Backstepping Control Scheme Research Articles

Trajectory tracking control of autonomous vehicles based on event‐triggered model predictive control

AbstractThis paper presents a lateral control scheme based on event‐triggered model predictive control for trajectory tracking of autonomous vehicles. Firstly, the augmentation system is constructed based on the known road curvature information, and the model predictive controller is utilized to obtain the optimal control sequence. Then, an event‐triggered mechanism is introduced to improve the real‐time performance of the control system. The strategy targets to reduce the computational complexity and solving frequency of the optimization problem. In addition, a contraction constraint is structured using the backstepping control strategy to ensure the stability of the control system. Finally, experiments are conducted through the CarSim/Simulink joint simulation platform, and compared with the traditional model predictive control, the method proposed in this paper has better tracking accuracy and improves the real‐time performance of the control system.

Disturbance Observer‐Based Neural Adaptive Command Filtered BacksStepping Funnel‐Like Control for the Chaotic PMSM With Asymmetric Prescribed Performance Constraints

ABSTRACTThis paper suggests a neural adaptive command filtered backstepping tracking control strategy for the chaotic permanent magnet synchronous motors with asymmetric prescribed performance constraints. Therefore, enable chaotic permanent magnet synchronous motors (PMSM) to obtain good robustness and better universality in practical industrial environments, and realizes more accurate control effect. The main challenge lies in devising a valid funnel‐like solution within the backstepping frame to handle the asymmetric performance constraints that traditional solutions cannot solve. To achieve this, a novel funnel‐like function is introduced, integrating a performance boundary function independent of initial output error, thereby transforming the system into an unbounded one. Additionally, the “explosion of complexity” with conventional backstepping is mitigated by introducing command filtering and constructing an error compensating system to reduce errors. By combining the theory of Lyapunov function and backstepping technique, the virtual controller and the real controller with adaptive law ensure the stability of the system. The disturbance observer and neural network solve the external disturbance and the uncertain nonlinear problem, respectively. Simulation comparisons confirm the robustness of the proposed control scheme and demonstrate its superiority over existing solutions.

Optimizing power output in hybrid photovoltaic/wind systems: a nonlinear back-stepping approach for enhanced efficiency and stability

Abstract This paper investigates the challenge of controlling hybrid renewable energy systems (HRES), specifically those combining wind energy and photovoltaic sources, under varying environmental conditions such as fluctuating wind speeds and partial shading. The primary objective is to develop a robust backstepping control strategy that enhances the system’s stability and energy efficiency while ensuring seamless grid integration through the use of dual-fed induction generators. The study uses advanced modeling techniques, including maximum power point tracking for wind turbines and particle swarm optimization for photovoltaic systems, to optimize energy capture. A detailed simulation framework was designed to validate the effectiveness of the control strategy under different climatic scenarios. Quantitative results show that the wind turbine achieved over 95% power recovery, the DC link voltage remained stable within 0.5% of the reference, and photovoltaic energy extraction was optimized with 98% accuracy, even under partial shading. These findings indicate that the proposed control strategy significantly enhances the performance, reliability, and adaptability of the HRES. This work offers a promising contribution to the integration of renewable energy sources into the electrical grid, supporting a more sustainable energy future.

Towards Sustainable Transportation: Adaptive Trajectory Tracking Control Strategies of a Four-Wheel-Steering Autonomous Vehicle for Improved Stability and Efficacy

The objective of continuous increase in the evolution of autonomous and intelligent vehicles is to attain a trustworthy, economical, and safe transportation system. Four-wheel steering (4WS) vehicles are favored over traditional front-wheel steering (FWS) vehicles because they have excellent dynamic characteristics. This paper exhibits the trajectory tracking task of a two degree of freedom (2DOF) underactuated 4WS Autonomous Vehicle (AV). Because the system is underactuated, MIMO, and has a nontriangular form, the traditional adaptive backstepping control scheme cannot be utilized to control it. For the purpose of rectifying this issue, two-state feedback-based methods grounded on the hierarchical steps of the block backstepping controller are proposed and compared in this paper. In the first strategy, a modified block backstepping is applied for the entire dynamic system. Global stability of the overall system is manifested by Lyapunov theory and Barbalat’s Lemma. In the second strategy, a block backstepping controller has been applied after a reduction of the high-order model into various first-order subsystems, consisting of Lyapunov-based design and stability warranty. A trajectory tracking controller that can follow a double lane change path with high accuracy is designed, and then simulation experiments of the CarSim/Simulink connection are carried out against various vehicle longitudinal speeds and road surface roughness to demonstrate the effectiveness of the presented controllers. Furthermore, a PID driver model is introduced for comparison with the two proposed controllers. Simulation outcomes show that the proposed controllers can attain good response implementation and enhance the 4WS AV performance and stability. Indeed, enhancement of the stability and efficacy of 4WS autonomous vehicles would afford a sustainable transportation system by lessening fuel consumption and gas emissions.

