Adaptive Backstepping Research Articles

Trajectory-Tracking Control for Quadrotors Using an Adaptive Integral Terminal Sliding Mode under External Disturbances

In the face of external disturbances affecting the trajectory tracking of quadrotors, a control scheme targeted at accurate position and attitude trajectory tracking was designed. Initially, a quadrotor dynamic model, essential for control design, was derived. Adaptive integral backstepping control (AIBS) was then employed within the position loop, enabling the upper boundaries of disturbances to be estimated through adaptive estimation. Subsequently, a new adaptive backstepping fast nonsingular integral terminal sliding mode control (ABFNITSM) was proposed to enable adherence to the desired Euler angles. Rapid convergence and accurate tracking were facilitated by the incorporation of the nonsingular terminal sliding mode and an integral component. The dead zone technique was deployed to curtail estimation errors, while a saturation function was used to eradicate the phenomenon of chattering. Finally, to validate the proposed control scheme, simulation experiments were conducted in the Simulink environment, and the results were contrasted with those obtained from traditional integral terminal sliding mode control (ITSM) and integral backstepping control (IBS), providing evidence of the effectiveness of the proposed method.

Intermittent monitoring‐based adaptive fault‐tolerant control for uncertain nonlinear systems with actuator switching

AbstractIn this paper, an adaptive fault‐tolerant control (FTC) scheme is proposed for a class of uncertain nonlinear systems with actuator failure, in which a healthy actuator is available as a backup. Instead of monitoring the failure in real‐time, an intermittent monitoring mechanism (IMM) is proposed by designing a set of monitoring functions operating only at discrete time instants, which makes the proposed scheme more applicable for networked control systems for which the actuator status has to be monitored via network. An adaptive backstepping controller is designed with the errors being modified to include shifting functions. Once actuator failure is detected by the monitoring functions, the actuator is switched to its backup and the controller is reconfigured by updating the shifting functions so that the tracking error can be driven into the prescribed performance in a given time.

Observer‐based adaptive controller for a class of fractional‐order uncertain systems subject to unknown input and output quantizers and input nonlinearities

This work addresses design of an adaptive controller for nonlinear fractional‐order (FO) systems in the strict‐feedback form. The system is subject to unknown dynamics, unavailable state variables, quantized input and output, and input nonlinearity. The fuzzy logic system (FLS) is used to estimate the unknown dynamics, and instead of updating all the regressor weights, only the maximum of their norms is updated, which significantly reduces the computational load. Limitations imposed by data transmission bandwidth have been addressed by incorporating sector‐bounded quantizers, which include both logarithmic and hysteresis quantizers at the system input and output, and their errors have been considered in the controller design. It is assumed that system states are not measured. To estimate the system states, a linear observer has been used. Because of output quantization, the continuous output signal is not available, and therefore the observer has been designed based on the quantized output signal. In addition, the constraints of input nonlinearities, including symmetric and asymmetric saturation, backlash, hysteresis, and dead‐zone, have been considered in the controller design. Input nonlinearity and input quantization have been investigated simultaneously, which makes the analysis more challenging. Moreover, it is assumed that the type of input nonlinearity and its characteristics are not known, which makes the controller design more difficult. These problems have been resolved by using two novel adaptive laws. The adaptive backstepping method and the direct Lyapunov stability analysis have been used to construct the controller, and a nonlinear modified FO filter is used to avoid the explosion of complexity occurring in the traditional backstepping technique. Stability of the closed loop system has been established, and it has been shown that the tracking and state estimation errors converge to a small neighborhood of the origin. Finally, the proposed controller performance has been demonstrated via three simulation examples.

Adaptive finite-time incremental backstepping fault-tolerant control for flying-wing aircraft with state constraints

This paper proposes an incremental nonlinear fault-tolerant control scheme for flying-wing aircraft subject to state constraints under model uncertainties, external disturbances, and actuator faults. Firstly, the aircraft attitude dynamics system with state constraints is transformed into a free-constrained system by a nonlinear state-dependent function (NSDF), which simplifies the controller design in a direct and concise way. Based on the NSDF, a novel finite-time incremental backstepping (FT-IBS) method is proposed to achieve rapid attitude tracking and reduce the reliance on model knowledge, simultaneously. In this method, a command filter is designed to address the issues of complexity explosion and singularity, and particular stability compensators ensures the closed-loop system to achieve finite-time stability. Then, to overcome the lumped disturbances composed of uncertainties and faults, a new adaptive multivariable finite-time disturbance observer (AMFTDO) is designed for rapid estimation and compensation, and its adaptive strategy ensure high-precision tracking performance under complex time-varying lumped disturbances. Finally, comparative simulation results confirm that the proposed control scheme can achieve faster convergence, higher tracking accuracy, and stronger robustness.

