Adaptive 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.

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.

Adaptive fuzzy event-triggered control for a class of nonlinear time-delay multi-agent systems with dead zone and partial state constraints

This paper presents an adaptive fuzzy event-triggered control (ETC) method for a class of time-delay nonlinear multi-agent systems (MASs) with dead zone (DZ) and partial state constraints (PSCs). It should be pointed out that the states considered in this paper are unmeasurable and part of the system states are constrained by time-varying boundary. By utilizing fuzzy logic systems (FLSs) and backstepping design framework, a fuzzy state observer is constructed to estimate the unmeasured states, while the introduction of a time-varying barrier Lyapunov function (BLF) addresses the partial state constrained problem. Furthermore, during the design process of the state observer, compensation for the influence of the unknown DZ input on the system is achieved through utilization of known designed event-triggered input signal and adaptive parameter. Building upon this foundation, employing the Lyapunov stability theory and adaptive backstepping technique with ETC strategy, the developed distributed control mechanism demonstrates that all variables of the closed-loop system are bounded, the consensus error of the system can converge to a small region of origin and Zeno behavior can be ruled out. Finally, two simulation examples further illustrate the proposed control strategy and theorem.

Observer-based adaptive neural network control design for nonlinear systems under cyber-attacks through sensor networks

This paper considers the adaptive neural tracking control for uncertain nonlinear strict-feedback systems under state-dependent cyber-attacks through sensor networks. As a distinctive feature, by constructing a novel adaptive neural observer, the estimates of system states are used for feedback control instead of the compromised system states corrupted by sensor attacks, such that the assumption on the derivative of attack weight can be removed from the adaptive controller design process. Then, an observer-based control scheme is developed such that all the system signals are bounded and the tracking error converges to a small neighborhood of zero. During the procedure of control design, adaptive backstepping technique is combined with radial basis function neural networks (RBFNNs) to construct controllers. Finally, two examples validate the efficacy of the proposed control scheme.

Adaptive formation control of nonholonomic multirobot systems with collision avoidance and connectivity maintenance

In this paper, an adaptive cooperative formation controller is developed to force a swarm of nonholonomic mobile robots with limited sensing ranges to move along the desired reference trajectory in a predetermined formation, while maintaining communication connectivity among the initial user-specified connected robots and guaranteeing no collision between the robots. Both kinematic models and dynamic systems with parametric uncertainties are discussed. The presence of parametric uncertainties is handled by adaptive control technique. A novel artificial potential function, which is based on a 4 times differential pseudo bump function, is constructed to achieve collision avoidance and connectivity maintenance. The control design is based on a fusion of potential function, adaptive backstepping technique, and Lyapunov synthesis. The cooperative formation controller is proven to be stable and can guarantee that there is no collision between any robots and the initial connectivity of the communication network can be always maintained. The proposed formation control approach is decentralized in the sense that the control action on each robot depends only on information from its neighbours and the desired trajectory of the group. Comparative simulation and experiment studies are performed to show the effectiveness of the proposed formation controller.

Finite-Time Adaptive Fuzzy Backstepping Control for Quadrotor UAV With Stochastic Disturbance

This paper proposes an adaptive fuzzy output feedback control approach for quadrotor unmanned aerial vehicles (QUAV) with stochastic disturbances, besides which we consider the unmeasurable states and unknown nonlinear functions. The QUAV system contains stochastic terms which are not bounded and not differentiable. By combining the It <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\hat{\rm \textbf{o}}$</tex-math> </inline-formula> differential equation with finite-time theory, a novel stochastic finite-time stability controller for QUAV is raised for the first time. The fuzzy logic system (FLS) is utilized to approximate the unknown nonlinear functions in the model. Dynamic surface control technology is introduced to reduce the complexity of differential. Furthermore, an observer with FLS is designed through the adaptive backstepping technique to estimate the immeasurable states. It is proved that this control approach can ensure that all states of the closed-loop QUAV system are semi-global and finite-time stable in probability. Meanwhile, the errors of system outputs and observer converge to a small neighborhood of origin. The simulation results show the effectiveness of the proposed method. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —In practical applications, many systems are often affected by internal and external disturbances, and not all of them can be described by mathematical models, so they are called stochastic disturbances. Taking the QUAV as an example, when the system is disturbed by internal parameters, external environment, system input, sensor error, and other stochastic factors, the deterministic system can no longer accurately describe the controlled object. In this paper, the QUAV is regarded as a stochastic system for the first time, and a novel controller is designed to solve the above problems. In addition, the QUAV needs fast action in some applications, such as emergency collision avoidance, which has high requirements for the convergence performance of the controller. Therefore, studying the finite-time control for QUAV systems with stochastic disturbances is necessary. At the same time, this paper also considers the problem that the state is not measurable and the system contains unknown nonlinear equations.

