Tangent Barrier Lyapunov Function Research Articles

Saturated FLS-based control of a marine manipulator with state delays and output constraints

In this paper, we propose a saturated fuzzy logic system (FLS) based robust tracking control method for a marine manipulator. To handle time-varying output constraints, we introduce a tangent barrier Lyapunov function (TBLF). Additionally, we employ a FLS to approximate the model uncertainties and unknown disturbances, ensuring no estimation drift through the use of a smooth projection function. To accurately simulate real operation scenarios, we consider state delays and input saturation. The state delay is addressed using a Lyapunov–Krasovskii functional technique. Through the developed control strategy, it is guaranteed that the tracking errors converge to the neighborhood of zero as the time approaches infinity, while respecting output constraints and input saturation. The effectiveness of the proposed controller is validated through extensive simulations.

Prescribed performance sliding mode control for the bursting oscillation of a fractional-order hydro-turbine governing system based on time-varying tangent barrier Lyapunov function

A dynamic model for a hydro-turbine governing system is established that accounts for the periodic excitation caused by the dynamic transfer coefficient. The dynamic analysis shows that the turbine regulation system produces bursting oscillatory behaviors when its transmission coefficient changes. The bursting oscillation behavior can adversely affect its stable operation. In response to this challenge, a prescribed performance sliding mode controller based on the time-varying tangent barrier Lyapunov function is proposed. Specifically, a time-varying constraint function of the exponential decay type is initially established. This function is then combined with the prescribed performance constraint function and the dynamic sliding surface to construct the time-varying tangent barrier Lyapunov function. In addition, to ensure that the system output exhibits a slight overshoot and fast-tracking speed at the initial time while satisfying the steady-state index, the relevant parameters of the time-varying constraint function are presented. Finally, the stability of the proposed controller is rigorously proven, verifying the effectiveness of the controller under five working conditions. The simulation results demonstrate that the prescribed performance sliding mode control based on the time-varying tangent barrier Lyapunov function can enable the hydro-turbine governing system to quickly break away from the bursting oscillation state. The proposed control strategy achieves faster convergence times for the rotor angle and generator speed (0.3 s) as well as the guide vane opening (0.3 s) than the ordinary sliding mode controller. The proposed strategy is also superior in controlling the steady-state error, which means that the proposed controller has a faster response speed, higher control accuracy, and optimized transient performance of the system than the traditional controller.

Adaptive Neural Control of Connected Vehicular Platoons With Actuator Faults and Constraints

This paper focuses on the adaptive neural control problem for a connected vehicles platoon system with external disturbances, actuator fault and constraints. Then, the tangent barrier Lyapunov function is introduced into the control design to solve the time-varying position and velocity constraints in a vehicle platoon. Since the selected engine dynamics model is nonlinear, the neural network is adopted to approximate the unknown internal vehicle dynamics. Moreover, the actuator fault effect is addressed by the designed adaptive law designed based on the projection operator. It can be eventually confirmed that all the involved closed-loop signals are bounded based on the Lyapunov stability theory. Finally, a comparative simulation shows the effectiveness of the proposed control scheme.

The Fixed-Time Observer-Based Adaptive Tracking Control for Aerial Flexible-Joint Robot with Input Saturation and Output Constraint

The aerial flexible-joint robot (AFJR) manipulation system has been widely used in recent years. To handle uncertainty, the input saturation and the output constraint existing in the system, a fixed-time observer-based adaptive control scheme (FTOAC) is proposed. First, to estimate the input saturation and disturbances from the internal force between the robot and the flight platform, a fixed-time observer is designed. Second, a tangent-barrier Lyapunov function is introduced to implement the output constraint. Third, adaptive neural networks are introduced for the online identification of nonlinear unknown dynamics in the system. In addition, a fixed-time compensator is designed in this paper to eliminate the adverse effects caused by filtering errors. The stability analysis shows that all the signals of the closed-loop system are bounded, and the system satisfies the condition of fixed-time convergence. Finally, the simulation results prove the superiority of the proposed control strategy by comparing it with the previous schemes.

Fixed-time self-structuring neural network fault-tolerant tracking control of underactuated surface vessels with state constraints

In this paper, a fixed-time fault-tolerant control strategy is proposed for trajectory tracking of underactuated surface vessels (USVs) with input saturation. A predefined region boundary function is proposed, which has all predefined fixed-time convergence properties and provides predefined specifications for tracking errors. To achieve the predetermined tracking performance, a fixed-time adaptive neural network state constrained fault-tolerant controller is proposed based on dynamic surface control technology, a back-stepping program, and an asymmetric time-varying tangent barrier Lyapunov function (ATVTBLF). The unknown external environment disturbances and complex continuous unknown nonlinear terms are approximated by a self-structuring neural network (SSNN), which can improve the robustness of the control system to unknown parameters and guarantee the tracking performance of the control system. The number of neurons of the SSNN can be adjusted online according to the approximation efficiency, which can reduce the amount of calculation of the control system. Based on Lyapunov stability theory, it is proven that the closed-loop system is bounded and stable in a fixed time, and the tracking error is always kept within the constraint range. The simulation results show that the underactuated surface vessel control system has good tracking performance.

