Barrier Lyapunov Function Research Articles

Improved Stanley guidance law–based adaptive path-following control of underactuated ship with state-constrained and time-varying drift angle

To improve the following performance in large curve path and time-varying drift angle, a reduced-order extended state observer is added to the Improved Stanley Guidance Law (EISGL). Combining with the dynamic surface control (DSC), an adaptive auxiliary system is simultaneously built to compensate for the effect of the state constraints on the system. A barrier Lyapunov function combined with a prescribed performance function is designed to constrain the heading angle error of path following. Adaptive laws are also designed to approximate errors, estimating perturbation in poor sea condition. Lyapunov stability analysis shows that all signals are semi-global coherent and eventually bounded. In conclusion, the numerical comparison simulation experiments verify that the scheme has a strong anti-jamming capability and achieves good path following in large curve path.

Event-Triggered Adaptive Fuzzy Control for Strict-Feedback Nonlinear FOSs Subjected to Finite-Time Full-State Constraints

In this article, an event-triggered adaptive fuzzy finite-time dynamic surface control (DSC) is presented for a class of strict-feedback nonlinear fractional-order systems (FOSs) with full-state constraints. The fuzzy logic systems (FLSs) are employed to approximate uncertain nonlinear functions in the backstepping process, the dynamic surface method is applied to overcome the inherent computational complexity from the virtual controller and its fractional-order derivative, and the barrier Lyapunov function (BLF) is used to handle the full-state constraints. By introducing the finite-time stability criteria from fractional-order Lyapunov method, it is verified that the tracking error converges to a small neighborhood near the zero and the full-state constraints are satisfied within a predetermined finite time. Moreover, reducing the communication burden can be guaranteed without the occurrence of Zeno behavior, and the example is given to demonstrate the effectiveness of the proposed controller.

Practical finite‐time fuzzy control of uncertain nonstrict‐feedback systems with actuator saturation and output constraints

SummaryThis article investigates the devise issue of a practical finite‐time output‐tracking control for uncertain nonlinear nonstrict‐feedback systems subject simultaneously to time‐varying output constraints (TVOC), actuator saturation, and bounded unmatched disturbances. An adaptive fuzzy approximator‐based control system is devised using the dynamic surface control (DSC) concept. System output constraints are addressed by employing an appropriate barrier Lyapunov function. Adaptive fuzzy disturbance observers are constructed to practically deal with time‐varying unmatched but bounded disturbances. It is verified via Lyapunov stability analysis and simulation experiments that all closed‐loop signals remain bounded, the output tracking error practically converges in finite time to a tiny but adjustable neighborhood around the origin, and the system output stays within its required time‐varying bounds.

Finite-Time Attitude Maneuver Control for Liquid-Filled Spacecraft with Attitude and Angular Velocity Constraints Based on Barrier Lyapunov Function

Finite-Time Attitude Maneuver Control for Liquid-Filled Spacecraft with Attitude and Angular Velocity Constraints Based on Barrier Lyapunov Function

Nonsingular finite-time heading tracking control of marine vehicles with tracking error constraints

This brief copes with the finite-time heading tracking control for marine vehicles. The tracking error constraints, stochastic disturbance and dead-zone output are simultaneously taken into consideration in the controlled systems. To manage the dead-zone output issue, a smooth approximation model is brought in to offset the nondifferentiable phenomena during the control, besides, the adaptive technique and the Nussbaum function are simultaneously integrated into the design. For the tracking error constraints, the prescribed performance functions (PPF) with error transformations are designed, and novel stochastic Barrier Lyapunov functions are constructed accordingly depending on the newly tracking errors to deal with the constrained tracking control issue. To avert the “differential explosion” issue in the backstepping, the improved first-order filter technique is invoked. The proposed finite-time heading tracking control tactic renders that all variables are bounded, meanwhile, the tracking errors are kept in the pregiven boundaries. The effectiveness of theory results is substantiated via simulations.

