Backstepping Control Technique Research Articles

Backstepping based intelligent control of tractor-trailer mobile manipulators with wheel slip consideration

In this research, a new hybrid backstepping control strategy based on a neural network is proposed for tractor-trailer mobile manipulators in the presence of unknown wheel slippage and disturbances. To minimise the negative impacts of wheel slippage, the desired velocities of the tractor’s wheels are computed with a proposed kinematic control model with an adaptive term. As the system’s dynamical model contains unavoidable uncertainties, model-based backstepping control technique is unable to effectively manage these systems. Hence, the proposed controller blends a radial basis function neural network with the merits of a dynamical model-based backstepping approach. The neural networks are employed to approximate the non-linear unknown smooth function. To minimise the impact of external disturbances, and network reconstruction error an adaptive term is added to the control law. The Lyapunov theorem and Barbalat’s lemma are employed to guarantee the stability of the control method. The tracking error is shown to be bounded and to rapidly converge to zero with the proposed method. To demonstrate the efficacy and validity of the control mechanism, comparison simulation results are presented.

Adaptive fault-tolerant control for uncalibrated camera–robot system with multiple uncertainties

In this paper, an adaptive fault-tolerant control scheme is proposed for uncalibrated visual servoing of robot manipulator with multiple uncertainties and possible actuator failures. First, to accommodate the partial-loss-of-effectiveness failures, a parametrization form of fault estimation is derived by applying the adaptive backstepping control technique. Furthermore, an on-line gradient descending minimization method developed based on the Slotine–Li algorithm is designed to handle the uncertainties of uncalibrated camera parameters. By utilizing the Lyapunov analysis method, it can be proved that all signals in the closed-loop system are bounded and the image tracking error converges to zero asymptotically. Simulation based on a 3-DOF manipulator validates the obtained results.

Adaptive neural quantized control for full-state constrained Markov jumping nonlinear systems with incomplete transition probabilities and unknown control directions

This article devises an adaptive quantized control scheme for full-state constrained Markov jumping nonlinear systems with incomplete transition probabilities and unknown control directions. First, the barrier Lyapunov functions were utilized to achieve full-state constraints on the investigated system, while the Nussbaum function has been adopted to overcome the issue of unknown control directions. Then, by means of command filtered backstepping control technique, an adaptive quantized controller is developed, where an improved error compensation mechanism was established to eliminate the effect of filter error, and a hysteresis quantizer was employed to diminish the transmission rate. Furthermore, it is demonstrated that the designed controller assures that all signals of the closed-loop system are bounded in the mean square sense. Finally, two illustrative examples were provided to validate the effectiveness of the proposed control method.

Distributed Robust Learning-Based Backstepping Control Aided With Neurodynamics for Consensus Formation Tracking of Underwater Vessels.

This article addresses distributed robust learning-based control for consensus formation tracking of multiple underwater vessels, in which the system parameters of the marine vessels are assumed to be entirely unknown and subject to the modeling mismatch, oceanic disturbances, and noises. Toward this end, graph theory is used to allow us to synthesize the distributed controller with a stability guarantee. Due to the fact that the parameter uncertainties only arise in the vessels' dynamic model, the backstepping control technique is then employed. Subsequently, to overcome the difficulties in handling time-varying and unknown systems, an online learning procedure is developed in the proposed distributed formation control protocol. Moreover, modeling errors, environmental disturbances, and measurement noises are considered and tackled by introducing a neurodynamics model in the controller design to obtain a robust solution. Then, the stability analysis of the overall closed-loop system under the proposed scheme is provided to ensure the robust adaptive performance at the theoretical level. Finally, extensive simulation experiments are conducted to further verify the efficacy of the presented distributed control protocol.