Adaptive neural network independent joint-based control for an ODE-PDE rigid-flexible manipulator with multiple constraints

This paper deals with the adaptive neural network control of a nonlinear rigid-flexible manipulator subject to external disturbances and multiple constraints. The system dynamic is modeled by ordinary and partial differential equation (ODE and PDE) based on Hamilton’s Principle. An adaptive neural network sliding mode control strategy is designed to estimate the unknown disturbances and uncertain parameter. The sliding surface consisting of angular error, angular velocity error, and end-point vibration information is proposed based on the energy analysis of the flexible beam. The tangent barrier Lyapunov function is used to ensure the angle errors and end-point deflection within the restrictions. It is shown that the joint motion and vibration of the flexible beam can be adjusted only with an independent joint control input, and no boundary force input is required for vibration suppression. The stability is obtained by semi-group theory and LaSalle’s Invariance Principle. Simulation results demonstrate the effectiveness of the control strategy.

Fuzzy Adaptive Control for Vehicular Platoons With Constraints and Unknown Dead-Zone Input

In this paper, an adaptive fuzzy control problem is studied for a connected automated vehicles platoon subject to unknown dead-zone input and constraints. To better handle the unknown nonlinear dynamical functions and disturbances, the nonlinear dynamics model is transformed to a new model. Then, the fuzzy logic system (FLS) is used to identify the unknown nonlinear functions. A dead-zone inverse technique is introduced to eliminate the negative effects of the unknown dead-zone input nonlinearity. In the framework of backstepping, the tangent barrier Lyapunov function (BLF) is introduced in this paper, and a distributed adaptive fuzzy control scheme is designed so that the position, velocity and acceleration of the vehicle platoon do not violate the given constrained boundaries. Finally, based on the Lyapunov stability theory, it is noted that all signals in the closed-loop system are bounded and the tracking errors converge to a small neighborhood of the origin. The effectiveness of the proposed approach is validated by simulation results.

Adaptive Output Feedback Fuzzy Fault-Tolerant Control for Nonlinear Full-State-Constrained Switched Systems.

In this article, an output feedback adaptive fuzzy tracking control method for a class of switched uncertain nonlinear systems with actuator failures and full-state constraints is proposed under an arbitrary switching signal combining the dynamic surface technique. Since the state variables of the system under study are not measurable, a fuzzy observer is constructed to identify the unmeasured states. The actuator failures are considered in the system. To compensate this failure, a fault-tolerant controller is proposed. Moreover, each state needs to be kept within the constraints, so the tangent Barrier Lyapunov function is selected to solve the full-state constraint problem, and the unknown nonlinear function is approximated by fuzzy-logic systems (FLSs). We also proved that all signals in the closed-loop system are bounded. Furthermore, the states can be kept within the predetermined range even if the actuator fails. Finally, a simulation example is given to verify the effectiveness of the proposed control strategy.

Tangent barrier Lyapunov function based adaptive event-triggered control for uncertain flexible beam systems

The adaptive event-triggered control problem is studied for the flexible beam system modeled by partial differential equations (PDEs) with uncertain system parameters and state constraint. In the design process of the controller, the event-triggered mechanism of relative threshold strategy is added to reduce the communication pressure. It further makes the communication process more flexible and improves the system working ability. The tangent barrier Lyapunov function (TAN-BLF) is selected to ensure that the system states satisfy their corresponding time-varying constraint bounds. The adaptive technique is chosen to solve the uncertain parameter problem. The system stability is verified on account of Lyapunov stability analysis method, and the boundedness of all system signals is proved. Furthermore, the Zeno behavior is successfully avoided. Finally, simulation results show the effectiveness and rationality of the proposed control strategy.

Adaptive time-varying constraint control for uncertain flexible beam systems

In this paper, the vibration control design of the Euler–Bernoulli beam with time-varying constraints is studied when the mass, bending stiffness and tension of the system parameters are known or unknown. For satisfying the time-varying constraints, the controller is designed and the system stability is analysed based on the tangent barrier Lyapunov function (TAN-BLF). Among them, the uncertainty of system parameters is dealt with by the adaptive method. In both cases, the vibration of the Euler–Bernoulli beam can be well restrained without violating the constraint conditions, and all signals in the system are bounded. Finally, the effectiveness of the proposed method is illustrated by a simulation example.

