Robust Control Term Research Articles

Robust Fuzzy Adaptive Fault‐Tolerant Control for a Class of Second‐Order Nonlinear Systems

ABSTRACTIn this brief, an optimal active fuzzy fault‐tolerant control (OAFFTC) scheme is proposed for a class of unknown perturbed multi‐input multi‐output (MIMO) nonlinear systems with nonaffine nonlinear actuator faults and time‐varying sensor faults. The control strategy can handle automatically (online updating) with three additives (bias, drift, and loss of accuracy) along with one multiplicative (loss of effectiveness) sensor faults and nonlinear state‐dependent actuator faults. In order to deal with uncertain system dynamics, sensor and actuator faults, and external disturbances, fuzzy systems (FSs) and backstepping techniques were combined to provide the adaptive control term as well as a robust control term. Butterworth filter is used to get rid the algebraic loop problem. The suggested robust term, can deal with approximation errors of the fuzzy systems (FSs). To automatically optimize the adaptive parameters and the starting conditions, particle swarm optimization (PSO) approach is introduced. The Lyapunov approach is employed to demonstrate the closed‐loop system's stability. To assess the efficacy and correctness of the suggested scheme, quadrotor dynamic model is performed on the simulation part.

Adaptive Robust Tracking Control of Robotic Manipulator based on SMC and Fuzzy Control Strategy

In recent years, robotic systems have been widely used in different applications, and this has motivated researchers to develop different control methods. A model-free, intelligent, robust control method for a nonlinear robotic manipulator system is proposed in this work. This paper presents a novel solution for the major drawbacks of the sliding mode control scheme, which are chattering. Prior knowledge is needed about the dynamic model of the controlled system and the upper bound of uncertainty. In this paper, a fuzzy-like PD controller with SMC (FLPDSM) is proposed. The fuzzy-like PD controller was designed according to fuzzy rules and membership functions based on the nominal model of the robot manipulator. A robust control term was added to the control signal to compensate for the system uncertainty, and external disturbances are compensated by adding an auxiliary robust term to the SMC control law. Two methods for designing robust control terms are proposed. The first proposed method assumes that the upper bound of system uncertainty is known although it cannot be exactly determined due to external disturbances and uncertainty. Hence, a second method was proposed that assumes this bound to be unknown, and an adaptive gain based on Lyapunov theory was used to derive the adaptation law. The Lyapunov second method was used to ensure the stability of the closed loop system. Performance tests on the proposed methods were implemented through simulation studies for the two-link robotic manipulator, and the test results were compared with the standard SMC to verify the effectiveness of the proposed method. A good trajectory tracking with a high robustness against parameter variations and external disturbances was observed under the presented control scheme.

Nonlinear Filtering and Reinforcement Learning Based Consensus Achievement of Uncertain Multi-Agent Systems

Abstract This paper introduces a novel approach for designing estimators to achieve consensus in uncertain multi-agent systems (MAS), even when various fault conditions are present and communication is assumed to be undirected and connected. The method includes an adaptive fault detection technique to detect faults and a unique adaptation in the unscented Kalman filter (UKF) to adjust noise covariance matrices and reconstruct uncertain states in the multi-agent system is proposed in the framework of Q-learning. Additionally, it involves training neural network internal parameters using previous measurements. A Chebyshev neural network (CNN) is employed to model the uncertain plant, and a hyperbolic tangent-based robust control term is used to mitigate neural network approximation errors. This novel approach is known as reinforced UKF (RUKF). The paper also discusses the asymptotic stability of the proposed method and presents numerical simulations to demonstrate its effectiveness with reduced computational load.

