Backstepping Technique Research Articles

Adaptive neural control for a class of random nonlinear Markov jump multi-agent systems with full state constraints

This paper proposes a consensus control protocol based on the adaptive backstepping technique for a class of random Markov jump multi-agent systems (MASs) with full state constraints. Each agent is described by the high-order random nonlinear uncertain system driven by random differential equations, where the random noise is the second-order stationary stochastic process. First, a distributed tracking controller is designed for Markov jump MASs, effectively handling the interaction and coupling terms between agents. Second, an appropriate tan-type barrier Lyapunov function is selected to keep the agents’ states from the violation of constraint boundaries, and the unknown nonlinear terms with Markov jump parameters are approximated by neural networks (NNs) theory. Moreover, to address the differential explosion problem, the extended state observer (ESO) is first introduced instead of employing NNs approximation or command filtering techniques. Finally, the exponentially noise-to-state stability in mean square is proved rigorously through the Lyapunov method, which guarantees all signals of the closed-loop system are bounded in probability and the tracking error converges to a small neighborhood around zero. Simulations are given to demonstrate the feasibility of theoretical results.

Neurodynamics-based formation tracking control of leader-follower nonholonomic multiagent systems

This paper uses a bioinspired neurodynamic (BIN) approach to investigate the formation control problem of leader-follower nonholonomic multiagent systems. In scenarios where not all followers can receive the leader's state, a distributed adaptive estimator is presented to estimate the leader's state. The distributed formation controller, designed using the backstepping technique, utilizes the estimated leader states and neighboring formation tracking error. To address the issue of impractical velocity jumps, a BIN-based approach is integrated into the backstepping controller. Furthermore, considering the practical applications of nonholonomic multiagent systems, a backstepping controller with a saturation velocity constraint is proposed. Rigorous proofs are provided. Finally, the effectiveness of the presented formation control law is illustrated through numerical simulations.

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.

Partial state-constrained integrated guidance and control for an STT missile with self-adjusting prescribed performance via non-barrier Lyapunov function method

A state-constrained guidance and control law is vital to the flight safety of an aerial interceptor against a maneuvering target. Taking the flight angle limitations, manipulation saturation, and terminal constraints into consideration, a novel integrated guidance and control (IGC) schema with a self-adjusting prescribed performance is proposed. To avoid the feasibility condition via the conventional barrier Lyapunov function-based method, a new state-dependent nonlinear mapping function is designed, based on which the state-constrained IGC system is converted into a constrained-free model. A novel prescribed performance with a self-tuning mechanism is proposed to guarantee satisfied transit and steady guidance performances. The backstepping technique combined with super-twisting integral sliding modes and newly defined predefined-time disturbance observers is implemented to generate state-constrained virtual command signals. All the signals in the closed-loop system are strictly proven to be bounded by Lyapunov stability theory. The simulation results show the effectiveness of the proposed IGC schema.

Dynamic event-triggered prescribed performance disturbance rejection fault-tolerant trajectory tracking for surface vehicles

In this article, a dynamic event-triggered prescribed performance disturbance rejection fault-tolerant scheme is designed for the trajectory tracking of surface vehicles. The external time-varying disturbances and loss-of-effectiveness thruster faults are addressed separately. By constructing the separate observers, the external time-varying disturbances and the loss-of-effectiveness thruster faults are on-line estimated, respectively. The prescribed performance and error transformation functions enable the transient and steady-state performance to settle within pre-specified function values. The dynamic event-triggering is introduced so that commanded control signals are temporarily kept under predefined conditions to reduce wear and tear on the thrusters especially in harsh environmental condition. With the aid of the vectorial backstepping technique, the finial control law is derived such that the position and heading of vehicles can be forced to track the reference trajectories in disturbance and fault conditions. Application example on a 1:70 scaled model vessel in the different cases clarify the scheme.

Self-triggered consensus resilient control for multi-agent systems against sensor deception attacks based on a single parameter learning method

This paper presents a self-triggered consensus resilient control method for nonlinear multi-agent systems (MASs) under sensor deception attacks. A single parameter learning method is integrated into backstepping technique to simplify design procedure. The neural networks are utilized to compensate for unknown dynamics of the MASs. Moreover, a self-triggered mechanism is presented for MASs to refrain from continuously monitoring triggering conditions and conserve communication resources. The designed controller can resist sensor deception attacks and guarantee that all signals of the MASs are uniformly bounded. An expository simulation example reveals the virtue of the presented method.

