a class of mechanical systems with unknown disturbances under actuator saturation

SummaryA robust adaptive tracking control scheme is presented for a class of multiple‐input and multiple‐output mechanical systems with unknown disturbances under actuator saturation. The unknown disturbances are expressed as the outputs of a linear exogenous system with unknown coefficient matrices. An adaptive disturbance observer is constructed for the online disturbance estimation. An actuator saturation compensator is introduced to attenuate the adverse effects of actuator saturation. The adaptive backstepping method is then applied to design the robust adaptive tracking control law. It is proved that the designed control law makes the system outputs track the desired trajectories and guarantees the global uniform ultimate stability of the closed‐loop control system. Simulations on a two‐link robotic manipulator verify the effectiveness of the proposed control scheme.

Adaptive neural dynamic surface control of MIMO pure-feedback nonlinear systems with output constraints

In this work, the problem of adaptive neural dynamic surface control (DSC) with the minimum adjustable parameters is discussed for a class of multi-input multi-output (MIMO) pure-feedback nonlinear systems with unmodeled dynamics and output constraints. An auxiliary signal designed by the characteristics of unmodeled dynamics is used to handle the dynamical uncertainties. The unknown continuous black-box functions produced in the controller design process are approximated by using radial basis function neural networks (RBFNNs). Based on an one-to-one nonlinear mapping(NM), the MIMO nonaffine nonlinear system with output constraints is transformed into a novel block-structure MIMO nonaffine nonlinear system without output constraints. Based on the transformed system and modified DSC, robust adaptive neural tracking control scheme is developed. Through theoretical analysis, all the signals in the closed-loop system are shown to be semi-globally uniformly ultimately bounded (SGUUB). A numerical example is provided to demonstrate the effectiveness of the proposed design strategy.

Robust Adaptive Fuzzy Control for HFV With Parameter Uncertainty and Unmodeled Dynamics

This paper proposes a robust adaptive fuzzy tracking controller for a hypersonic flight vehicle (HFV) subject to both parametric uncertainties and unmodeled dynamics. First, the nonlinear model of HFV is input/ouput linearization and the internal dynamics of HFV are established. Second, the ideal internal dynamics (IID) are calculated and then an IID-based controller designing method is utilized. With considering parameter uncertainties and unmodeled dynamics, a full state tracking error system is built. Fuzzy logical system (FLS) is utilized to identify the nonlinear system with parameter uncertainty and unmodeled dynamics. An adaptive fuzzy controller is proposed to guarantee the stability of the whole system with parameter uncertainty and unmodeled dynamics. Comparison simulations show remarkable efficiency of the proposed method.