FTDO-based adaptive fuzzy fixed-time tracking control for uncertain unmanned helicopter with output constraints

During the actual flight of unmanned helicopters, there are widespread output constraints, system uncertainties and external disturbances, which bring significant threats to their safe flight. To keep the output constraints from violating predefined boundaries, the barrier Lyapunov function (BLF) is utilized in this paper. The system uncertainties are estimated by the fuzzy logic system (FLS). The compound disturbances composed of the external disturbances and the approximation errors caused by FLS are approximated by the fixed-time disturbance observers (FTDOs). According to the analysis of FTDOs and fixed-time stability theory, the observer errors and state errors converge to a region of the origin in fixed-time, and the appropriate parameters of FTDOs and controller are designed to ensure that the disturbance convergence time is faster than the one of the proposed controller, which further improves the stability of the system. Moreover, the convergence time of the FTDOs FTDOs and the proposed approach only depends on the design parameters under any initial conditions with constrained outputs. The performance of the proposed control approach is verified through the simulation results.

Adaptive Safe Reinforcement Learning With Full-State Constraints and Constrained Adaptation for Autonomous Vehicles.

High-performance learning-based control for the typical safety-critical autonomous vehicles invariably requires that the full-state variables are constrained within the safety region even during the learning process. To solve this technically critical and challenging problem, this work proposes an adaptive safe reinforcement learning (RL) algorithm that invokes innovative safety-related RL methods with the consideration of constraining the full-state variables within the safety region with adaptation. These are developed toward assuring the attainment of the specified requirements on the full-state variables with two notable aspects. First, thus, an appropriately optimized backstepping technique and the asymmetric barrier Lyapunov function (BLF) methodology are used to establish the safe learning framework to ensure system full-state constraints requirements. More specifically, each subsystem's control and partial derivative of the value function are decomposed with asymmetric BLF-related items and an independent learning part. Then, the independent learning part is updated to solve the Hamilton-Jacobi-Bellman equation through an adaptive learning implementation to attain the desired performance in system control. Second, with further Lyapunov-based analysis, it is demonstrated that safety performance is effectively doubly assured via a methodology of a constrained adaptation algorithm during optimization (which incorporates the projection operator and can deal with the conflict between safety and optimization). Therefore, this algorithm optimizes system control and ensures that the full set of state variables involved is always constrained within the safety region during the whole learning process. Comparison simulations and ablation studies are carried out on motion control problems for autonomous vehicles, which have verified superior performance with smaller variance and better convergence performance under uncertain circumstances. The effectiveness of the safe performance of overall system control with the proposed method accordingly has been verified.

Asymmetric integral barrier Lyapunov function-based three-dimensional integrated guidance and control design with field-of-view constraint and input saturation

This paper proposes an adaptive integrated guidance control (IGC) scheme for the flight vehicle intercepting the maneuvering target with asymmetric field-of-view angle constraint, input magnitude and rate saturation, and system uncertainties. A novel nonlinear three-dimensional IGC model is established in the body line-of-sight (LOS) coordinate system by employing the dual-integral control law. Based on this model, the input magnitude and rate saturation for the conventional IGC system can be converted to the limitations of the new augmented states. Asymmetric integral barrier Lyapunov function and dynamic surface control approach are applied to deal with the asymmetric state constraints of the proposed IGC model, and adaptive control laws are designed to compensate for model uncertainties. Furthermore, based on the Lyapunov stability theory, it is proved that all signals in the closed-loop system are bounded while the constrained states are not violated. Finally, the effectiveness and robustness of the proposed IGC scheme are illustrated with numerical simulations.

Dynamic Event-Triggered-Based Adaptive Finite-Time Neural Control for Active Suspension Systems With Displacement Constraint.

In this article, we give an event-based control algorithm for nonlinear active suspension systems (ASSs) with the vertical displacement constraint. For in-vehicle communication networks, the controller area network (CAN) is a widely used standard for interconnecting electronic control units (ECUs). The main task in this work is, thus, to reduce the communication burden on the CAN. To this end, we develop a dynamic event-triggered communication mechanism in ASSs. Meanwhile, in practice, the vehicle safety is degraded when the body vibration exceeds the allowable maximum. Thus, the vertical displacement of ASSs should be constrained within a reliable range. For this purpose, we present a novel finite-time integral barrier Lyapunov function (FTIBLF), which not only guarantees that the vertical displacement constraint bounds are not violated, but also enables the position of the suspension to be stabilized in the neighborhood of a desired position in finite settling time. Furthermore, neural networks (NNs) are utilized to identify the unknown nonlinear characteristics in ASSs subjected to the modeling error and unknown mass. As a result, we propose an adaptive neural control technique based on the dynamic event-triggered condition, which helps to improve the ride comfort while ensuring the driving safety and handling stability. Finally, simulation results are provided to verify the validity of the presented methodology.