Command filter‐based adaptive finite‐time control of fractional‐order nonlinear constrained systems with input saturation

AbstractIn this article, the command filter‐based finite‐time tracking control issue is explored for fractional‐order nonlinear constrained systems (FONCSs) with saturated input. Firstly, a novel fractional‐order Lyapunov stability lemma is put forward, thereby offering a reliable strategy for finite‐time convergence of FONCSs. By employing an improved error compensation system and introducing auxiliary signal, a new finite‐time command filtered backstepping technique is developed. The proposed control strategy guarantees the finite‐time convergence characteristic of filtering signals, in addition to alleviate the impacts produced by saturated input. After that, a modified nonlinear state‐dependent function (NSDF) is developed to solve the state constraint problem while fulfilling the concavity condition. In comparison to the existing constrained control techniques in FONCSs, this approach not only ensures finite‐time convergence of the tracking error but also gets rid of feasibility demands. Ultimately, two simulation scenarios are supplied to illustrate the feasibility and usefulness of the suggested strategy.

Fixed-Time Congestion Control for a Class of Uncertain Multi-Bottleneck TCP/AWM Networks

As network technology continues to advance, network congestion has become an inevitable aspect of network communication. Considering the external interference, unmodeled uncertainty and the interaction between nodes, a multi-bottleneck TCP/AWM network model is established in this paper. A new fixed-time congestion controller was designed by combining a neural network and the backstepping technique. The neural network approximation property is used to eliminate the interference of unmodeled uncertainty and UDP flow in the system. The controller designed in this paper can ensure the stability of the TCP/AWM closed-loop system in a fixed time. Finally, the simulation results demonstrate the effectiveness of the proposed TCP/AWM controller.

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

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

Predefined time fuzzy adaptive control for stochastic nonlinear systems with limited time interval output constraints

This article investigates the problem of fuzzy adaptive predefined time tracking control for stochastic nonlinear systems with limited time interval output constraints. Firstly, the considered output constraints occur within a finite time interval after the system starts running. By constructing shift functions and barrier Lyapunov functions (BLFs), the constrained system is converted into an unconstrained system, which solves the problem of function discontinuity resulting from output constraints within limited time intervals. Then, with the help of adaptive backstepping technique and predefined time control method, which reduces the parameters to be designed and removes the limitation of relatively large initial control input in existing approaches. The designed control technique ensures the boundedness of all variables of the stochastic system, the tracking error converges within a predetermined time, and the outputs do not exceed their constraint boundaries in a finite time interval. And this algorithm is applicable to both infinite time constraints and unconstrained outputs cases. Finally, the validity of this approach is demonstrated through simulation examples.

Neuroadaptive high-order fully-actuated system approach for roll autopilot with unknown uncertainties

In this paper, a neuroadaptive high-order fully-actuated system approach control scheme incorporating the disturbance observer technique is proposed for the missile roll autopilot, subject to model uncertainties generated by the induced roll moment, along with actuator control efficiency deterioration and external disturbance. To address model uncertainties, the radial basis function neural network is implemented. The external disturbance and approximation error are treated as compound disturbances and estimated by a nonlinear disturbance. To avoid the “differential explosion” inherent in the backstepping technique, the high-order fully-actuated system approach is invoked to track the desired roll angle command. The semi-globally uniformly bounded of the closed-loop system is demonstrated via the Lyapunov method. Numerous simulations under various conditions have been conducted to verify the effectiveness of the proposed roll autopilot.