Neural network compensator-based robust iterative learning control scheme for mobile robots nonlinear systems with disturbances and uncertain parameters

Aiming at the problem of trajectory tracking control for mobile robot nonlinear systems with non-repetitive uncertain parameters, we propose a novel neural network compensator-based robust iterative learning control (NNRILC) scheme to achieve excellent tracking performance and uncertainty compensation. The NNRILC scheme consists of a parallel structure that includes a robust iterative learning control (RILC) term and a neural network (NN) compensator. The RILC term is used to ensure robust control performance and promise closed-loop stability. The compensator based on the neural network is employed to handle the uncertainties resulted from the nonlinear dynamics as well as the suppressed disturbances in the mobile robot nonlinear systems. Additionally, the fourth-order Runge-Kutta algorithm is employed to solve the state differential equation of the mobile robot. Consequently, The H∞ robust technique is used to construct an iterative learning control update rule to reduce the impact of disturbances. Meanwhile, the RILC scheme is designed to optimize the neural network initial parameters and weights of the NN compensator at each trial. Then the convergence of the proposed NNRILC scheme is analyzed, and the results are incorporated into the control update for the next process trial. Finally, the effectiveness of the proposed method is verified by mobile robot simulation.

Adaptive iterative learning control for a class of parameterized fractional-order systems subjected to backlash-like hysteresis

In this article, a fractional-order adaptive iterative learning control scheme is proposed for a class of parameterized fractional-order systems with unknown control gain and backlash-like hysteresis nonlinearity under disturbance. Based on the sufficient condition for the stability of linear fractional-order systems, a sliding mode surface of tracking errors is constructed to facilitate the controller design and stability analysis. A new boundary layer function is designed by using Mittag-Leffler function to relax the restriction of the identical initial condition of iterative learning control design. The fractional-order differential-type adaptive laws and difference-type learning law are designed to estimate unknown constant parameters and time-varying parameter, respectively. To deal with the influence of backlash-like hysteresis nonlinearity reminder term and unknown bounded external disturbance, a robust control term is designed by employing the hyperbolic tangent function with a convergent series sequence which can guarantee the learning convergence along iteration axis. By constructing Lyapunov-like composite energy function, the stability analysis is presented to prove the convergence of the system output to a small neighborhood of the desired trajectory and the boundedness of all the closed-loop signals. Finally, a simulation example of second-order nonlinear fractional-order system is presented, which demonstrates the effectiveness of the proposed fractional-order adaptive iterative learning control scheme.

Adaptive Neural Network Control for Fixed-Wing UAV With Disturbance Observer Under Switching Disturbance.

The adaptive neural network (NN) control for the fixed-wing unmanned aerial vehicle (FUAV) under the unmodeled dynamics and the time-varying switching disturbance (TVSD) is investigated in this article. To better describe the TVSD induced by the change in the flight area of the FUAV, a switching augmented model (SAM) based on the known information about the TVSD is proposed first. The parameter adaptation technique is used to estimate the related TVSD. Thereafter, the time-varying disturbance that cannot be described by the SAM is estimated by the disturbance observer (DO). The radial basis function NN (RBFNN) is adopted to approximate the unknown unmodeled dynamics. The coupling terms derived from the co-design of DO and the parameter adaptation (PA) are separated by some inequality techniques. Then, the separated unknown terms are eliminated by designing the parameters of the controller and that of the adaptive law. The separated known terms are tackled by adding robust control terms to the controller. In addition, to improve the estimation performance for the TVSD and RBFNN, the auxiliary system in the DO form is designed. Sufficient stable conditions about the closed-loop switched system (CLSS) are obtained with and without the inequality about the switching times. Finally, an illustrative example is given to show the feasibility and advantage of the proposed control strategy by the attitude model of the FUAV.

Adaptive control of a class of uncertain nonlinear systems using brain emotional learning and Legendre polynomials

In this paper, an adaptive controller for a class of uncertain nonlinear systems is presented using a combination of Legendre polynomials and brain emotional learning-based intelligent controller (BELBIC). Recently, some versions of BELBIC have been presented with the aim of satisfying the universal approximation property using Gaussian basis function. However, the size of regressor vector is too large that imposes a heavy computational load to the processor. The novelty of this paper is presenting a new version of BELBIC with less computational burden using Legendre polynomials. Moreover, there are very few tuning parameters in Legendre polynomials. Another contribution of this paper is editing the stability analysis presented in recent related works. Due to the intrinsic non-differentiability of the adaptation rules of BELBIC, the second time derivative of Lyapunov function is undefined and thus, the Barbalat’s lemma cannot be applied to verify the asymptotic convergence of the error function. Therefore, bounded-input-bounded-output (BIBO) stability can only be claimed for this controller. Simulation results on different case studies show that Legendre polynomials can improve the universal approximation property of BELBIC with less tuning parameters. Moreover, in the absence of the robust control term in the control law, the performance Legendre polynomials will not deteriorate, while the performance degrade in Gaussian basis function is quite considerable.