Barrier Lyapunov function–based command-filtered adaptive fuzzy control of random quadrotor systems

This paper is devoted to adaptive trajectory tracking of quadrotor systems with full-state constraints and random disturbances. The command-filtering technology combined with error compensation mechanisms is proposed to deal with the “explosion of complexity” problem in traditional backstepping design and reduction of the filtering errors. The Barrier Lyapunov functions (BLFs) are constructed to ensure that all system states do not violate the boundary of its constraints. The command-filtered adaptive fuzzy controller is designed such that the state constraints are not breached almost surely, all signals in the closed-loop system are bounded almost surely, and the first-order moment of the tracking error converges to an arbitrarily small neighborhood of zero by parameters tuning. Finally, the effectiveness of the proposed control method is illustrated by simulation results.

Adaptive fast finite‐time control for nonlinear systems subject to output hysteresis by fuzzy approach

SummaryThis article investigates an adaptive fast finite‐time tracking control problem for a class of uncertain nonlinear systems with output hysteresis. The idea of output hysteresis compensation is skillfully extended to adaptive design by employing a hysteresis inverse transformation and barrier Lyapunov function. The backstepping technique is adopted to establish the fast finite‐time control strategy, which can realize finite‐time convergence of the closed‐loop system. A rigorous theoretical analysis is performed to illustrate that the signals in the closed‐loop systems are bounded in finite time, and the tracking error can converge into a compact set with sufficient accuracy. Finally, a numerical simulation is given to confirm the effectiveness of the presented strategy.

A Novel, Finite-Time, Active Fault-Tolerant Control Framework for Autonomous Surface Vehicle with Guaranteed Performance

In this paper, a finite-time, active fault-tolerant control (AFTC) scheme is proposed for a class of autonomous surface vehicles (ASVs) with component faults. The designed AFTC framework is based on an integrated design of fault detection (FD), fault estimation (FE), and controller reconfiguration. First, a nominal controller based on the Barrier Lyapunov function is presented, which guarantees that the tracking error converges to the predefined performance constraints within a settling time. Then, a performance-based monitoring function with low complexity is designed to supervise the tracking behaviors and detect the fault. Different from existing results where the fault is bounded by a known scalar, the FE in this study is implemented by a finite-time estimator without requiring any prioir information of fault. Furthermore, under the proposed finite-time AFTC scheme, both the transient and steady-state performance of the ASV can be guaranteed regardless of the occurrence of faults. Finally, a simulation example on CyberShip II is given to confirm the effectiveness of the proposed AFTC method.

Event-triggered error-constrained switching guidance-based marine surface vessel path-following control and collision avoidance

For marine surface vessel with input saturation, model uncertainties, and unknown disturbances, this article proposes a path-following control and collision avoidance method based on error-constrained event-triggered switching line-of-sight guidance. This method can autonomously switch between path-following and collision avoidance modes, constrain the position and heading errors to satisfy safe navigation in confined waters, and reduce the computational frequency of the controller and the mechanical wear of the actuator. In the path-following mode, we construct an asymmetric modified barrier Lyapunov function to constrain the position errors and use the relative threshold event-triggered mechanism to reduce the update frequency of the guidance heading angle. In the collision avoidance mode, static or dynamic obstacles are avoided through the response of collision avoidance radius. In the heading and velocity control design, asymmetric modified barrier Lyapunov function and event-triggered mechanism are also applied, so that the marine surface vessel can track the guided heading angle and meet the heading error-constrained while reducing the update frequency of the controller. The adaptive auxiliary systems are used to compensate for the input saturation, and radial basis function neural networks and adaptive laws are used to approximate the model uncertainties and composite disturbances. According to the Lyapunov stability theory, all signals are semi-globally uniformly ultimately bounded and the Zeno phenomenon is avoided. Finally, the comparative experiment shows the superiority of the designed control strategy.