Event-Triggered Backstepping Control of Fractional-Order Chaotic Systems with Dead Zone Via Disturbance Observer

This paper comes up with an adaptive event-triggered tracking control scheme for a kind of fractional-order strict feedback nonlinear systems with actuator dead-zone inputs and uncertain external disturbances. The presented strategy can overcome the defect in standard backstepping control scheme which leads to the “explosion of complexity” problem of virtual signals, and strengthen the transmission efficiency by an event-triggered scheme. An error compensation mechanism is presented for promoting the tracking accuracy and reducing the effect filter error. The designed controller guarantees that the tracking error converges into a small neighborhood near the origin, and all closed-loop signals are bounded. Moreover, Zeno behavior will be avoided. The numerical simulation is given to verify the accuracy and effectiveness of the designed technique.

Robust adaptive control law design for enhanced stability of agriculture UAV used for pesticide spraying

In precision agriculture, such as crop spraying, controlling UAVs presents various challenges such as variable payload, inertial coefficient variation, influence of external disturbances such as wind gusts, and uncertainties associated with the dynamics. To address these challenges, this paper proposes a hybrid control technique that combines higher-order integral sliding mode control, fast-terminal sliding mode control, and adaptive law. The objective is to mitigate the effects of variable payload, external disturbances, and uncertainties while maintaining the stability and performance of the UAV during spraying. Initially, a mathematical model is constructed for a coaxial octocopter UAV that is fitted with a spraying tank. This model takes into account the variation in mass and moment of inertia. Then, a two-loop control structure is employed to attain control of both the translational and rotational axis of the UAV. The numerical simulations are performed on a nonlinear model of the agricultural UAV system and compared with neural network based sliding mode control and robust adaptive backstepping control schemes. The robustness of the proposed scheme is tested in wind gusts and sensor measurement error conditions. Finally, hardware-in-loop simulations are performed using the Pixhawk Orange Cube flight controller to validate the real-time capability of the proposed scheme.

A fast fixed-time backstepping control method for systems with mismatched disturbances

In this paper, a fast fixed-time backstepping control approach is developed for systems with mismatched disturbances. A novel fast fixed-time disturbance observer (FFTDO), which is convergent within fixed time regardless of initial conditions, is designed to efficiently estimate and compensate the disturbances. On the basis of FFTDO, a novel fast fixed-time backstepping control scheme is proposed, which can guarantee fast fixed-time convergence and high steady-state precision. In addition, a novel fixed-time filter is used to circumvent the problem of “explosion and complexity,” and to ensure overall fixed-time convergence. The fixed-time stability of the closed-loop system under the proposed controller is proved by the Lyapunov stability theory. The simulation results are carried out to confirm the feasibility and superiority of the proposed control strategy.

Adaptive predefined-time consensus for nonlinear multi-agent systems with input delay and performance constraints

This paper investigates the predefined-time tracking consensus issue for a class of non strict-feedback nonlinear multi-agent systems (MASs) under input delay and error performance constraints by adaptive backstepping control strategy. Firstly, the impact of input delay is eliminated by Pade approximation. With the help of an intermediate state variable, the considered MASs with input delay are revised as the independent-delay systems. Secondly, under constrained distributed error and corrected nth virtual error, the ln-type barrier Lyapunov function (BLF) is adopted to solve the error performance constrains and reduce the complexity of differentiation. Meanwhile, an adaptive predefined-time controller is designed to realize the tracking purpose by backstepping method and radial basis function neural networks (RBFNNs) approximation. Finally, a numerical simulation example and a practical application are presented to test the effectiveness for the proposed control strategy.

