Asymmetric Barrier Lyapunov Function Research Articles

Fixed-Time Adaptive Event-Triggered Control for Uncertain Nonlinear Systems Under Full-State Constraints

The problem of adaptive event-triggered control for uncertain nonlinear systems with full-state constraints was investigated. State constraints can significantly affect system performance, especially when time-varying external disturbances are present, potentially leading to instability. Thus, a fixed-time disturbance observer was designed. It estimated unknown uncertainties within a predetermined time. Meanwhile, an asymmetric barrier Lyapunov function was developed. It ensured the stability of the system state under constraints. Furthermore, to reduce the utilization rate of the system’s communication resources, an adaptive event-triggered control scheme was proposed, and an integrated control method was established to preset the convergence time of the system’s state error, greatly improving the convergence speed. Theoretical analysis and simulations demonstrated the effectiveness of the proposed approach. The results show that the system achieved stable control within a fixed time, even under full-state constraints and external disturbances, while using fewer communication resources.

Preassigned Fixed-Time Synergistic Constrained Control for Fixed-Wing Multi-UAVs with Actuator Faults

This study focuses on the distributed fixed-time fault-tolerant control problem for a network of six-degree-of-freedom (DOF) fixed-wing unmanned aerial vehicles (UAVs), which are subject to full-state constraints and actuator faults. The novelty of the proposed design lies in the incorporation of an enhanced asymmetric time-varying tan-type barrier Lyapunov function (BLF), which is applicable in both constrained and unconstrained scenarios. This function ensures that the UAV states remain within compact sets at all times while achieving fixed-time convergence. Additionally, a fixed-time performance function (FTPF) is developed to eliminate the dependency on exponential functions commonly used in traditional fixed-time control methods. The adverse effects of actuator faults, including lock-in-place and loss of effectiveness, are mitigated through a bounded uniform tracking control design. A rigorous Lyapunov function analysis demonstrates that all closed-loop signals are semi-globally uniformly ultimately bounded (SGUUB), with both velocity and attitude tracking errors converging to residual sets near the origin. Experimental validation tests are conducted to confirm the effectiveness of the theoretical findings.

Uniform-performance-constrained fixed-time neuro-control for stochastic nonlinear systems under dynamic event triggering.

Uniform-performance-constrained fixed-time neuro-control for stochastic nonlinear systems under dynamic event triggering.

Adaptive fuzzy command filtered control for uncertain fractional order nonlinear systems with full state constraints

This paper investigates the tracking control problem for fractional-order (FO) nonlinear systems with model uncertainties and external disturbances under full-state constraints. An adaptive fuzzy control strategy based on a command filter is proposed, where the asymmetric Barrier Lyapunov Function is adopted to ensure that the states do not violate their constraints, and a fuzzy logic system is used to approximate the unknown nonlinear terms. Additionally, a FO command filter is implemented to approximate the virtual control signals and their derivatives, effectively addressing the explosion of complexity problem, while an error compensation function is incorporated to compensate for the filtering errors. Overall, the stability analysis is conducted based on the Lyapunov method to ensure the boundedness of all signals. Ultimately, the performance of the proposed controller is demonstrated through two simulation examples.

Adaptive-constrained admittance control for physical human–robot interaction

In this paper, an adaptive constrained admittance control scheme is proposed, which can effectively solve physical human–robot interaction (pHRI) tasks with output constraints. To ensure the safety of robot behavior, the constraint controller is designed in the trajectory planning layer and the control layer. The asymmetric soft saturation function (ASSF) is designed to obtain variable compliant motion trajectories generated from the desired admittance model. In addition, the controller based on the asymmetric integral barrier Lyapunov function (AIBLF) is designed to deal directly with asymmetric Cartesian space constraints. Finally, radial basis function neural network (RBFNN) is utilized to approximate the dynamics uncertainty of the robot manipulator and to improve the tracking accuracy. According to the Lyapunov stability principles, it can be proved that all states of the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). Finally, the effectiveness of the proposed control scheme is demonstrated by several simulations and experiments.

Advanced Control for Shipboard Cranes with Asymmetric Output Constraints

Considering the anti-swing control and output constraint problems of shipboard cranes, a nonlinear anti-swing controller based on asymmetric barrier Lyapunov functions (BLFs) is designed. First, model transformation mitigates the explicit effects of ship roll on the desired position and payload fluctuations. Then, a newly constructed BLF is introduced into the energy-based Lyapunov candidate function to generate nonlinear displacement and angle constraint terms to control the rope length and boom luffing angle. Among these, constraints with positive bounds are effectively handled by the proposed BLF. For the swing constraints of the unactuated payload, a carefully designed relevant constraint term is embedded in the controller by constructing an auxiliary signal, and strict theoretical analysis is provided by using a reductio ad absurdum argument. Additionally, the auxiliary signal effectively couples the boom and payload motions, thereby improving swing suppression performance. Finally, the asymptotic stability is proven using LaSalle’s invariance principle. The simulation comparison results indicate that the proposed method exhibits satisfactory performance in swing suppression control and output constraints. In all simulation cases, the payload swing angle complies with the 3° constraint and converges to the desired range within 6 s. This study provides an effective solution to the control challenges of shipboard crane systems operating in confined spaces, offering significant practical value and applicability.

