Command-filtered Backstepping Research Articles

Robust neuro-adaptive command-filtered back-stepping fault-tolerant control of satellite using composite learning

This study proposes an adaptive neural command-filtered backstepping control system for precise and fast attitude control of a satellite considering different uncertain dynamics. Mission success crucially depends on robust attitude control resilient to model uncertainties, unmodeled dynamics, external disturbances, and actuator faults. The proposed approach synergistically combines a neural network for handling model uncertainties, unmodeled dynamics, and actuator faults, with a disturbance observer for compensating external disturbances and neural network estimation errors. The command-filtered backstepping technique avoids the explosion of complexity inherent to traditional backstepping, while integrating integral action into the design results in the elimination of the steady-state tracking error. Besides, a composite learning method optimizes the update laws for the neural network and disturbance observer weights, enhancing control performance. Despite the presence of uncertainties, the closed-loop system stability is guaranteed by the Lyapunov stability theorem. Simulation results demonstrate the proposed controller’s ability to handle severe actuator faults, unmodeled dynamics, and measurement noise without requiring explicit fault detection and isolation schemes.

Adaptive finite‐time tracking control of nonlinear systems subject to input hysteresis and multiple objective constraints

AbstractIn this article, the problem of adaptive finite‐time tracking control for a class of nonlinear systems subject to backlash‐like input hysteresis and multiple objective constraints is investigated. For the purpose of realizing multiple objective constraints, a new time‐varying barrier function (TVBF) is introduced to ensure that all objective constraint functions are always within the defined range. Meanwhile, based on the combination of the command filter approach and adaptive backstepping control, an error compensation system (ECS) is supplied to reduce the impact of filter error on control performance. Additionally, the problem of “singularity” caused by hysteresis is avoided by linearizing the backlash‐like hysteresis model, and Nussbaum‐type function is also applied to reduce the influence of hysteresis on the stability of the system. Then, by combining multi‐dimensional Taylor network (MTN) technology and command filter backstepping approach, an adaptive finite‐time control strategy is designed. The proposed control strategy ensures that all the signals in the closed‐loop system realize finite‐time semi‐globally uniformly ultimately bounded (SGUUB), and the output signal of the system can track the reference signal greatly while adhering to multiple objective constraints. Finally, the effectiveness of the proposed control strategy is verified by a practical simulation example.

Distributed Adaptive Formation Tracking for a Class of Uncertain Nonlinear Multiagent Systems: Guaranteed Connectivity Under Moving Obstacles.

This article explores a guaranteed network connectivity problem during moving obstacle avoidance within a distributed formation tracking framework for uncertain nonlinear multiagent systems with range constraints. We investigate this problem based on a new adaptive distributed design using nonlinear errors and auxiliary signals. Within the detection range, each agent regards other agents and static or dynamic objects as obstacles. The nonlinear error variables for formation tracking and collision avoidance are presented, and the auxiliary signals in formation tracking errors are introduced to maintain network connectivity under the avoidance mechanism. The adaptive formation controllers using command-filtered backstepping are constructed to ensure closed-loop stability with collision avoidance and preserved connectivity. Compared with the previous formation results, the resulting features are as follows: 1) the nonlinear error function for the avoidance mechanism is considered an error variable, and an adaptive tuning mechanism for estimating the dynamic obstacle velocity is derived in a Lyapunov-based control design procedure; 2) network connectivity during dynamic obstacle avoidance is preserved by constructing the auxiliary signals; and 3) owing to neural networks-based compensating variables, the bounding conditions of time derivatives of virtual controllers are not required in the stability analysis.

Event-Triggered Adaptive Neural Network Tracking Control for Uncertain Systems With Unknown Input Saturation Based on Command Filters.

This brief presents a modified event-triggered command filter backstepping tracking control scheme for a class of uncertain nonlinear systems with unknown input saturation based on the adaptive neural network (NN) technique. First, the virtual control functions are reconstructed to address the uncertainties in subsystems by using command filters. A piecewise continuous function is employed to deal with the unknown input saturation problem. Next, an event-triggered tracking controller is developed by utilizing the adaptive NN technique. Compared with standard NN control schemes based on multiple-function-approximators, our controller only requires a single NN. The closed-loop system stability is analyzed based on the Lyapunov stability theorem, and it is shown that the Zeno behavior is also avoided under the designed event-triggering mechanism. Simulation studies are performed to validate the effectiveness of our controller.

Observer-based Fixed-time Output Feedback Control for Flexible-joint Manipulators via Improved Command-filtered Backstepping

Observer-based Fixed-time Output Feedback Control for Flexible-joint Manipulators via Improved Command-filtered Backstepping

Event-Triggered Adaptive Fuzzy Neural Network Output Feedback Control for Constrained Stochastic Nonlinear Systems.