Backstepping control of multilevel modified SVM inverter in variable speed DFIG-based dual-rotor wind power system

The backstepping control (BC) scheme has been successfully used in a variety of high-effectiveness industrial AC drives. This study presents the application of the BC technique based on multilevel modified space vector modulation (BC-MSVM) to get better the energy performance of a dual-rotor wind turbine system (DRWT). Two techniques are suggested to command the stator power of a doubly-fed induction generator (DFIG) driven by a DRWT. This work addresses the problems of the DRWT-based energy production system, such as stream fineness, power overshoot, and torque ripples. The use of a multilevel inverter in BC-MSVM led to an enhancement in the competence of the multilevel BC-MSVM technique and the system as a whole, and this is proven by the results performed using MATLAB software on a 1500 kW DFIG-DRWT. The use of a seven-level inverter led to a minimization in the rates of overshoot, ripples, steady-state error, and response time of active power by 26.66%, 53.84%, 2.09%, and 9.09%, respectively. Regarding the reactive power, the ratios were estimated at 18.12%, 34%, 25%, and 1.41%, respectively. These ratios prove that using a higher-level inverter significantly improves the voltage quality and characteristics of the DFIG-DRWT.

Adaptive finite time command filtered backstepping control scheme of uncertain strict-feedback nonlinear systems

This paper proposes an adaptive finite time command filtered backstepping control scheme for single‐input and single‐output (SISO) uncertain strict-feedback nonlinear systems. The problem of the explosion of complexity existing in the adaptive backstepping control design and the singularity problem are solved by using the proposed adaptive finite time control method. In addition, the compensating signals are introduced to deal with the effect of the known filtering errors caused by the command filters. By using the finite time Lyapunov stability theory, the proposed adaptive finite time control strategy guarantees that all the signals in the closed-loop system are practical finite time stable, and the tracking errors converge to an arbitrarily small neighbourhood of the origin in finite time. Simulation and experimental results of the DC-DC buck converter are given to illustrate the effectiveness of the proposed adaptive finite time control scheme.

Cooperative Adaptive Command Filtered Backstepping Control for EVs to UPS-Microgrid via Virtual Synchronous Generator.

Multiple batteries in uninterruptible power supply (UPS)-microgrid systems based on multiagents composed of multiple electric vehicles (EVs) can encounter state of charge (SoC) consistency problems. To solve this differential expansion and controller saturation problem, an adaptive command filter sliding-mode control strategy based on virtual synchronous generators (VSGs) and considering the power allocation principle is proposed. First, based on directed graph theory, an SoC consistency algorithm and power allocation strategy for multiple EVs were proposed, forming a dc power system with a fixed communication topology. Second, the rotor motion equation of synchronous generator (SG) is introduced into the inverter control algorithm to form the mathematical model of VSG. Third, a low-pass filter (LFP) was introduced in the voltage control process to simulate the excitation attenuation characteristics of the SG. Based on the above, a backstepping control strategy, including a command filter and sliding mode controller is proposed, which improves the operating stability of the system based on the system errors of angle, frequency, and power output. Finally, the UPS-microgrid system based on multiagents is simulated to demonstrate the stability of the system and the effectiveness of the proposed control strategy.

Distributed fixed-time control for high-order multi-agent systems with FTESO and feasibility constraints

In this study, a fixed-time distributed anti-disturbance control strategy is designed for a class of higher-order multi-agent systems in an undirected static topology. Inspired by the existing literature, the strategy introduces a unique way of defining neighborhood errors during the design process to deal with the connectivity maintenance and collision avoidance problems among the neighbor agents in the system. The control strategy not only solves the full state constraint and transient steady state performance constraint control problems simultaneously, but also considers the effects of internal uncertainties and external disturbances of the system, which enhances the difficulty of controller design. To address these challenges, a fixed-time extended state observer is introduced to obtain the estimation of uncertainty and disturbance . Subsequently, an integrated backstepping control scheme is designed to feed-forward compensate for uncertainties and disturbances, while constraining the transient steady-state performance of the system to remain within a predefined performance boundaries. This is achieved by combining the fixed-time prescribed performance and the barrier Lyapunov function. Finally, a simulation case is presented to verify the effectiveness of the designed control strategy.

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 minimize 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 minimize 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.

Event-Triggered Adaptive Containment Control for Heterogeneous Stochastic Nonlinear Multiagent Systems.