Fixed-Time Fault-Tolerant Adaptive Neural Network Control for a Twin-Rotor UAV System with Sensor Faults and Disturbances

This paper presents a fixed-time fault-tolerant adaptive neural network control scheme for the Twin-Rotor Multi-Input Multi-Output System (TRMS), which is challenging due to its complex, unstable dynamics and helicopter-like behavior with two degrees of freedom (DOFs). The control objective is to stabilize the TRMS in trajectory tracking in the presence of unknown nonlinear dynamics, external disturbances, and sensor faults. The proposed approach employs the backstepping technique combined with adaptive neural network estimators to achieve fixed-time convergence. The unknown nonlinear functions and disturbances of the system are processed via an adaptive radial basis function neural network (RBFNN), while the sensor faults are actively estimated using robust terms. The developed controller is applied to the TRMS using a decentralized structure where each DOF is controlled independently to simplify the control scheme. Moreover, the parameters of the proposed controller are optimized by the gray-wolf optimization algorithm to ensure high flight performance. The system’s stability analysis is proven using a Lyapunov approach, and simulation results demonstrate the effectiveness of the proposed controller.

Evaluation of advanced control strategies for PMSG in wind turbines: backstepping fuzzy logic control and adaptive neural network control approaches

This study presents a comparative analysis of two advanced control strategies for Permanent Magnet Synchronous Generators (PMSGs) in wind turbines: Backstepping Fuzzy Logic Control and Adaptive Neural Network Control. The aim is to evaluate their effectiveness in handling structured and unstructured uncertainties and enhancing system performance. Backstepping Fuzzy Logic Control integrates backstepping techniques with fuzzy logic regulation to improve flexibility and robustness. This method addresses the limitations of traditional PI controllers by enhancing adaptability to parameter variations and external disturbances. In contrast, Adaptive Neural Network Control employs neural networks with dynamic compensators to address high uncertainties and nonlinearities, aiming to surpass the performance of conventional PI controllers. The study involves simulations to compare these control strategies based on several criteria: robustness in managing parameter changes and external disturbances, flexibility in adapting to dynamic conditions, and overall performance including efficiency and stability. Simulation results indicate that both strategies offer significant improvements over traditional PI controllers. Backstepping Fuzzy Logic Control demonstrates strong adaptability and robustness, while Adaptive Neural Network Control shows superior efficiency and optimality, particularly in high-uncertainty environments. This comparative analysis provides insights into the strengths and limitations of each approach, offering guidance for selecting the most suitable control strategy based on specific operational requirements. The findings contribute to advancing control methodologies in wind energy systems and suggest directions for future research and practical implementation.

Optimized Backstepping Cooperative Control for Output-Constrained Stochastic Nonlinear Network Systems via a Multibridge-Hole Function.

In this article, a new leader-following tracking control approach is investigated for stochastic multiagent systems with multibridge-hole output constraints. The multibridge-hole output constraints mean that the output of the system is constrained in some intervals and unconstrained in other intervals. The constrained and unconstrained intervals can be set arbitrarily. By designing a new shift function to construct the barrier Lyapunov function, the optimal controller is constructed by combining the backstepping technique with the adaptive dynamic programming technique. The model network is used to estimate the unknown disturbances and uncertainty terms in the system. The critic network and the actor network are constructed such that the designed controller adheres to the Bellman optimality principle and gives the optimal solution of the system. The proposed control method is versatile and compatible with various types of output constrained control problems, such as unconstrained control problems, constrained control problems, and delay constrained problems without changing the structure of the controller. Finally, some simulation results are given to verify the effectiveness of the method.

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.

Output-feedback formation tracking control of autonomous surface vessels with collision avoidance

In this paper, a formation control problem with collision avoidance is investigated for underactuated surface vessels with position–heading measurements. Each vessels is subject to actuator magnitude and rate saturations. At first, an anti-saturation nonlinear extended state observer is developed to recover the linear velocity and yaw rate as well as unknown uncertainty and disturbances. Then, observer-based formation control laws are designed based on an artificial potential functions, obstacle avoidance yaw references and a backstepping technique. The stability of closed-loop formation control system is proved. The salient features of this paper are as follows. First, formation control with the capability of collision avoidance is achieved by using artificial potential functions and obstacle avoidance yaw references, which is more aggressive. Second, the proposed controller is able to deal with the magnitude and rate constraints of the actuator. Third, the proposed anti-saturation nonlinear extended state observer can achieve better estimation results for rapidly changing signals. Simulation results are given to substantiate the proposed formation control laws.