Adaptive fixed‐time anti‐synchronization and synchronization control for Liu‐Chen‐Liu chaotic systems with actuator faults

SummaryIn this paper, the fixed‐time anti‐synchronization and synchronization fault‐tolerant control problem is considered for two identical Liu‐Chen‐Liu chaotic systems with uncertain parameters. With the help of fixed‐time stability theory and adaptive backstepping method, we propose two novel adaptive controllers. In the control scheme proposed in this paper, the adaptive backstepping technique is used to deal with the unknown parameters contained in the chaotic systems. Besides, the piecewise functional method is used to solve the singularity problem in the controller design process. The designed controllers achieve anti‐synchronization and synchronization of two identical Liu‐Chen‐Liu chaotic systems within the preset time interval. Simulation results are conducted to show the effectiveness of two proposed adaptive controllers.

Adaptive fuzzy finite-time output feedback fault-tolerant control for MIMO stochastic nonlinear systems with non-affine nonlinear faults

This paper investigates adaptive fuzzy finite-time output feedback fault-tolerant tracking control problem for multiple-input multiple-output (MIMO) stochastic non-strict feedback nonlinear systems with non-affine nonlinear faults and states unmeasured. Firstly, high-gain fuzzy state observers are constructed to overcome the state unmeasured problem in the system. Secondly, the mean-value theorem and input compensation techniques are employed to decouple non-affine nonlinear faults, and the resulting unknown control coefficients problem is handled using Nussbaum functions. In addition, dynamic surface control techniques and error compensation mechanisms are considered in the controller design, which effectively decreases the computational complexity of the control scheme. By combining the adaptive backstepping technique with finite-time control, a novel adaptive fuzzy dynamic surface finite-time output feedback fault-tolerant tracking control algorithm is proposed. The designed controller guarantees that all signals in the stochastic systems are semi-global finite-time stable in probability (SGFSP) as well as the tracking errors can converge to a small neighborhood within the origin in finite-time. Finally, two simulation examples are introduced to verify the effectiveness of the suggested control strategy.

Fault-tolerant controller design based on adaptive backstepping for tower cranes with actuator faults

Due to the widespread application and significant investment required for a single crane, there is an increased emphasis on crane safety and service life. Fault-tolerant control as an effective solution to unexpected faults has been widely studied recently. However, most fault-tolerant control methods require redundant actuators or a complex design process, which is unsuitable for the tower crane. Following these problems, a fault-tolerant controller based on an adaptive backstepping technique is proposed. Firstly, the system states are reconstructed and written as a cascade system. Secondly, a fixed-time convergence optimized backstepping controller is proposed to achieve smooth control of the tower crane without generating sudden or abrupt values. Then, an adaptive approach has been proposed to update fault parameters for the crane system in case of a sudden fault occurrence. Finally, after conducting comparison tests, it has been determined that the proposed controller not only performs exceptionally well in terms of position accuracy and swing elimination, but also maintains a satisfactory control performance when faced with sudden faults.

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.

Adaptive Fuzzy Output Feedback Fault-Tolerant Control for Active Suspension Systems

In this paper, a novel adaptive fuzzy output feedback fault-tolerant control (FTC) method is proposed for active suspension systems. The quarter active suspension systems studied in this paper contains electromagnetic actuator faults and unavailable state variables, such as the velocity of active suspensions and the electric current intensity of electromagnetic actuators. First, the complex spring nonlinear dynamics are approximated by fuzzy logic systems (FLSs), and the unmeasurable states are estimated by a fuzzy state observer. Based on an adaptive backstepping technique along with specific Lyapunov functions, a novel adaptive fuzzy output feedback FTC design is presented. To eliminate the need for knowing efficiency indexes, a fault compensation strategy is also developed by utilizing parameter estimation technique. In the presence of electromagnetic actuator failure, all vertical vibration states of the active suspension system remain stabilized. Eventually, the feasibility of the proposed control algorithm is evaluated through random road surface and bump road surface tests.