Optimal adaptive fuzzy fault-tolerant control applied on a quadrotor attitude stabilization based on particle swarm optimization

This article discusses the problem of stabilizing the attitude control of a quadrotor system, which is subject to uncertainty, external disturbances, and sensor and actuator faults. To address these challenges, the control stage employs universal approximators, such as fuzzy systems, which estimate the system’s uncertainties and eliminate nonaffine nonlinear actuator faults. In addition, the particle swarm optimization technique is used to adjust the adaptive parameters and fuzzy initial values. The robust control term is carefully designed to handle approximation errors, time-varying sensors, and external disturbances. To solve the issue of the unavoidable algebraic loop during the actuator approximation phase, a Butterworth low-pass filter is integrated. This approach automatically deals with external disturbances, and no further approximation is necessary. Furthermore, the controller can be reconfigured online to enable fast-fault compensation without requiring a fault detection or isolation unit. To prove the global stability and boundedness of all signals in the closed-loop system, Lyapunov theory is used.

Reinforced unscented Kalman filter for consensus achievement of uncertain multi‐agent systems subject to actuator faults

AbstractIn this paper, actuator fault detection and reconstruction in consensus tracking of uncertain multi‐agent systems (MAS) is addressed. The communication is assumed to be connected undirected. An adaptive fault detection method is developed to detect actuator faults. A novel‐reinforced unscented Kalman filter (RUKF) is employed to reconstruct the faults by adjusting the noise covariance matrices of unscented Kalman filter (UKF) as well as to train neural network internal parameters by providing a set of previous measurements. A Chebyshev neural network (CNN) is incorporated to learn the uncertain plant. To prevent the neural network approximation errors a hyperbolic tangent function‐based robust control term is applied. The Lyapunov stability approach guarantees the stability of the proposed RUKF, which runs in conjunction with robust control method. Lastly, numerical simulations are presented to show the effectiveness of the proposed RUKF under actuator abrupt, intermittent, and transient fault conditions.

Iterative neural network adaptive robust control of a maglev planar motor with uncertainty compensation ability

In this paper, an iterative neural network adaptive robust control (INNARC) strategy is proposed for the maglev planar motor (MLPM) to achieve good tracking performance and uncertainty compensation. The INNARC scheme consists of adaptive robust control (ARC) term and iterative neural network (INN) compensator in a parallel structure. The ARC term founded on the system model realizes the parametric adaptation and promises the closed-loop stability. The INN compensator based on the radial basis function (RBF) neural network is employed to handle the uncertainties resulted from the unmodeled non-linear dynamics in the MLPM. Additionally, the iterative learning update laws are introduced to tune the network parameters and weights of the INN compensator simultaneously, so the approximation accuracy is improved along the system repetition. The stability of the INNARC method is proved via the Lyapunov theory, and the experiments are conducted on an home-made MLPM. The results consistently demonstrate that the INNARC strategy possesses the satisfactory tracking performance and uncertainty compensation, and the proposed INNARC is an effective and systematic intelligent control method for MLPM.

Composite anti-disturbance control for ship dynamic positioning systems with thruster faults

Anti-disturbance control problem is studied for ship dynamic positioning systems with model uncertainties and ocean disturbances under thruster faults. For the ocean disturbance, a stochastic disturbance observer (SDO) is established to give the online estimation. For thruster faults, an adaptive law is used to evaluate, which is obtain from Lyapunov function. For model uncertainties, a robust control term with adaptive technology is used to attenuate it. Then, a composite anti-disturbance control (CADC) strategy is raised by combining disturbance observer-based control (DOBC), adaptive technology, and robust control term, which makes the position and yaw angle of ship reach the desired values. Finally, the simulation example proves the validity of the controller.