Adaptive neural network backstepping control method for aerial manipulator based on coupling disturbance compensation

The aerial manipulator, designed for complex aerial tasks, encounters multifaceted operational environments influenced by various internal and external disturbances. This paper introduces an adaptive neural network backstepping control technique fortified with coupling disturbance compensation to enhance the resilience of the aerial manipulator against these disturbances. Firstly, we propose a cutting-edge coupling disturbance feedforward compensator based on variable inertia parameters, which offers precise and prompt compensation for significant internal coupling disturbances without needing external sensors or alternative disturbance estimation techniques. Subsequently, radial basis function neural networks with an online adaptive weight updating mechanism are designed to estimate and counteract lumped disturbances stemming from unmodeled dynamics, uncertainties, and external factors in real-time. Utilizing the Lyapunov stability criteria, we validate that the aerial manipulator can reliably track desired trajectories under our proposed controller. Experimental results and simulations further underscore the effectiveness and superiority of our control approach.

Discrete-time integral terminal sliding mode load following controller coupled with disturbance observer for a modular high-temperature gas-cooled reactor

With the appearance of digital computers and microprocessor technologies, the control systems used in nuclear reactors continue to transform from analog devices to digital ones in recent years. A heavy challenge is that applying the pre-existing intelligent load following control algorithms developed in the continuous-time domain to the current digital devices of the nuclear reactors may yield the so-called digital chattering effects, and even trigger system instability. To this end, this paper presents a discrete-time integral terminal sliding mode controller (DTITSMC) coupled with a discrete-time disturbance observer (DTDO) for the load following of a modular high-temperature gas-cooled reactor (MHTGR). The common continuous-time MHTGR model is first transformed into a discrete-time form with consideration of model uncertainties, exogenous disturbances, and discretization errors. Then, on the basis of this discrete-time MHTGR model, a DTDO that can estimate the lumped disturbances, composed of model uncertainties, exogenous disturbances, discretization errors, and unmeasured system states, is developed, subsequently being combined with the designed DTITSMC scheme in order to enhance the system robustness. The proposed DTITSMC scheme coupled with the DTDO is novel in that it can be directly implemented on the digital control system of the MHTGR, while at the same time providing an improved load following control performance, owing to the integration of the state-of-the-art sliding mode control techniques, backstepping control techniques, and the disturbance feedforward compensation supported by the disturbance observer techniques. Both the estimation error convergence of the DTDO and the overall system stability are theoretically proved by the Lyapunov stability theory in this paper. Finally, the feasibility and superiority of the proposed DTITSMC scheme coupled with the DTDO over the previous discrete-time linear sliding mode controller (DTLSMC) and discrete-time proportional–integral–derivative controller (DTPIDC) are further confirmed by simulation studies, where in the absence of lumped disturbances, the value of the accumulative absolute load error (AALE) produced by the proposed DTSMPPC scheme coupled with the DTDO is merely 0.0575% and 0.2675% to that of the previous DTLSMC and the optimized DTPIDC, respectively, while in the presence of lumped disturbances, the value of the AALE produced by the proposed DTSMPPC scheme coupled with the DTDO is merely 0.006% and 0.1952% to that of the previous DTLSMC and the optimized DTPIDC, respectively.

Application of Backstepping Control With Nonsingular Terminal Sliding Mode Surface Technique to Improve the Robustness of Stator Power Control of Asynchronous Generator-Based Multi-Rotor Wind Turbine System

The conventional backstepping control (CBC) technique for the asynchronous generator (AG) incorporated in a multi-rotor wind turbine (MRWT) system faces several challenges, including torque and stator power ripples, lack of robustness, and low-quality stator currents. Furthermore, the CBC performs poorly under distorted grid voltage conditions. To address these issues, this study proposes applying backstepping nonsingular terminal sliding mode control (BNTSMC). The controller design involves incorporating a NTSMC into the control law of the CBC technique, where Lyapunov theory was used to analyze the stability of the suggested approach. The synthesis of the suggested controller revolves around two sliding mode surfaces, specifically the stator powers of the AG, which are used to determine the final control laws. The advantages of this technique are excellent robustness against internal and external disturbances based on NTSMC, and the controller exhibits asymptotic stability based on the backstepping technique. Simulation tests in MATLAB software on a 1.5 MW AG-based MRWT system clearly demonstrate the advantages of BNTSMC over CBC.