This article investigates the event-triggered adaptive containment control problem for a class of stochastic nonlinear multiagent systems with unmeasurable states. A stochastic system with unknown heterogeneous dynamics is established to describe the agents in a random vibration environment. Besides, the uncertain nonlinear dynamics are approximated by radial basis function neural networks (NNs), and the unmeasured states are estimated by constructing the NN-based observer. In addition, the switching-threshold-based event-triggered control method is adopted with the hope of reducing communication consumption and balancing system performance and network constraints. Moreover, we develop the novel distributed containment controller by utilizing the adaptive backstepping control strategy and the dynamic surface control (DSC) approach such that the output of each follower converges to the convex hull spanned by multiple leaders, and all signals of the closed-loop system are cooperatively semi-globally uniformly ultimately bounded in mean square. Finally, we verify the efficiency of the proposed controller by the simulation examples.

An adaptive backstepping control strategy based on radial basis function neural networks for the magnetorheological semi-active suspension

Owing to nonlinear issues such as external disturbances and uncertain parameters within the semi-active suspension system (SASS), the vibration amplitude of the suspension system tends to increase, and the time required for the suspension system to reach a steady-state response is prolonged. Hence, this paper proposes an adaptive backstepping control strategy based on radial basis function neural networks (RBF-NNs). Firstly, the damping force characteristics of the magnetorheological (MR) damper are tested, and the experimental data are utilized for parameters identification and fitting of the Bouc-Wen model. To establish a connection between the controller and the forward model of the MR damper, the forward model of the MR damper, the inverse model of the MR damper, and the model of the MR-SASS are constructed. Secondly, the backstepping controller and the adaptive backstepping controller based on RBF-NNs are designed. The stability and reliability of the closed-loop suspension system are verified through stability analysis using Lyapunov function. Finally, the dynamic characteristics of the passive control, backstepping control, and adaptive backstepping control strategies based on RBF-NNs applied to MR-SASS are analyzed under B-Class road excitation and speed bump road excitation. The acceleration, suspension dynamic deflection, and tire dynamic load are selected as the evaluation indices. The results demonstrate that the adaptive backstepping controller based on RBF-NNs significantly enhances the ride comfort of the SASS.

A model free adaptive‐robust design for control of robot manipulators: Time delay estimation approach

SummaryThis paper addresses a new robust control scheme for tracking control of the robot manipulators. This algorithm employs time delay estimation (TDE) technique in combination with backstepping control strategy. The suggested control scheme has no dependency on the robot dynamic model and knowing the bound of the inertia matrix is enough to develop this controller. To develop the idea, at first the boundedness of the TDE errors is analyzed by Lyapunov‐Krasovskii approach. Next, the proposed TDE based adaptive backstepping nonsingular terminal sliding mode control (ABNTSMC) algorithm is developed. In this way, a novel adaptive‐robust term is employed to defeat the chattering phenomenon. Moreover, the closed‐loop stability of the system is proven through Lyapunov second approach. Fast transient response, supreme robustness, and chattering‐free as the premier specifications are gained employing the proposed control algorithm. The efficiency of the suggested control scheme is illustrated through some simulations on an industrial robot and the results are compared with some other control algorithms. Finally, the practical effectiveness of the proposed TDE based control algorithm is verified through some experiments on a parallelogram robot manipulator.

Adaptive backstepping controller based on a novel framework for dynamic solution of an ankle rehabilitation spherical parallel robot

AbstractThis research offers an adaptive model-based methodology for autonomous control of 3-RRR spherical parallel manipulator (RSPM) based on a novel modeling framework. RSPM is an overconstrained parallel mechanism that has a variety of applications in medical procedures such as ankle rehabilitation because of its precision and accuracy. However, obtaining a complete explicit dynamic model of these mechanisms for tracking purposes has been a problematic challenge due to their inherent singularities, coupling effects of the limbs, and redundant constraints imposed by the intermediate joints. This paper presents a novel algorithm to obtain the analytical kinematic solutions of RSPMs based on the closed-loop vector method, which includes constraint analysis. By incorporating constrained kinematics into the dynamic model, a comprehensive explicit dynamic solution of the non-overconstrained version 3-RCC of RSPM is developed in task space, based on screw theory and the linear homogeneous property of algebraic equations on the manipulator twist. Based on the proposed computational framework, a robust self-tuning backstepping control (STBC) strategy is applied to the robot to overcome the effect of external disturbances and time-varying uncertainties. Furthermore, an observer-based compensation (OBC) method is presented for dealing with the nonlinear hysteresis loops of the ankle during trajectory tracking purposes. The closed-loop stability of the whole system including STBC and OBC is theoretically performed by Lyapunov methods. The proposed methodologies are validated by realistic co-simulations in different scenarios. For instant, in the presence of external disturbances, the maximum tracking error norm of STBC is 37.5% less than the sliding mode approach.