Adaptive tracking control-based Nussbaum gain for a class of multi-input and multi-output nonlinear systems with time-varying state constraints

This article studies an adaptive backstepping barrier Lyapunov function-based control scheme for a class of multi-input and multi-output nonlinear systems in the presence of time-varying asymmetric full-state constraints and external disturbances. Simultaneously, a prominent feature of these systems is the unknown time-varying control direction. To stabilize such systems, Nussbaum gain technique is constructively framed to overcome the unknown control direction problem. To prevent that the constraints are overstepped, the time-varying asymmetric barrier Lyapunov functions are employed in each step of the backstepping design. The design involves an adaptive-based online approximator to cope with unknown dynamics of the system. A simulation example on aircraft skin inspection robot with three-dimensional trajectory is given to show the effectiveness of the proposed control scheme.

Composite Learning Adaptive Tracking Control for Full-State Constrained Multiagent Systems Without Using the Feasibility Condition.

This article proposes a distributed consensus tracking controller for a class of nonlinear multiagent systems under a directed graph, in which all agents are subject to time-varying asymmetric full-state constraints, internal uncertainties, and external disturbances. The feasibility condition generally required in the existing constrained control is removed by using the proposed nonlinear mapping function (NMF)-based state reconstruction technology, and the Lipschitz condition usually needed in the consensus tracking is also canceled based on the adaptive command-filtered backstepping framework. The composite learning of the neural network-based function approximator (NN-FAP) and the finite-time smooth disturbance observer (DOB) provides a novel scheme for handling internal and external uncertainties simultaneously. One advantage of this scheme is that the use of online historical data of the closed-loop system strengthens the excitation of NN's learning. Another advantage is that the DOB with NN-FAP embedding realizes that the finite-time observation for external disturbance in the case of the system dynamics is unknown. A complete controller design, sufficient stability analysis, and numerical simulation are provided.

Observer-Based Adaptive Fuzzy Consensus Control of Nonlinear Multiagent Systems Encountering Deception Attacks

This paper investigates the fuzzy adaptive output- feedback consensus control problem for nonlinear multi-agent systems (MASs) with network communication encountering deception attacks. Fuzzy logic systems (FLSs) are used to approximate unknown nonlinear functions, and a novel fuzzy state observer is established to estimate the states of encountered deception attacks. For the case of unknown time-varying gains caused by deception attacks, a projection operator-based compensation mechanism is designed. Consequently, under the framework of adaptive backstepping, a novel adaptive fuzzy output- feedback consensus control method is proposed. The proposed control method can not only ensure that all signals remain bounded, but also make all followers maintain consensus with the trajectory of the leader. Finally, the simulation results are given to confirm the effectiveness of the proposed control scheme.

Predefined time backstepping control of photovoltaic grid connected inverter

The large-scale grid connection of photovoltaic (PV) systems creates great hazards to the operation of power equipment and has a great impact on the stability and reliability of power systems. To achieve stable control and flexible management of PV grid connection, a predefined time adaptive backstepping control method based on the predefined boundary is proposed. Based on the predefined boundary time-varying function, the user’s predefined boundary design of the control signal is accomplished to ensure the boundedness of the global signal, which is independent of the initial state of the system. The controller with predefined boundaries is designed based on backstepping control, and the estimation and compensation of perturbations are attained based on adaptive control. The global predefined time stability of the predefined boundary of the closed-loop system is certified using the Lyapunov function. Simulation studies attest to the performance of the predefined time control strategy.

Robust fractional-order sliding mode tracker for quad-rotor UAVs: Event-triggered adaptive backstepping approach under disturbance and uncertainty

In this paper, tracking control of the quad-rotor UAVs in the presence of exterior perturbations and dynamical uncertainties is accomplished using an event-triggered adaptive backstepping fractional-order sliding mode control scheme. For this reason, tracking errors are considered as the difference between the actual and desired states of the quad-rotor system. Moreover, event-triggering errors are defined as the difference between tracking errors at time ti and tracking errors at time t. Afterward, a dynamical model of the quad-rotor system under external disturbance and model uncertainty is obtained based on the tracking errors’ states. Then, the fractional-order sliding mode surface based on the tracking errors and virtual control inputs is proposed to guarantee the convergence of desired tracking errors. Hence, to avoid the complexity in the control process, the virtual control inputs are presented as fractional-order integral-type laws to avoid high derivatives of virtual control inputs. In addition, the event-triggering condition is applied for backstepping fractional-order sliding mode control to prevent frequent periodic action of control inputs. Moreover, employing the backstepping control procedure and the Lyapunov stability concept, the convergence of fractional-order sliding surfaces is guaranteed. Later, the fractional-order adaptive laws are designed to estimate the unknown upper bounds of perturbations and uncertainties. Finally, to demonstrate the efficiency of the control algorithm recommended in this paper, the simulation results on MATLAB/Simulink environment are presented. A comparison between the control method in this paper and another existing technique is prepared to prove the productivity of performance of the offered control method on the quad-rotor system.