Current source converter-based optimal power extraction and power control of a doubly fed induction generator (DFIG) using backstepping control

An improved backstepping control technique for the operation of a doubly fed induction generator (DFIG) powered by a wind turbine (WT) was developed and discussed. It is derived from a current source converter (CSC). The optimal backstepping control (BSC) settings are determined using the CSC approach, which can improve the drive by providing a more rapid dynamic response, greater precision, and stable performance. The CSC approach control function was constructed using the index criterion integral time square error (ITSE) and integral time absolute error (ITAE). With the simulation technique in the MATLAB/Simulink environment, the proposed BSC-CSC effectiveness is confirmed, and analyse the performance by using the PI and SMC control. The results indicate the goals of this work have been achieved in the form of resilience, improved dynamic system efficiency, lowering the harmonic distortion, optimization of stator power, and successfully addressing the problem of model parameter uncertainty.

Reduced Order Synchronization of Two Non-Identical Special Class of Strict Feedback Systems Via Back-Stepping Control Technique

Abstract This work offers a systematic technique to achieve reduced order synchronization (ROS) between two different order general classes of chaotic systems in a master-slave configuration. In this study, the dynamics of the master and slave systems are assumed to follow a special class of strict-feedback form, namely, the generalized triangular feedback form. The main objective is to design a suitable scalar controller using a Lyapunov theory-based back-stepping approach such that the mth order slave system gets synchronized with the nth order master system. Due to the difference in the order of the systems (m<n and m=(n−1)), it is only possible to achieve the synchronization between m numbers of states of the slave systems with (n−1) numbers of states of the master system, respectively. We cannot conclude on the stability of the nth state of the master system as there is no counterpart (state) available in the slave system to be synchronized with. Adding an additional (m+1)th state dynamics along with a nonlinear feedback controller (U1) to the slave system ensures that the nth state of the master system is synchronized with the (m+1)th state dynamics of the slave system. With the suggested technique proposed in this article, complete state-to-state synchronization can be achieved with only two controllers. The analytical results are successfully validated through numerical simulations presented in the end.

Disturbance Observer-Based Event-Triggered Adaptive Command Filtered Backstepping Control for Fractional-Order Nonlinear Systems and Its Application

This paper considers the disturbance observer-based event-triggered adaptive fuzzy tracking control issue for a class of fractional-order nonlinear systems (FONSs) with quantized signals and unknown disturbances. To improve the disturbance rejection ability, a fractional-order nonlinear disturbance observer (FONDO) is designed to estimate the unknown composite disturbances. Furthermore, by combining an improved fractional-order command-filtered backstepping control technique and an event-triggered control mechanism, an event-triggered adaptive fuzzy quantized control scheme is established, which guarantees the desired tracking performance can be achieved even in the presence of network constraint. Finally, the validity and superiority of the theoretic results are verified by a fractional-order horizontal platform system.

Control of constrained mobile manipulators with unknown wheel slippage, using neural network based backstepping control technique

Control of constrained mobile manipulators with unknown wheel slippage, using neural network based backstepping control technique

Adaptive neural dynamic surface composite control for path following of underactuated vessels with fixed-time convergence

The article discusses the path following control issue for underactuated marine surface vessels (MSVs) subject to nonlinear uncertainties. Firstly, the tracking goal of MSVs will be changed from the earth-fixed position to the line-of-sight (LOS) angle with the aid of LOS approach. To deal with the nonlinear uncertainties existing in MSVs, radial basis function neural networks (RBFNNs) are utilized. In particular, the fixed-time serial–parallel estimation models are used to boost the approximation of RBFNNs and determine whether RBFNNs really estimate the unknown nonlinearities by using the forecast and the track biases to change the weight of RBFNNs. Then, a fixed-time filter is produced to handle the ‘explosion of complex’ issue and improve the structure of the developed controller. In addition, the function tanh with smooth derivative function is utilized to overcome the singularity issue of the virtual controller derivations caused by fixed-time control. Finally, an adaptive neural fixed-time dynamic surface composite control method is developed for the path following control problem based on the adaptive backstepping control technique. The stability analysis results show the yaw angle ψ converges to the LOS angle ψs when t≥TS where Ts given later is not determined by the system initial variables. The system internal variables also reach a bounded compact set, which indicates the RBFNNs indeed estimate the uncertainties existing in MSVs by using fixed-time serial–parallel estimation models. And comparation simulation results also certificate the utilizability of the developed controller.