Adaptive Event-Triggered Output Feedback Control for Nonlinear Switched Systems Based on Full State Constraints

Aiming at the research content of tracking control for a class of nonlinear uncertain switched systems including full state constraints, a novel event-triggered adaptive fuzzy output feedback control scheme is given. The systems studied need to use the approximation principle of fuzzy logic systems (FLSs) to solve the nonlinear smooth function with unknown terms. For ensuring that all states of the systems are within the time-varying constraint limits, the stability of the switched systems is verified by utilizing tangent barrier Lyapunov function (Tan-BLF). Based on the potential barrier Lyapunov function (BLF) and backstepping recursive construction method, the adaptive law, controller and event-triggered mechanism of the subsystem are designed. The proposed method will make that the signal is bounded. Moreover, the tracking error can be adjusted to the neighborhood closed to the origin. Simulation examples indicate the feasibility of the method.

Finite-Time Output Feedback Robust Controller Based on Tangent Barrier Lyapunov Function for Restricted State Space for Biped Robot

This study has the aim of introducing a new type of trajectory tracking robust controllers for a class of rehabilitation robotic system considering the articulations restrictions. The robotic device consists of a suspended biped configuration. The suggested robust control considers the application of state depending gains which provide finite-time convergence for the tracking deviation. The state restrictions are fulfilled by the implementation of controller gains estimated by a class of the controlled tangent barrier Lyapunov function. Stability analysis for the tracking error yields the explicit design of the state dependent gains. The rate of convergence for the controller design is enhanced using a matrix inequality convex optimization method. Based on the forward complete characteristic of the suggested rehabilitation device, it is allowed using a finite-time convergent super-twisting-based differentiator to concrete an output feedback realization of the proposed controller. A computerized model of the tendered rehabilitation robot provides a reliable testing platform to the suggested roust controller. Numerical evaluations appear to serve as an indirect confirmation for the tracking error convergence, satisfying the articulation restrictions, and the effect of the gain optimization design. For comparison purposes, the regular state feedback control design is considered as benchmark. The faster convergence of the mean square estimation of the tracking error justifies the design of the proposed control design as well as the state feedback structure justifies the origin is a fixed-time stable equilibrium point for the space of tracking error at the same time that state space restrictions remain satisfied. The experimental evaluations of the proposed controller justifies the barrier controller which, in spite of the modeling uncertainties and the implementation issues, tracked the reference trajectories.

Adaptive Fuzzy Tracking Control of Switched MIMO Nonlinear Systems With Full State Constraints and Unknown Control Directions

In this brief, an adaptive fuzzy tracking control method is proposed for switched multi-input multi-output (MIMO) nonlinear systems with time-varying full state constrains (TFSCs) and unknown control directions. First, the fuzzy logic systems are utilized to approximate unknown dynamic functions. A tangent barrier Lyapunov function (BLF-Tan) is used to solve the problem of TFSCs, and the unknown control directions problem is addressed by applying Nussbaum-type function. Then, an adaptive tracking controller is constructed by the backstepping technique. Under the designed control scheme, all the systems signals are derived to be bounded, and the tracking error of the systems is converged to a neighborhood near zero. Finally, the simulation example illustrates the control design programme is reasonable and effective.

Adaptive neural network state constrained fault-tolerant control for a class of pure-feedback systems with actuator faults

In this paper, an adaptive neural network (NN) constrained fault-tolerant control (FTC) method is proposed for a class of nonlinear pure feedback systems with actuator faults and state constraints. By designing a fault-tolerant compensation controller and a new asymmetric time-varying tangent Barrier Lyapunov function (ATVTBLF), the problem of time-varying asymmetric state constraints caused by actuator failure is solved. The actuator takes into account both loss of effectiveness and bias fault. Different from the existing asymmetric BLF, the new BLF solves the problem of asymmetry under tangent constraints and expands the application range of the asymmetric constraint. NN is used to approximate the unknown items generated in the process of designing fault-tolerant controllers. Based on the Lyapunov stability analysis, it is proved that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB), and all states do not violate the bounds. Finally, the simulation example verifies the effectiveness of the proposed method.