Autonomous Vertical Landing Guidance with Specified Path Angle Considering Field-of-view Constraints with Time-varying Asymmetric Barrier Lyapunov Function for Unmanned Aerial Vehicles

Autonomous Vertical Landing Guidance with Specified Path Angle Considering Field-of-view Constraints with Time-varying Asymmetric Barrier Lyapunov Function for Unmanned Aerial Vehicles

Adaptive Fuzzy Fault‐Tolerant Control for CSTR With State Constraints Dependent on Temperature and Concentration

ABSTRACTThe indispensable experimental equipment of the continuous stirred tank reactor (CSTR) is crucial in chemical production processes. This paper presents a novel adaptive state‐dependent constraint control method for nonlinear CSTR system. The CSTR system is transformed into the nonlinear system with a pure feedback structure begins with the mean value theorem. Subsequently, the Fuzzy logic systems (FLS) is used to approximate unknown dynamics. Reactant concentration and mixture temperature are crucial variables in CSTR system. When these variables surpass the specified constraints, it can lead to a decrease in product quality and yield. The constraint boundaries considered in this paper are dependent on both state and time. Therefore, the time‐varying asymmetric Barrier Lyapunov Function (BLF) is proposed to deal with state‐dependent constraints. Additionally, the actuator fault is resolved in this paper, by considering fault‐tolerant control strategy. Lyapunov stability analysis shows that all signals in a closed‐loop system are bounded. Finally, the effectiveness of the control scheme is verified by the simulation of CSTR system.

Fast finite‐time stabilization of stochastic nonlinear systems with output constraints and an application to single‐link robot

AbstractThis article studies the fast finite‐time stabilization problem for stochastic nonlinear systems with asymmetric output constraints. To address the issue of slow convergence encountered in previous finite‐time control designs of stochastic nonlinear constrained systems, this paper extends the fast finite‐time stabilization mechanism to such systems. First, a novel asymmetric barrier Lyapunov function is employed to tackle the output constraint. Then, by adding a power integrator technique and the barrier Lyapunov function, a state‐feedback controller for stochastic nonlinear systems is explicitly designed using the backstepping method. The designed controller achieves fast finite‐time stability in probability of the stochastic nonlinear system while ensuring no violation of the output constraints. Finally, two examples are presented to demonstrate the effectiveness of the controller scheme.

Barrier Lyapunov Based Adaptive Control for Hydraulic Servo Systems with Parametrical Nonlinearities and Modeling Uncertainties

Load variations, friction, and external disturbance degrade the control performance of hydraulic servo systems. To attain the high precision trajectory tracking performance for the hydraulic servo systems, a barrier Lyapunov based adaptive controller (BLBAC) is proposed in this paper. For the controller, the adaptive law is developed in each step of backstepping design such that the tracking error can converge to a prescribed accuracy. The state-constrained control of hydraulic servo systems is another issue worthy of attention. Hence, a novel time-varying asymmetric barrier Lyapunov function (TABLF) are adopted to guarantee that the states are not to violate their constraints. The closed-loop signals stability is proved by Lyapunov theory. Comparative simulation results verify the effectiveness of the proposed controller in comparison with the other two controllers for hydraulic servo systems.

A state-constrained safety adaptive trajectory tracking control scheme for a hovercraft with enhanced prescribed performance

In this paper, a state-constrained safety adaptive trajectory tracking control scheme for a hovercraft with enhanced prescribed performance is studied. Firstly, considering the position error, a novel pair of prescribed monotone tube boundary functions combined with a sliding mode is introduced to obtain virtual velocity control laws, and the position error is simplified into an equivalent unconstrained control system by adopting the transformed error function. Unlike traditional prescribed performance control, the new function has a quantitative relationship between (transient and steady-state) control performance and some practical user-defined metrics such as overshoot, precision, and convergence time, and is less conservative. Therefore, this method is convenient for design and engineering practice. Secondly, in order to solve problems of velocity safety constraints, a novel asymmetric integral barrier Lyapunov function (AIBLF) has been adopted to limit velocities of hovercraft within the asymmetric safety constraints. Moreover, a bioinspired neurodynamic model is introduced to handle differential explosion of virtual control laws. For the sake of estimating the unknown terms such as the control system uncertainties, the neural networks (NNs) are utilized. Total control system is ultimately uniformly bounded according to Lyapunov stability theories. Effectiveness and superiority of the proposed control scheme are verified by comparative simulation.