Distributed adaptive tracking consensus control for a class of heterogeneous nonlinear multi-agent systems

The proposed approach differs from existing works in that it models the constraints of each follower as a nonlinear strict feedback system, rather than relying on a desired reference trajectory for accessible subsystems. To address the limitations caused by uncertain terms in systems, radial basis functions neural networks are utilized to compensate for these unknown nonlinear terms. This leads to a novel distributed adaptive consensus tracking control protocol for high-order nonlinear heterogeneous multi-agent systems, based on the backstepping technique. By introducing a non-zero parameter in the traditional radial basis functions neural network, a new universal approximation is constructed, which overcomes the limitation of the approximation’s finite domain. Additionally, the approximation precision can be adjusted online using provided laws, and the dimension explosion of virtual and real control gains can be avoided through the use of the designed control approach. Simulation results are provided to demonstrate the effectiveness of the proposed control scheme.

Observer-based reinforcement learning for optimal fault-tolerant consensus control of nonlinear multi-agent systems via a dynamic event-triggered mechanism

In this article, an adaptive optimized consensus tracking control problem is studied for nonlinear strict-feedback dynamic multi-agent systems (MASs), considering both unmeasurable system states and time-varying bias faults. By utilizing the backstepping technique, we develop an adaptive reinforcement learning (RL) algorithm within the observer-critic-actor architecture, specially designed to compensate for the lack of state information and derive control inputs, thereby achieving approximate optimal control. Moreover, an event-triggered mechanism is introduced in the sensor-to-controller channel, which dynamically adjusts the triggering threshold online and employs event-sampled states to initiate control actions. To address discontinuities caused by state triggering, we construct virtual controllers that continuously sample state signals and reconfigure the actual controller based on previously triggered states. The outputs of the MASs are shown to accurately track the desired reference signals while ensuring the boundedness of all closed-loop signals. Additionally, the proposed controller is verified to be devoid of Zeno behavior. Finally, the effectiveness of our control methodology is demonstrated through numerical simulation.

Finite-time error constraint control for multi-AUV systems with unknown uncertainties based on observer and tan-type barrier Lyapunov function

PurposeAutonomous underwater vehicle (AUV) is widely used in resource prospection and underwater detection due to its excellent performance. This study considers input saturation, nonlinear model uncertainties and external ocean current disturbances. The containment errors can be limited to a small neighborhood of zero in finite time by employing control strategy. The control strategy can keep errors within a certain range between the trajectory followed by AUVs and their intended targets. This can mitigate the issues of collisions and disruptions in communication which may arise from AUVs being in close proximity or excessively distant from each other.Design/methodology/approachThe tracking errors are constrained. Based on the directed communication topology, a cooperative formation control algorithm for multi-AUV systems with constrained errors is designed. By using the saturation function, state observers are designed to estimate the AUV’s velocity in six degrees of freedom. A new virtual control algorithm is designed through combining backstepping technique and the tan-type barrier Lyapunov function. Neural networks are used to estimate and compensate for the nonlinear model uncertainties and external ocean current disturbances. A neural network adaptive law is designed.FindingsThe containment errors can be limited to a small neighborhood of zero in finite time so that follower AUVs can arrive at the convex hull consisting of leader AUVs within finite time. The validity of the results is indicated by simulations.Originality/valueThe state observers are designed to approximate the speed of the AUV and improve the accuracy of the control method. The anti-saturation function and neural network adaptive law are designed to deal with input saturation and general disturbances, respectively. It can ensure the safety and reliability of the multiple AUV systems.

Adaptive deep neural network optimized control for a class of nonlinear strict‐feedback systems with prescribed performance

SummaryIn this article, an adaptive deep neural network (DNN) optimized control strategy is developed for a class of nonlinear strict‐feedback systems with prescribed performance. First, the DNN is applied to approximate the unknown function, and the weight update law is designed to reduce the mathematical challenge based on the first‐order Taylor's series. Second, the optimized backstepping technique is utilized to construct virtual and actual controllers in the backstepping process to achieve the overall control optimization of the system. Next, a control strategy based on the time‐varying switching function and the quartic barrier Lyapunov function is employed to achieve the prescribed performance. Then, the tracking error can converge to the prescribed accuracy within the prescribed time, and every signal within the system has a bound. Finally, the particle swarm optimization algorithm is utilized to search for the designed parameters and simulation examples to verify the effectiveness of the control strategy.