Fuzzy adaptive time‐varying formation control of USVs with actuator faults

SummaryThis paper investigates the fuzzy adaptive time‐varying formation control problem for fully‐actuated unmanned surface vehicles (USVs) systems. The studied USVs systems include uncertain dynamics and actuator faults. Fuzzy logic systems (FLSs) and disturbance observer are employed to estimate uncertain nonlinear dynamics in system model and external time‐varying disturbances, respectively. Meanwhile, the prescribed performance control (PPC) technique is applied to construct the constraint requirements of collision avoidance and connectivity preservation in time‐varying formation control. Additionally, a new robust adaptive fault‐tolerant control (FTC) algorithm is presented. Hence, by the aid of adaptive backstepping technique with performance functions, a robust fuzzy adaptive time‐varying formation FTC scheme of time‐varying formation is developed. The proposed formation control scheme not only has the advantages of avoiding collision and preserving connectivity, but also ensures all the signals are uniformly ultimately bounded (UUB). Finally, the simulation results are provided to demonstrate the effectiveness of the proposed approach.

Multi-stage trajectory tracking of robot manipulators under stochastic environments

For robot manipulators composed of Lagrange subsystems driven by direct current (DC) motors under stochastic environments, multi-stage trajectory tracking is investigated in this paper. The main challenge is how to achieve the end-effector drive of manipulators from a given initial state to a final state. First, the inverse kinematics method and the partition of the task space are adopted to tackle multi-stage trajectory planning. Second, the adaptive backstepping technique is used to design tracking controller for stochastic Lagrangian subsystems. Then, based on the state-dependent switching signal, a multi-stage switched controller is designed for trajectory tracking of robot manipulators. All signals in the close-loop error switched system are bounded in probability, and the tracking error in mean square can be made arbitrarily small enough by parameters-tuning The effectiveness of the proposed control method is illustrated by simulation results.

Adaptive fixed-time path following cooperative control for autonomous surface vehicles based on path-dependent constraints

This paper introduces a fixed-time adaptive path-following cooperative control approach for autonomous surface vehicles (ASVs), aimed at improving navigation accuracy and safety in practical scenarios. The scheme ensures that ASVs accurately follow the reference path during navigation while satisfying position and heading angle constraints. To address the position constraint challenge, an adapted version of the universal barrier Lyapunov function is employed for path-dependent constraint function. Furthermore, a novel form of path-dependent constraint function is introduced, relying on path parameters instead of direct time variables. A new adaptive backstepping technique is also developed to tackle fixed-time convergence issues, mitigate the complexity surge in controller design, and account for the model’s uncertain dynamics. The study demonstrates that this control scheme enables the ASV’s position and heading errors to converge near the equilibrium point at a fixed time rate while consistently satisfying path-dependent constraints. The efficacy of the proposed scheme is further verified through simulation and experimental studies.

Event-triggered adaptive control for upper-extremity therapeutic robot in active-assist mode: A simulation study

Upper extremity rehabilitation exercises are essential for individuals recovering from injuries or conditions that affect their arm and hand functionality. Robot-assisted therapy has gained popularity as it offers precise control, objective assessment, and customizable treatment programs. However, several challenges persist, including uncertainties in the patient’s and robot dynamics, limited communication, and the need to maintain a compliant patient-robot interaction. Therefore, an event-triggered adaptive backstepping (ETAB) admittance control strategy is proposed in this work to address these challenges. Initially, the framework of the robot-assisted therapeutic process is briefly explained. The architecture of the proposed control strategy is formulated with two control modules. Thereafter, the adaptive backstepping technique is employed with an online adaptation law to deal with dynamic uncertainties. Moreover, the problem of limited communication is handled using the proposed design of a Lyapunov-based event-triggered mechanism. The admittance controller is integrated to maintain a compliant patient-robot interaction and consider the participation of the patient in the therapeutic sessions. The effectiveness of the proposed control strategy is verified using an end-effector type rehabilitation robot performing two different rehabilitation exercises. Furthermore, a comparative performance analysis is carried out with the proportional-integral-derivative controller (PID) and the adaptive sliding mode controller (ASMC). Based on the simulation runs, the proposed controller has shown promising tracking behavior, appropriate compliant interaction, and considerable reduction in the transmitted signals during the passive and active-assist training exercises.