Predefined-Time Adaptive Neural Tracking Control of Switched Nonlinear Systems.

This article investigates the neural-network-based adaptive predefined-time tracking control problem for switched nonlinear systems. Neural networks are employed to approximate the unknown part of nonlinear functions. The finite-time differentiators are introduced to estimate the first derivative of the virtual controllers. Then, a novel adaptive predefined-time controller is proposed by utilizing the backstepping control technique and the common Lyapunov function (CLF) method. It is explained by the theoretical analysis that the developed controller guarantees that all signals of the switched closed-loop systems are bounded under arbitrary switchings and the tracking error converges to zero within the predefined time. A simulation is shown to verify the validity of the developed predefined-time control approach.

Neural network-based output tracking control of high-order nonlinear systems with DoS attacks and perturbations

This paper focuses on the output feedback tracking control of a high-order nonlinear system with denial-of-service (DoS) attacks and exogenous disturbances. A radial basis function neural network (RBFNN)-based state observer is employed to estimate the system states. A new nonlinear filter with adaptive regulation is developed to eliminate the impacts of perturbed factors such as RBFNN approximation errors and disturbances. Constituting with filtering operation and backstepping control technique, a RBFNN-based security controller is constructed to suppress the influences of perturbations and DoS attacks based on the observation signals. The uniformly ultimately bounded output tracking result is established by using the security control signals via Lyapunov criterion in the cases of DoS attacks, nonlinearities, and disturbances. Comparative results are provided to validate the efficiency of the developed RBFNN-based observation and security control strategies of a nonlinear system.

Improved finite-time prescribed performance based adaptive neural control for nonlinear systems with sensor faults

In this article, based on a novel finite-time prescribed performance function, we consider the issue of the adaptive neural fault-tolerant tracking control problem for a type of nonlinear system with sensor faults. The control performance of the system may be affected when sensor faults occur. For the controlled system with sensor faults, an improved finite-time performance function is proposed so that its initial conditions do not need to be set in advance. Compared with existing performance functions, the performance functions in this paper can ensure that the system is always controllable, even if the sensor faults occur suddenly during the steady operation. Moreover, Radial basis function (RBF) neural networks (NNs) are employed to estimate the uncertain smooth nonlinear functions. With the help of the adaptive backstepping control technique, an improved adaptive prescribed performance control technique is developed, which can realize the boundedness of every signal in the closed-loop system, and the tracking error can be limited within the neighborhood near the origin. Simulation results demonstrate the effectiveness of the proposed control scheme.

Fixed time prescribed performance dynamic positioning control design for surface vessels

This paper addresses the problem of fixed time dynamic positioning (DP) control for surface vessels under the influence of external disturbances, while considering input and output constraints. Using the hyperbolic tangent function, a saturation handling method with an auxiliary control system is constructed, which can handle the saturation constraints of both the control input and its rate of change within a same control framework. By incorporating an auxiliary sliding mode variable, a fixed time disturbance observer (FTDO) is developed to estimate external disturbances. This FTDO ensures that the estimation error converges within a fixed time and provides users with the flexibility to determine the desired convergence time. Moreover, a nonlinear function is introduced in the FTDO to reduce the possibility of singular problems in the control system. Combining the developed FTDO, prescribed performance control strategy and backstepping control technique, a novel DP control strategy is proposed, which not only ensures that the positioning error satisfies the output constraint requirements within a fixed time but also guarantees the fixed time stability of the closed-loop system. Finally, to validate the effectiveness of the proposed DP control law, numerical simulation analysis is carried out on a supply vessel.