Observer-Based Adaptive Neural Output Feedback Constraint Controller Design for Switched Systems Under Average Dwell Time

Aiming at a class of switched uncertain nonlinear strict-feedback systems under the action of average dwell time switching signal, this paper proposes a novel adaptive neural network output feedback tracking control based on the consideration of the full state constraints. The controller is proposed based on neural networks. One of the key characteristics of the system discussed is that the state variables cannot be measured and the system states need to be kept within the constraint ranges. For the sake of estimating the unmeasured states, the observer is constructed. In order to ensure all states which are within the time-varying boundary, the tangent barrier Lyapunov function (BLF-Tan) is selected in the design process. The boundedness of the closed-loop signals with average dwell time is guaranteed by the designed controllers and all the states limit in their constrained sets. It has been proved that the output tracking error converge to a small neighborhood of zero. In addition, the significance of the presented control strategy is verified and tested by a simulation example.

Design and analysis of robust state constraint control for direct yaw moment control system

ABSTRACT This paper is concerned with the problem of robust constraint control for direct yaw moment control (DYC) system with sideslip angle. A two degree of freedom vehicle dynamics model is considered here. The tangent barrier Lyapunov function (BLFs-Tan) is embedded into the systematic controller design for handling sideslip angle constraint problems. A robust nonlinear constraint control scheme based on BLFs-Tan is proposed not only to track the reference trajectory but also to guarantee no violation on the sideslip angle constraint and refrain from vehicle instability. Simulation results indicate that the proposed scheme can guarantee there will be no violation on sideslip angle constraints and avoid vehicle instability.

Fixed-Time Tracking Control for Flexible Joint Manipulator With Prescribed Performance Constraint

This paper studies the transient and steady performance constraints on flexible joint manipulator system with exogenous disturbance, and proposes a fixed-time prescribe performance tracking control method based on the singular perturbation model. For the fast subsystem, a subcontroller with superior transient performance is proposed that guarantees the suppression of flexible vibration in fixed-time. The remaining slow subsystem can be linked with rigid methods to achieve output constraints, a type of time-varying error constraint boundary is first constructed, which broadens the initial error constraint boundary of the time-varying tangent barrier Lyapunov function. Then, a slow subcontroller based on a non-singular fast-integration terminal sliding mode is constructed to make any initial tracking error converge in fixed-time. Finally, a nonlinear disturbance observer is used to counteract the exogenous disturbance. The simulation results show that the controller achieves the prescribe performance.

Adaptive neural torsional vibration suppression of the rolling mill main drive system subject to state and input constraints with sensor errors

Torsional vibration often occurs in rolling mill drive system, which seriously affects the product quality accuracy and the service life of transmission equipment. This paper studies the adaptive neural torsional vibration suppression control problem for the rolling mill main drive system with state and input constraints subject to unknown measurement sensitivities. Firstly, considering the nonlinear friction between the work roll and strip, nonlinear damping at the motor and the load and unknown uncertainties on system parameters, a new torsional vibration model of the main drive system of rolling mill is established. Then, by selecting the proper asymmetric tangent barrier Lyapunov function, the motor torque control law is proposed based on backstepping algorithm. The adaptive neural networks are introduced to solve the unknown uncertainties and the unknown measurement errors and a continuous differentiable Gaussian error function is employed to deal with actuator saturation. It is strictly proved that the designed main drive torsional vibration system is stable and the performances of the transformed states are preserved. Finally, simulation shows the validity and the advantages of the proposed algorithm.

Adaptive Finite-Time Tracking Control for Continuous Stirred Tank Reactor With Time-Varying Output Constraint

This article proposes an adaptive finite-time control plan for a nonlinear uncertain continuous stirred tank reactor (CSTR) with time-varying output constraint. The challenge in designing this control plan is how to achieve that system output never exceeding the specified time-varying compact as well as achieves finite-time convergence. By introducing the mean value theorem, the considered CSTR is decomposed to nonlinear systems (NSs) with pure-feedback structure. To deal with time-varying output constraint, tangent barrier Lyapunov function (TBLF) is applied in the adaptive finite-time controller design process. The closed-loop system stability can be identified by the presented adaptive finite-time control approach with the TBLF. Finally, the simulation graphics on CSTR are given to indicate the validity of the presented control approach.

Adaptive fault tolerant control for hypersonic vehicle with input saturation and state constraints

This paper proposes an adaptive control scheme for hypersonic vehicle with external disturbances, parametric uncertainties, actuator failures, input saturation and state constraints. Firstly, the longitudinal model of generic hypersonic vehicle is divided into velocity subsystem and altitude subsystem. Secondly, based on the tangent barrier Lyapunov function and auxiliary system, two adaptive fault tolerant controllers are designed for velocity subsystem and altitude subsystem, respectively, which can solve the problem of input saturation. By using the controllers, the flight states containing the angle of attack, flight path angle, pitch angle and pitch angle rate can be guaranteed in prospective ranges. Finally, the Lyapunov stability theory and numerical simulations are adopted to verify the effectiveness of the presented controllers.