Adaptive fuzzy fault‐tolerant control of stochastic nonlinear multiagent systems with input quantization and state constraints

SummaryThis paper is dedicated to the problem of adaptive fuzzy fault‐tolerant control (FTC) for a class of stochastic nonstrict feedback nonlinear multi‐agent systems (MASs) with input quantization and full state constraints. Firstly, based on the backstepping technique and the bounded estimation method, the effect of actuator faults can be eliminated by the proposed adaptive updating laws. Secondly, the stochastic barrier Lyapunov functions (BLFs) are constructed to ensure that all state constraints are not violated. Meanwhile, the introduction of input quantization can effectively save network resources and reduce computational burden. It is further shown that all the closed‐loop signals are uniformly bounded, and the consensus tracking errors asymptotically tend to zero. The effectiveness of the proposed control scheme is illustrated by a numerical example.

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

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

Adaptive Iterative Learning Fault-Tolerant Control for State Constrained Nonlinear Systems With Randomly Varying Iteration Lengths.

This article presents an adaptive iterative learning fault-tolerant control algorithm for state constrained nonlinear systems with randomly varying iteration lengths subjected to actuator faults. First, the modified parameters updating laws are designed through a new defined tracking error to handle the randomly varying iteration lengths. Second, the radial basis function neural network method is used to deal with the time-iteration-dependent unknown nonlinearity, and a barrier Lyapunov function is given to cope with the state constraint. Finally, a new barrier composite energy function is used to achieve the tracking error convergence of the presented control algorithm along the iteration axis with the state constraint and then followed with the extension to the high-order case. A simulation for a single-link manipulator is given to illustrate the effectiveness of the theoretical studies.

Fixed-Time Observer-Based Output Feedback Control for Nonlinear Systems With Full-State Constraints

This brief investigates the problem of fixed-time state observer-based output feedback control design for nonlinear systems with full-state constraints. First, a fixed-time state observer is constructed to estimate the unknown states, which can accurately estimate the system states within a fixed settling time. Then, by combining the integral barrier Lyapunov function with the backstepping method, the full-state constraints are realized after the fixed time. Meanwhile, the proposed control strategy can directly constrain the states rather than impose constraints on errors, which reduces the conservativeness of the constraint satisfaction condition. The proposed control method ensures that all signals in the closed-loop system are bounded and symmetric state constraints are strictly maintained after the fixed settling time. Finally, simulation results prove the effectiveness of the proposed method.

Adaptive prescribed‐time tracking control for uncertain nonlinear systems with full state constraints

SummaryThis paper investigates the adaptive tracking control in a prescribed‐time for a class of uncertain nonlinear systems with a full state constraint. Firstly, in order to restrict the state constraints, the barrier Lyapunov function is employed and parameter uncertainty is handled based on linear‐in‐the‐parameters (LIP). A prescribed‐time adaptive controller is then designed by backstepping to ensure that the closed‐loop system can reach zero in a prescribed finite time under any given initial conditions. The prescribed‐time is independent of the design of the parameters. Finally, two simulation examples verify the effectiveness and usability of the proposed method.

Adaptive time-varying state safety constraint control for discrete-time nonlinear systems with random actuator failures

This work investigates the adaptive time-varying state safety constraint control problem for a class of discrete-time nonlinear systems subject to large parameter uncertainties and stochastic actuator failures for the first time. The existence of time-varying full-state constraints, large parameter uncertainties and stochastic actuator failures leads to a series of difficulties for realizing all control objectives. Due to the absence of the linearity property of the derivative in discrete-time log type barrier Lyapunov functions, they are not used to deal with the state constraint problem of nonlinear discrete-time systems. The discrete quadratic-fraction time-varying barrier Lyapunov function is employed to guarantee that all states are constrained in the time-varying predefined regions. By virtue of the constructed multiple-model set, an adaptive identification algorithm is developed to deal with large parameter uncertainties and it has a clear advantage that this method does not requires cn (where n is the dimension of the parameter vector and c is an integer) identification models and only relies on n+1 identification models, thereby heavily reducing the computational burden. By employing the discrete-time filter and backstepping techniques, the adaptive failure compensation controller is designed to ensure the boundedness in probability of the considered systems with respect to stochastic actuator failures. Finally, the effectiveness of the proposed scheme is proved by two simulation examples.

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

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