This article investigates the problem of command-filtered event-triggered adaptive fuzzy neural network (FNN) output feedback control for stochastic nonlinear systems (SNSs) with time-varying asymmetric constraints and input saturation. By constructing quartic asymmetric time-varying barrier Lyapunov functions (TVBLFs), all the state variables are not to transgress the prescribed dynamic constraints. The command-filtered backstepping method and the error compensation mechanism are combined to eliminate the issue of "computational explosion" and compensate the filtering errors. An FNN observer is developed to estimate the unmeasured states. The event-triggered mechanism is introduced to improve the efficiency in resource utilization. It is shown that the tracking error can converge to a small neighborhood of the origin, and all signals in the closed-loop systems are bounded. Finally, a physical example is used to verify the feasibility of the theoretical results.

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.

Fixed-time consensus control of stochastic nonlinear multi-agent systems with input saturation using command-filtered backstepping

<abstract><p>In this paper, a fixed-time consensus control algorithm is proposed for non-triangular structure stochastic nonlinear multi-agent systems (SNMASs) with input saturation via the command-filtered backstepping design method. Fuzzy logic systems are employed to identify the nonlinear dynamics of each agent. By introducing the fixed-time command filter and constructing the fractional power error compensation mechanism, the "complexity explosion" problem is effectively avoided, and the influence of filtered errors is eliminated in a fixed time. Based on the fixed-time stability theory, it strictly proves that all signals in the closed-loop system are fixed-time bounded in probability, and the consensus error converges to a sufficiently small neighborhood of the origin in probability within a fixed time. Finally, a comparison simulation example verifies the effectiveness and superiority of the proposed fixed-time consensus control strategy.</p></abstract>

Adaptive Command Filter Backstepping Sliding Mode Control for Variable Stiffness Exoskeleton With Input Saturation Constraint

Adaptive Command Filter Backstepping Sliding Mode Control for Variable Stiffness Exoskeleton With Input Saturation Constraint

Dynamic Threshold Finite-Time Prescribed Performance Control for Nonlinear Systems With Dead-Zone Output.

This article investigates the tracking control problem for nonlinear systems. An adaptive model is proposed to represent the dead-zone phenomenon and solve its control challenge with a Nussbaum function in conjunction. Drawing inspiration from the existing prescribed performance control schemes, a novel dynamic threshold scheme is developed that fuses a proposed continuous function with a finite-time performance function. A dynamic event-triggered strategy is applied to reduce the redundant transmission. The proposed time-varying threshold control strategy has fewer updates than the traditional fixed threshold and improves the efficiency of resource utilization. A command filter backstepping approach is employed to prevent the complexity explosion faced by the computation. The suggested control strategy ensures that all system signals are bounded. The validity of the simulation results has been verified.

Control of Uncertain High-Order Fully Actuated Strict-Feedback Systems: A Backstepping Approach With High-Gain Observer-Based Derivative Approximation.

In this article, a high-gain observer (HGO)-based differentiator is proposed to approximate the derivatives of the virtual control to ease the "explosion of complexity" problem in backstepping for the second-order strict-feedback systems (SOSFSs) and high-order strict-feedback systems (HOSFSs). Unlike the existing high-order command-filtered backstepping or extended dynamic surface control that needs to tune a large number of parameters, this proposed high-order HGO-based backstepping (HOHGOB) scheme can improve the derivative approximation performance by only tuning a single parameter, i.e., the observer gain. A further advantage of the proposed HOHGOB scheme, in addition to its simplicity and ease of implementation, is that the estimation error of the derivatives shrinks to zero as the observer gain grows to infinity. We have also rigorously established that the states of the closed-loop system achieve uniform ultimate boundedness under the designed high-order backstepping controller. Additionally, the output tracking error can be made arbitrarily small by the designer. The efficacy of the proposed scheme is numerically validated through a benchmark application to a single-link robot arm.

Rotation matrix-based finite-time trajectory tracking control of AUV with output constraints and input quantization

This study investigated a rotation-matrix-based finite-time trajectory tracking problem for autonomous underwater vehicles (AUVs) in the presence of output constraints, input quantization, and uncertainties. First, a rotation matrix-based attitude representation is introduced, which allow attitude dynamics to be globally and uniquely represented without unwinding. To satisfy the finite-time stability of AUV tracking control and the output constraints imposed by introducing the new attitude error vector, a novel finite-time command-filtered backstepping controller (FTCFBC) is proposed based on the asymmetrical time-varying barrier Lyapunov function (TVBLF). Subsequently, a second-order auxiliary dynamic system (ADS) is proposed to estimate the negative effects that of input quantization errors. Because the quantized control inputs can be switched at an appropriate earlier or later switching timing depending on the output of the ADS, the negative impact of quantization errors on the control accuracy is reduced. Moreover, an adaptive finite-time disturbance observer (AFTDO) is developed to estimate the lumped uncertainties without prior information on the bounds of the uncertainties. Finally, the results of the theoretical analysis verified that the tracking errors can converge within a finite time. Numerical simulations confirmed the effectiveness of the proposed control scheme.