Ship Dynamic Positioning Output Feedback Control with Position Constraint Considering Thruster System Dynamics

In order to simultaneously address the issues of ship operating area limitation, unknown time-varying disturbances, immeasurable ship speed, unknown dynamics, and input saturation, this paper investigates the position-constrained ship dynamic positioning output feedback control, taking thruster system dynamics into account. Firstly, a barrier Lyapunov function (BLF) is utilized to limit the ship position inside the dynamic positioning system’s acceptable working range and to limit the ship position error. Second, the set total disturbance, which is made up of unknown time-varying disturbances and unknown dynamics and is further handled by the control strategy, is estimated using a fixed-time extended state observer (FDESO). Additionally, the thruster system dynamics equations are incorporated into the controller design process so that the generated thrust signal varies gradually without abrupt fluctuations, in keeping with engineering realities. Furthermore, the thruster input saturation issue is dealt with using a finite-time auxiliary dynamic system. Finally, a robust control term is introduced to handle the errors generated in the controller design. The stability proof section demonstrates that the designed control strategy can cause the ship to arrive and maintain at the desired location and heading, as well as stay continuously inside the designated operating area with all signals of the closed-loop control system being consistently and eventually bounded. The simulation results demonstrate that the proposed system is valid.

Disturbance observer based adaptive fuzzy synchronization controller design for uncertain fractional-order chaotic systems

This study premeditated the synchronization of two fractional-order chaotic systems (FOCSs) with uncertainties and external disturbances. We utilized fuzzy logic systems (FLSs) to estimate unknown nonlinearities, and implemented disturbance observers to estimate unknown bounded external disturbances. Then, a robust control term was devised to compensate for the unavoidable approximation error of the fuzzy system. In addition, a sliding mode surface was devised to construct an adaptive fuzzy sliding mode controller (AFSMC) that can guarantee that the synchronization error converges to a small neighborhood of zero. Finally, the validity of the proposed control strategy was verified via a numerical simulation.

Adaptive Fuzzy Backstepping Asymptotic Disturbance Rejection of Multiagent Systems With Unknown Model Dynamics

This article presentsan adaptive fuzzy asymptotic disturbance rejection scheme for multiagent mechanical systems with unknown model dynamics and unknown frequency disturbances. The mechanical motion equations are expressed as the parameterized equations and the disturbances are described by unknown parametric exogenous system. The unknown parametric exogenous system is transformed into the canonical model with unknown disturbances as the inputs. The disturbance filter provides estimations of the state vector in the canonical model such that disturbances are represented as parameterized forms with exponentially decaying errors. The disturbance rejection can be converted into the adaptive control. Based on the adaptive vectorial fuzzy backstepping, the disturbance rejection formation controller is designed with the fuzzy logic systems approximating the model unknown dynamics. The adaptive robust control term attenuates fuzzy approximation errors. In contrast to the existing results, the adaptive fuzzy disturbance rejection formation control realizes the estimation and rejection for unknown frequency disturbances without requiring the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge of model dynamics. Based on the Barbalat’s lemma, it is shown that the adaptive disturbance rejection controller achieves the asymptotic formation tracking. Application on the surface vessel formation confirms the availability.

Nonlinear Integral Sliding Mode Control with Adaptive Extreme Learning Machine and Robust Control Term for Anti-External Disturbance Robotic Manipulator

Nonlinear Integral Sliding Mode Control with Adaptive Extreme Learning Machine and Robust Control Term for Anti-External Disturbance Robotic Manipulator

Robust tracking control for quadrotor with unknown nonlinear dynamics using adaptive neural network based fractional-order backstepping control

This work aims to design a neural network-based fractional-order backstepping controller (NNFOBC) to control a multiple-input multiple-output (MIMO) quadrotor unmanned aerial vehicle (QUAV) system under uncertainties and disturbances and unknown dynamics. First, we investigated the dynamic of QUAV composed of six inter-connected nonlinear subsystems. Then, to increase the convergence speed and control precision of the classical backstepping controller (BC), we design a fractional-order BC (FOBC) that provides further degrees of freedom in the control parameters for every subsystem. Besides, designing control is a challenge as the FOBC requires knowledge of accurate mathematical model and the physical parameters of QUAV system. To address this problem, we propose an adaptive approximator that is a radial basis function neural network (RBFNN) included in FOBC to fix the unknown dynamics problem which results in the new approach NNFOBC. Furthermore, a robust control term is introduced to increase the tracking performance of a reference signal as parametric uncertainties and disturbances occur. We have used Lyapunov's theorem to derive adaptive laws of control parameters. Finally, the outcoming results confirm that the performance of the proposed NNFOBC controller outperforms both the classical BC , FOBC and a neural network-based classical BC controller (NNBC) and under parametric uncertainties and disturbances.