Synchronous control of tri-motor vibration system considering an adaptive back-stepping control strategy

In oil and gas drilling engineering, the anti-phase synchronization of two co-rotating rotors in a tri-motor vibration system is easy to implement owing to its inherent coupling characteristics, which can lead to the exciting force generated by the vibrating system being very small. Thus, an adaptive back-stepping control strategy is proposed to apply in a tri-motor vibrating system and improve the processing capacity of drilling fluid shaker screens. The algorithm developed in this paper is that a complex higher-order nonlinear system is simplified into lower-order subsystems by the adaptive back-stepping control theory, and then the adaptive law for varying load torque is derived by combining with the adaptive theory to regulate the velocity of motors in a closed loop. Firstly, a dynamical model to describe the tri-motor vibration system is established, and the dynamical equations of the vibrating system are derived based on the Lagrange equation. Then, the speed error controller and the phase difference error controller are designed by combining the adaptive back-stepping control algorithm with the master–slave control (MSC) structure. According to Barbalat’s lemma, the stability of the control system is analyzed to verify the feasibility of the control method. Finally, the dynamical equations of the vibrating system are used to establish an electromechanical coupling control model of a tri-motor driven planar system through the Runge–Kutta method, and it verified the reliability of the control strategy, the robustness, and the stability of the control system, respectively, and intuitively revealed the synchronization characteristics of tri-motor vibration control system. The results demonstrate the phase difference among the three motors can be accurately stabilized at zero by a phase synchronization control strategy based on the adaptive back-stepping control method, and the method is simple and fast-speed and the control system has better robustness.

Command filter-based event-triggered fixed-time control for nonlinear systems with prescribed performance and actuator faults

This paper investigates command filter-based adaptive neural network (NN) minimal learning practical fixed-time control for stochastic nonlinear systems with prescribed performance and actuator faults. The considered system is in a high-order nonstrict-feedback stochastic structure with unknown dynamics and external disturbances. By combining NN with minimal learning parameter method, the need for prior knowledge of nonlinear functions is eliminated, and the number of weights’ updating laws for the NN is reduced to one, regardless of the system's order and number of neural nodes. This reduction significantly decreases the computational burden. Additionally, a unique property of the Gaussian basis function of NNs is applied to solve the algebraic loop problem of the nonstrict-feedback structure. A novel event-triggered control mechanism is proposed to save communication resources. In order to surmount the "explosion of complexity" and "singularity" problems, a novel fixed-time command filter is suggested, and then, a modified compensation mechanism is proposed to mitigate the errors that emerge from command filters. Furthermore, to improve the transient and steady-state performance of the tracking error, a prescribed performance function is taken into account. Via the Lyapunov stability theory, it will be shown that the developed adaptive backstepping control scheme, guarantees that the closed-loop system signals are bounded in probability in a fixed time, that the convergence time is independent of the initial value, and the tracking error remains within the decaying prescribed performance bounds all the time. Finally, the effectiveness and practicability of the theoretical results are verified by a practical simulation example.

Command filter-based adaptive neural tracking control of nonlinear systems with multiple actuator constraints and disturbances

In this paper, the adaptive practical finite-time tracking control problem for a class of strictly feedback nonlinear systems with multiple actuator constraints is investigated using backstepping techniques and practical finite-time stability theory. The effects of deadband and saturated nonlinear constraints on the controller design of nonlinear systems are addressed by the equivalent transformation method. The problem of complexity explosion due to the derivatives of virtual control signals is solved by using the virtual control signals as inputs to the command filters and using the outputs of the command filters to perform the corresponding control tasks. An adaptive neural network tracking backstepping control strategy based on the command filter technique and the backstepping design algorithm is proposed by approximating an unknown nonlinear function using a neural network. The control strategy ensures the boundedness of all variables in the closed-loop system, and the output tracking error fluctuates in a small region near the origin. Finally, simulations verify the effectiveness of the control strategy designed in this paper.