Adaptive dynamic positioning control of an offshore wind turbine installation vessel subjected to thruster dynamics and input constraints

This paper suggests an adaptive positioning control method for a DP-equipped offshore wind turbine installation vessel. The method combines a finite-time disturbance observer (FTDO) with adaptive command filtered backstepping (CFB) to handle issues related to thruster dynamics, input saturation, model parameter uncertainties, and unknown environmental disturbances. By analyzing the environmental loads acting on the pile legs, a mathematical model for the installation vessel is established. To counteract the unknown disturbance actively, a FTDO is utilized. Additionally, an auxiliary dynamic system (ADS) is used to mitigate the thruster input saturation issue. Then an adaptive positioning controller is designed based on the FTDO and ADS, and Lyapunov stability theory is used to prove that all signals in the control system remain uniformly ultimately bounded. Numerical simulations are conducted to verify the effectiveness of the proposed control approaches.

Adaptive fuzzy extended state observer for a class of nonlinear systems with output constraint

Abstract In this study, an adaptive fuzzy extended state observer (AFESO) for single-input–single-output nonlinear affine systems in the presence of external disturbances and output constraints is proposed. In this regard, an extended state observer (ESO) was employed to estimate the unmeasured states and external disturbances simultaneously. To improve the estimation accuracy, the observer gains were adjusted using an adaptation law. To obtain a more comprehensive mathematical analysis and an accurate model for the ESO and to increase the degree of freedom, a Takagi–Sugeno fuzzy system was employed. The proposed AFESO relaxes the limitations of the ESO and improves the system performance as compared with the classical methods in the presence of time-varying disturbances. Next, a command-filtered backstepping controller is designed based on the barrier Lyapunov function method, which guarantees fast convergence of the tracking error as well as satisfying the output constraints of the system. The stability analysis showed that both the estimation error of the AFESO and the tracking error of the controller are bounded, and the tracking error converges to a small neighborhood of the origin. A simulating example of a flexible-joint manipulator shows the effectiveness of the proposed method as compared with the recently proposed method in the literature.

Practical finite-/fixed-time improved command-filtered backstepping control for nonlinear systems via immersion and invariance

This paper presents a practical finite-/fixed-time adaptive tracking control scheme based on improved command filtered backstepping (ICFBS) and immersion and invariance (I&I) for a class of single-input single-output (SISO) strict-feedback nonlinear systems with uncertainty parameterization. The conventional command-filtered backstepping method (CFBS) is improved by introducing any bounded function such that ICFBS relaxes the boundedness assumption of the control direction function and elevates the tunable space of the design scheme, with almost no increase in computational complexity. The higher-power composite term of a parameter estimation is designed in the parameter update law based on I&I and the inequality constructed by us proves that this form of the adaptive update law can be augmented to suit for not only uniform ultimate bounded (UUB) and practical finite-time stability but also practical fixed-time stability of the whole closed-loop system. The error compensation system is also extended to realize the practical finite-/fixed-time convergence of the error compensation signals. The proposed controller guarantees practical finite-/fixed-time stability of the closed-loop system. Therefore, our work solves two unsolved problems: both practical fixed-time and practical finite-/fixed-time ICFBS and I&I adaptive tracking control. Finally, the proposed control scheme is validated by a practical electromechanical system and a nonlinear system with unbounded control direction functions.

Adaptive practical prescribed-time formation tracking of networked nonlinear multiagent systems with quantized inter-agent communication

This paper presents an adaptive practical prescribed-time (PPT) control design for distributed time-varying formation tracking of networked uncertain strict-feedback nonlinear systems with quantized inter-agent communication under a directed network. The primary contribution of this study is to develop a time-varying formation tracking strategy to resolve the quantized inter-agent communication problem in the prescribed-time control field. A practical finite-time function is introduced to design an adaptive PPT formation tracker using quantized output information of neighbors, which can be used continuously after a prescribed time. A neural-network-based design methodology that utilizes the quantization-based distributed errors is presented to deal with the unknown virtual and actual control coefficient functions in the command-filtered backstepping design. Distributed adaptive compensating signals are constructed using the practical finite-time function to compensate for command-filter errors, unknown nonlinearities, and quantization errors in the PPT tracking framework. We prove that despite the presence of quantized inter-agent communication, the time-varying formation tracking errors converge to a compact set including the origin within the pre-assigned convergence time, where the compact set can be adjusted by choosing a design parameter of the practical finite-time function, and the prescribed settling time is independent of the initial system conditions and design parameters. The effectiveness of the proposed theoretical approach is confirmed through two simulation examples.