Robust adaptive trajectory tracking for wheeled mobile robots based on Gaussian process regression

In this paper, we propose a novel learning-based robust adaptive trajectory tracking controller for wheeled mobile robots (WMR) subject to velocity input uncertainties. Gaussian process regression (GPR) is employed in view of its powerful estimation ability and wide scope of applications as a nonparametric regression method. The velocity uncertainties are estimated online using the real-time measured data. The prediction mean and variance of the GPR are used to counteract the effect of the uncertainties and to design the robust control term, respectively. A continuous robust controller is proposed which has the advantage of achieving asymptotic convergence of the trajectory tracking error instead of uniformly ultimately boundedness. Comparisons with the neural network based adaptive controller and a state of the art GPR-based design demonstrate the effectiveness of the proposed control strategy.

Feedback error learning neural network for stable control of nonlinear nonaffine systems

This study presents a stable feedback error learning (FEL) scheme for nonlinear nonaffine systems in the presence of uncertainty and disturbances. The distinguishing feature of the FEL method, which can have a significant effect on both transient and steady-state performance, has led us to adopt this approach. The nonlinear system studied here is nonaffine. In other words, the function that describes the dynamic equations of the system is an implicit function of the control input rather than a particular class of systems. We aim to develop a stable FEL control system with three components: a neural network (NN), a linear controller, and a robustifying control term. To this end, all the adaptation laws for the NN weights are derived from a Lyapunov function, ensuring that the closed-loop system is uniformly asymptotically stable (UAS). Thus, an NN learning control approach that effectively improves the transient performance, as well as the steady-state performance, is proposed, and its remarkable effectiveness is illustrated in comparison with the existing methods.

Robust adaptive backstepping control of uncertain fractional-order nonlinear systems with input time delay

In the present work, a fractional adaptive backstepping control approach is proposed for controlling a class of uncertain fractional-order nonlinear systems subjected to unknown external disturbance and input delay. In control design, by introducing fractional command-filter, the key issue of the common backstepping method called the “explosion of complexity” is addressed. Furthermore, the Szász–Mirakyan operator is used as a simple but efficient universal approximator to approximate uncertain or unknown terms and reduce the design complexity. In addition, to enhance the capability of the proposed controller in dealing with the approximation error and the unknown disturbance, an efficient robust control term is also incorporated into it. One advantage of the suggested control approach is that the input-delay fractional-order system is effectively treated by introducing a new variable as a non-delayed fractional-order system. The other advantage is that the number of tuning variables is considerably low; specifically, for an n-order fractional nonlinear system, only n adaptive parameters are adjusted online. This makes the implementation of the proposed approach simpler. The Lyapunov stability theorem is used to prove that all of the closed-loop system’s signals are semi-globally uniformly ultimately bounded. The feasibility of the suggested control approach is shown by comparing the simulation results obtained with the fuzzy system.

A novel model-based robust control design for collaborative robot joint module

In order to reduce the impact of load and system parameter changes on the dynamic performance of collaborative robot joint module, a novel robust control algorithm is proposed in this paper to solve the problem of dynamic control of collaborative robot joint module trajectory tracking. The controller is composed of two parts: one is a nominal control term designed based on the dynamical model, aiming to stabilize the nominal robot system; the other is a robust control term based on the Lyapunov method, aiming to eliminate the influence of uncertainty on tracking performance, where the uncertainties include nonlinear friction, parameter uncertainty, and external disturbances. The Lyapunov minimax method is adopted to prove that the system is uniformly bounded and uniformly ultimately bounded. We performed numerical simulation and experimental validation based on an actual collaborative robot joint module experimental platform and the rapid controller prototype cSPACE. The numerical simulation and experimental results show that the controller has excellent control performance for the collaborative robot joint module and provides more accurate trajectory tracking under the influence of uncertainties.