Experimental Study on Adaptive Backstepping Synchronous following Control and Thrust Allocation for a Dynamic Positioning Vessel

Cargo transfer vessels (CTVs) are designed to transfer cargo from a floating production storage and offloading (FPSO) unit into conventional tankers. The dynamic positioning system allows the CTV to maintain a safe position relative to the FPSO unit using a flexible cargo transmission pipe, and the CTV tows the tanker during operating conditions. The operation mode can be considered a synchronization tracking control problem. In this paper, a synchronization control strategy is presented based on the virtual leader–follower configuration and an adaptive backstepping control method. The position and heading of the following vessel are proven to be able to globally exponentially converge to the virtual ship by the contraction theorem. Then, the optimization problem of the desired thrust command from the controller is solved through an improved firefly algorithm, which fully considers the physical characteristics of the azimuth thruster and the thrust forbidden zone caused by hydrodynamic interference. To validate the effectiveness of the presented synchronous following strategy and thrust allocation algorithm, a scale model experiment is carried out under a sea state of 4 in a seakeeping basin. The experimental results show that the CTV can effectively maintain a safe distance of 100 m with a maximum deviation of 3.78 m and an average deviation of only 0.99 m in the wave heading 180°, which effectively verifies that the control strategy proposed in this paper can achieve safe and cooperative operation between the CTV and the FPSO unit. To verify the advantages of the SAF algorithm in the thrust allocation, the SQP algorithm and PSO algorithm are used to compare the experimental results. The SAF algorithm outperforms the SQP and PSO algorithms in longitudinal and lateral forces, with the R-squared (R2) values of 0.9996 (yaw moment), 0.9878 (sway force), and 0.9596 (surge force) for the actual thrusts and control commands in the wave heading 180°. The experimental results can provide technical support to improve the safe operation of CTVs.

Adaptive fuzzy finite-time PID backstepping control for chaotic systems with full states constraints and unmodeled dynamics

To solve the problem that the controlled object and system model cannot be fully mastered or the system parameters cannot be well obtained through conventional measurement methods, in this paper, a novel adaptive fuzzy finite-time PID backstepping control method is developed for a class of nonlinear chaotic systems with full state constraints and unmodeled dynamics. The unmodeled dynamics are handled by employing a dynamic signal. To avoid the violations of full state constraints (FSCs), a barrier Lyapunov function is used to implement a PID backstepping framework, whose merit consists in that three control gain constants KP, KI and KD with corresponding proportional relationships are designed to further improve control precision. Besides, the PID control method also embodies three dynamic gain components ΔKP, ΔKI and ΔKD, all of which are free functions that can be self-tuning online, and have a significant link with the adaptive law and modify accordingly. Finally, theoretical analysis confirms that all signals are ultimately uniformly bounded, the error signal converges to a nearby area near the origin in a finite-time, and the FSCs are not smashed. The practicality of the proposed method is confirmed by two simulation studies using the second-order Duffing chaotic system and third-order Chua's circuit.

Predefined‐time adaptive backstepping control for a class of nonlinear dynamical systems with parametric uncertainties

SummaryIn this article, we address the problem of achieving predefined‐time control for a class of nonlinear dynamical systems with parameter uncertainties. We introduce an adaptive predefined‐time control algorithm based on integrator backstepping for th order nonlinear systems. Using Lyapunov's stability theory, we establish that the proposed predefined time control approach, combined with an adaptive law, ensures the boundedness of all signals within the closed‐loop system. A notable advantage of our method is its potential to achieve convergence within a predetermined time frame. To validate our approach's efficacy, we present a practical example involving a 2 DOF helicopter, demonstrating the effectiveness of the proposed scheme.