Neural-Network-Based Adaptive Finite-Time Output Feedback Control for Spacecraft Attitude Tracking.

This brief is concerned with neural network (NN)-based adaptive finite-time output feedback attitude tracking control for rigid spacecraft in the presence of actuator saturation, inertial uncertainty, and external disturbance. First, a neural state observer is designed to estimate the unknown state. Then, based on the estimated state, the adaptive neural finite-time command filtered backstepping (CFB) is applied to construct virtual control signal and controller with updating law. The finite-time command filter is given to avoid the computation complexity problem in traditional backstepping, and the compensation signals based on fractional power are constructed to remove filtering errors. Using Lyapunov stability theory, we show that the attitude tracking error (TE) can converge into the desired neighborhood of the origin in finite time and all the signals in the closed-loop system are bounded in finite time although input saturation exists. The numerical simulations are used to show the effectiveness of the given algorithm.

Switching ETM-based neural adaptive output feedback control for nonaffine stochastic MIMO nonlinear systems subject to deferred constraint

This article focuses on the neural adaptive output feedback control study related to nonaffine stochastic multiple-input, multiple-output nonlinear plants. First, a K-filter state observer based on a radial basis function neural network is designed to estimate the remaining unavailable states. Then, a novel adaptive command-filtered backstepping output feedback control framework is established, where an improved command filter with a fractional-order parameter is applied to conquer the calculation size problem. Specifically, the highlight of this work is that it designs a modified error compensation signal and incorporates the concept of deferred constraint to eradicate the negative effect caused by the filter errors. In addition, the network bandwidth resources, control impulse, and control accuracy are synthesized using an amended switching event-triggered mechanism. The theoretical analysis proved that the proposed control approach guarantees that the tracking error can converge to a preassigned region within a user-defined time while the violation of the deferred output constraint can be excluded. Two illustrative studies are provided to demonstrate the validity and superiority of the developed control method.

Convex Optimization-Based Adaptive Fuzzy Control for Uncertain Nonlinear Systems With Input Saturation Using Command Filtered Backstepping

This paper presents a modified command filter backstepping tracking control strategy for a class of uncertain nonlinear systems with input saturation based on the convex optimization method and the adaptive fuzzy logic system control technique. Firstly, the effect of complex uncertainties is eliminated by introducing n command filters and a single fuzzy logic system (FLS). And then, the update laws of FLS weights are designed based on the convex optimization technique. Next, a new piece-wise continuous function is employed to deal with the input saturation problem. The closed-loop system performance is also analyzed using the Lyapunov stability theorem and the Lasalle invariant principle. Finally, simulation and experimental results are presented to show the effectiveness of our controller.

Multiagent-Based Consensus Optimal Control for Microgrid With External Disturbances via Zero-Sum Game Strategy

Due to the fact that the external disturbances are unavoidable in nonlinear microgrids (MGs) systems, which could induce the oscillate of controller, leading to the excessive line loss, and the nonlinear could also result in the controller design difficulty in MGs. Therefore, based on the distributed consensus algorithm of multi-agent systems, this paper studies the distributed voltage recovery consensus optimal control problem for the MGs with nonlinear item and external disturbances. Firstly, the distributed secondary voltage restoration consensus control problem can be transformed into a distributed zero-sum (ZS) differential game problem of the voltage restoration consensus tracking error dynamics via applying the adaptive command-filtered backstepping technique, in which the auxiliary system and neural networks (NNs) are introduced to solve the unknown nonlinearities and external disturbances. Subsequently, the distributed voltage restoration consensus optimal control protocol is constructed via ZS differential game algorithm to achieve the voltage recovery of island MGs, in which a critic network is proposed to estimate the associated cooperative cost function online with a designed weight update law. Further, the consensus optimal control protocol proposed not only ensures the cooperative cost function to be minimized, but also ensures in the closed-loop systems all signals to be cooperatively uniformly ultimately bounded (CUUB). In addition, based on the Lyapunov stability theory, it is proved that the voltage recovery synchronization error can converge to an arbitrarily small range near the origin. Finally, simulation results verify the effectiveness of the proposed controller in island MG.