Adaptive ELM-Based Security Control for a Class of Nonlinear-Interconnected Systems With DoS Attacks

This article is concerned with the output feedback security control of a class of high-order nonlinear-interconnected systems with denial-of-service (DoS) attacks, nonlinear dynamics, and exogenous disturbances. First, extreme learning machine (ELM) and adaptive techniques are adopted to approximate the unknown nonlinearities. Then, novel adaptive ELM-based nonlinear state observers with adaptive compensation functions are developed to estimate the unmeasurable states during DoS attacks under the influence of the disturbances. Further, by combining with the backstepping control and filtering techniques, adaptive ELM-based controllers are proposed to achieve uniformly ultimately bounded results based on the observation and adaption control signals under the influence of DoS attacks, nonlinear dynamics, and exogenous disturbances. Comparative studies are carried out to validate the effectiveness of the developed ELM-based adaptive observation and control strategies for two interconnected power systems.

Adaptive observer-based control of arbitrarily switched fractional-order uncertain nonlinear system subject to input nonlinearities and asymmetric output constraints

This paper addresses an adaptive observer-based control for a switched fractional-order uncertain nonlinear system subject to input nonlinearities and asymmetric output constraints. The switching signal is arbitrary, and the designed controller needs no information regarding this signal. By employing a universal framework, the designed controller can cope with different input nonlinearities in different modes without having any information about their characteristics. It is assumed that only system output is measured, and a designed observer estimates the system states for control implementation. The uncertainties are approximated by intelligent approximators like fuzzy logic systems (FLS) or neural networks (NN). The time-varying asymmetric output constraints have been satisfied using a common barrier Lyapunov function (BLF). Using the common Lyapunov function (CLF) method and the backstepping control technique, the virtual controllers, adaptive law and control input have been designed, and the boundedness of closed-loop signals has been guaranteed. The effectiveness of the designed control scheme has been demonstrated through a numerical and two practical simulation examples.

Cross-Domain Fixed-Time Formation Control for an Air-Sea Heterogeneous Unmanned System with Disturbances

This paper studied the cross-domain fixed-time formation control problem of an air-sea heterogeneous unmanned system (ASHS). Taking advantage of individual characteristics of unmanned aerial vehicles (UAVs), unmanned surface vehicles (USVs), and unmanned underwater vehicles (UUVs), the ASHS was introduced to accomplish the ocean stereoscopic observation mission, which was transformed into the formation control problem. Due to the difference of dimension and the communication constraint between UAV, USV, and UUV, a cross-domain communication protocol was proposed to achieve the state information flow between heterogeneous unmanned vehicles with different dimensions rather than construct the identical low-dimensional output. The high-dimensional unmanned vehicle can receive full state information from low-dimensional neighbors, while the low-dimensional follower can only receive partial state information from high-dimensional neighbors. Moreover, by means of fixed-time control theory and the backstepping control technique, the distributed fixed-time observer and controller were designed to solve the formation control problem for the ASHS with disturbances. Simulation results show that the ASHS can achieve fixed-time formation control with the proposed coordinated control protocols. Meanwhile, the convergence time of the proposed fixed-time formation control protocols is independent of the initial state.

Composite-disturbance-observer-based backstepping control for three-phase inverters with multiple disturbances

This paper deals with the output voltage tracking control problem of three-phase inverters with multiple disturbances (including parametric perturbations of filter, abrupt disturbances caused by load switching, and harmonic disturbances brought by unbalanced loads and nonlinear loads). Some novel composite disturbance observers are designed to estimate the above multiple disturbances. Based on the disturbance estimates and backstepping control technique, an innovative feedforward-feedback composite tracking control scheme is proposed. The new control scheme has a good disturbance rejection ability and ensures good tracking performances. In the meantime, rigorous stability proof is presented. Simulation and experimental results are illustrated to verify the feasibility and effectiveness of the proposed control scheme.