Refined sliding mode disturbance observer‐based finite‐time composite control for Euler–Lagrange systems with multiple disturbances

AbstractA wide range of practical control systems such as robot manipulators and spacecrafts can be modeled by Euler–Lagrange systems. On one hand, the requirements for system control accuracy, response speed, and robustness are ever increasing. On the other hand, the control performances are inevitably degraded by multiple disturbances. In this paper, a novel finite‐time composite control law is proposed for a class of Euler–Lagrange systems subject to multiple heterogeneous disturbances including a neutrally stable disturbance and a norm‐bounded disturbance. More specifically, a refined sliding mode disturbance observer (RSMDO) is proposed to estimate and reject the neutrally stable disturbance in the feedforward channel, while an adaptive nonsingular backstepping control (ANBC) is designed in the feedback channel to stabilize the system and attenuate the observer error as well as the norm‐bounded disturbance. The proposed RSMDO can not only fully utilize the disturbance information, but also quantify the convergence time and steady‐state accuracy of the estimation error. The finite‐time stability analysis is carried out for the closed‐loop system. Finally, an example of spacecraft attitude control system is given to demonstrate the effectiveness of the proposed methods.

Event-triggered adaptive leaderless consensus control for nonlinear multi-agent systems with unknown dead-zones and output constraints

This article investigates the event-triggered adaptive control problem for a class of leaderless multi-agent systems with output constraints and unknown dead-zones. The adaptive updating laws are designed to eliminate the effects of unknown dead-zones by employing adaptive backstepping technique. The barrier Lyapunov function (BLF) is introduced to guarantee that the output constraints are not violated. Then, a generalized relative threshold is proposed by utilizing the neighboring controller errors to alleviate the computation burden dramatically. It is further shown that all the closed-loop signals are uniformly bounded and that the consensus tracking errors asymptotically tend to zero. A simulation example verifies the validation of the developed control strategy.

Event‐Triggered Adaptive Neural Network Backstepping Sliding Fault‐Tolerant Control of Spacecraft Formation Flying With Input Saturation

This study explores the challenge of tracking control for spacecraft formation flying (SFF) in the presence of dynamic uncertainties and external perturbations. Firstly, sliding mode control combined with backstepping control is used to address saturation issues. Then, neural networks, minimal parameter learning, and adaptive control are integrated to handle dynamic uncertainties and actuator failures. To alleviate the communication load, an event‐triggered mechanism is ultimately implemented, which leads to the development of an adaptive sliding mode fault‐tolerant control algorithm based on an event‐triggered neural network. This control architecture achieves significant advancements over traditional techniques: (1) ensuring system robustness and adaptability in complex scenarios with uncertain system dynamics and external disturbances, effectively counteracting actuator failures and input saturation issues; (2) significantly reducing transmission and computational burdens in resource‐limited networked systems through the adoption of event‐triggered control (ETC) mechanisms; (3) achieving high‐precision tracking performance for SFF without relying on prior knowledge of the system’s inherent dynamics, environmental disturbances, or potential actuator deficiencies. The Lyapunov approach is utilized to confirm the closed‐loop system’s boundedness. Finally, the proposed method’s efficacy is confirmed via simulations with a two‐satellite formation.

Adaptive Backstepping Fractional-order Nonsingular Terminal Sliding Mode Control of the Continuous Polymerization Reactor

Adaptive Backstepping Fractional-order Nonsingular Terminal Sliding Mode Control of the Continuous Polymerization Reactor

Adaptive Backstepping Control Based on Global HOSM Differentiators With Dynamic Gains

Adaptive Backstepping Control Based on Global HOSM Differentiators With Dynamic Gains

Composite Learning Based Adaptive Control of Linear 2×2 Hyperbolic PDE Systems.

This article considers the adaptive stability control of a class of 2×2 linear hyperbolic PDE systems. The PDE model is subject to constant but in-domain and boundary unknown parameters. A novel adaptive controller is developed by leveraging the swapping design technique and composite parameter learning law. With swapping design, several linear and static combinations, including carefully designed filters, unknown parameters, and error terms, are constructed to express the system states. From the static combinations, a composite learning based forgetting-factor least squares law is introduced to guarantee exponential parameter convergence without the persistent excitation (PE). Although inaccurate parameter estimation in the adaptive backstepping control results in asymptotic stability of the system, accurate parameter estimation ensures the exponential convergence of closed-loop system and concomitantly improves the transient performance. Finally, a comparative numerical simulation is performed to validate the effectiveness and advantage of the developed adaptive control scheme.

Adaptive Backstepping Control for Underactuated 6-DoF USV with Uncertain Dynamics

Adaptive Backstepping Control for Underactuated 6-DoF USV with Uncertain Dynamics

Enhancing Fault Ride-Through Capacity of DFIG-Based WPs by Adaptive Backstepping Command Using Parametric Estimation in Non-Linear Forward Power Controller Design

Enhancing Fault Ride-Through Capacity of DFIG-Based WPs by Adaptive Backstepping Command Using Parametric Estimation in Non-Linear Forward Power Controller Design