Adaptive asymptotic tracking control of autonomous underwater vehicles based on Bernstein polynomial approximation

In this article, an adaptive asymptotic tracking control approach is first proposed for the autonomous underwater vehicle (AUV) on the horizontal plane by using the Bernstein polynomial approximation. Bernstein polynomials aim to compensate for the synthetical uncertainties including unknown model dynamics and environmental disturbances. However, they cannot be directly used due to the unknown polynomial coefficients. To avoid this trouble, the adaptive backstepping technique is applied to estimation. Considering that the adaptive backstepping can only procure the bounded steady tracking errors and suffer from the redundancy of adaptive parameters, we further integrate the σ-modification and the minimum learning parameter (MLP) technique with the Bernstein polynomial approximation, so as to guarantee the high-precision tracking performance of AUVs with the asymptotic convergent tracking errors and less computation burden. The direct Lyapunov’s method and the Barbalat’s lemma are introduced for proving the stability of the control system. Finally, simulation reveals the advantage of the proposed scheme.

Adaptive Finite-Time Tracking Control of Nonlinear Systems With Dynamics Uncertainties

In this paper, the problem of adaptive backstepping finite-time tracking control is investigated for a class of strict-feedback nonlinear systems with unmodeled dynamics and dynamic disturbances. A modified finite-time dynamic signal is first introduced to dominate the dynamic disturbance. By using the adaptive control, backstepping technique, and finite-time stability theory, an adaptive finite-time tracking controller is developed. Under the proposed control scheme, the finite-time tracking performance and the boundedness property of all signals in the closed-loop system are ensured. Finally, simulation results check the effectiveness of the suggested approach.

Output-Feedback Adaptive Neural Network Control for Uncertain Nonsmooth Nonlinear Systems With Input Deadzone and Saturation.

Nonsmooth nonlinear systems can model many practical processes with discontinuous property and are difficult to be stabilized by classical control methods like smooth nonlinear systems. This article considers the output-feedback adaptive neural network (NN) control problem for nonsmooth nonlinear systems with input deadzone and saturation. First, the nonsmooth input deadzone and saturation is converted to a smooth function of affine form with bounded estimation error by means of the mean-value theorem. Second, with the help of approximation theorem and Filippov's differential inclusion theory, the given nonsmooth system is converted to an equivalent smooth system model. Then, by introducing a proper logarithmic barrier Lyapunov function (BLF), an output-feedback adaptive NN strategy is set up by constructing an appropriate observer and adopting the adaptive backstepping technique. A new stability criterion is established to guarantee that all the signals in the closed-loop system are semiglobally uniformly ultimately bounded (SGUUB). Finally, comparative simulations through Chua's oscillator are offered to verify the effectiveness of the proposed control algorithm.

Adaptive event-triggered fuzzy tracking control for underactuated surface vehicles under external disturbances

In this paper, the tracking control problem of underactuated surface vehicles with modeling uncertainties and unknown external disturbances is studied. The fuzzy logic system is applied to approximate the uncertainties in the model. A new disturbance observer with a learning factor is introduced to compensate external disturbances. It can improve observation precision and lead to faster tracking of the system. According to this, and combining the adaptive backstepping technique with the command-filter and event-triggered mechanism, the adaptive fuzzy control method is proposed to guarantee the boundedness of all the closed-loop signals. It is also proved that the tracking errors of the position and yaw angle can keep within a certain precision in finite time. Simulation on the surface vessel verifies the feasibility, and the proposed method is insensitive to the main design parameters.

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.