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

Three-dimensional adaptive dynamic surface guidance law for missile with terminal angle and field-of-view constraints

Cascaded safety trajectory tracking control for a hovercraft with double-loop prescribed performance and state constraints

ABSTRACT This paper presents a cascaded safety trajectory tracking control scheme for hovercraft, addressing dump disturbances with a novel double-loop strategy that enforces prescribed performance and state constraints. Initially, an Adaptive Prescribed-Time Extended State Observer (APESO) is meticulously crafted to estimate lumped disturbances accurately. Subsequent to this, virtual velocity control laws are established through Double Power Appointed-Time Performance Function (DPATPF) combined with an Asymmetric Barrier Lyapunov Function (ABLF), streamlining the position error into a more manageable, equivalent unconstrained control system format. To effectively manage velocity safety constraints, a Unified Barrier Function (UBF) is introduced, ensuring that hovercraft velocities adhere to asymmetric safety boundary. The entire system state is rigorously ultimately uniformly bounded, in strict compliance with cascade control theories and Lyapunov stability criteria. Through simulation, we demonstrate the superior performance and effectiveness of the proposed control strategy, showcasing its potential for enhancing hovercraft navigational safety and reliability.

Adaptive fuzzy ABLF function fixed‐time tracking control method for nonlinear fault‐tolerant control systems with event triggering mechanism

SummaryAs the nonlinearities of many real physical controlled systems become stronger and stronger, they are difficult to be described by accurate mathematical models. For a class of nonlinear single‐input single‐output systems with all‐state constraints and actuator faults, an event‐triggered adaptive fuzzy ABLF function fixed‐time tracking control method is proposed. The asymmetric barrier Lyapunov function (ABLF) combined with backward step technique is used to ensure the boundedness of the closed‐loop system output. In order to solve the problem of limited bandwidth resources, this paper adopts the event trigger mechanism and fuzzy control technology to approximate the unknown function to ensure the convergence of the system in a fixed time. After theoretical analysis, it is proved that the tracking error of the system converges in the small neighborhood of the origin, and it still has good tracking performance when the actuator faults. Finally, by comparing the proposed method with the asymmetric barrier Lyapunov function, which verifies the effectiveness of the proposed method.

Disturbance Observer-Based Adaptive Fault Tolerant Control with Prescribed Performance of a Continuum Robot

This paper studies an adaptive fault tolerant control (AFTC) scheme for a continuum robot subjected to unknown actuator faults, dynamics uncertainties, unknown disturbances, and prescribed performance. Specifically, to deal with uncertainties, a function approximation technique (FAT) is employed to evaluate the unknown actuator faults and uncertain dynamics of the continuum robot. Then, a nonlinear disturbance observer (DO) is developed to estimate the unknown compounded disturbance, which contains the unknown disturbances and approximation errors of the FAT. Furthermore, the prescribed error bound is treated as a time-varying constraint, and the controller design method is based on an asymmetric barrier Lyapunov function (BLF), which is operated to strictly ensure the steady-state and transient performance of the continuum robot. Afterwards, the simulation results validate the effectiveness of the proposed AFTC in dealing with the unknown actuator faults, uncertainties, unknown disturbances, and prescribed performance. Finally, the effectiveness of the proposed AFTC scheme is verified through experiments.

State-feedback control for full-state constrained nonlinear systems in a prescribed time

State-feedback control for full-state constrained nonlinear systems in a prescribed time

Guaranteed Performance Event-Triggered Adaptive Consensus Control for Multiagent Systems under Time-Varying Actuator Faults

A guaranteed performance event-triggered adaptive consensus control is established for uncertain multiagent systems under time-varying actuator faults. To eliminate the impact caused by actuator faults, an adaptive neural network compensation strategy is developed. Simultaneously, by implementing the asymmetric barrier Lyapunov function and transform function, a prescribed time consensus control with guaranteed performance, is constructed. Furthermore, to reduce the frequency of information transmission, an adjustable switching event-triggered control (ASETC) is proposed by using a modified hyperbolic tangent function. It combines the advantage of the relative threshold strategies and the characteristics of the hyperbolic tangent function, giving better flexibility in saving network resources and guaranteeing system performance. By applying the constructed control method, systems with prescribed performance consensus in a prescribed time are achievable while limited network resources and unknown time-varying faults are present. Some simulation examples implemented in MATLAB (R2022a) are given to demonstrate the above results.

Fixed-Time Adaptive Event-Triggered Guaranteed Performance Tracking Control of Nonholonomic Mobile Robots under Asymmetric State Constraints

A fixed-time adaptive guaranteed performance tracking control is investigated for a category of nonholonomic mobile robots (NMRs) under asymmetric state constraints. For the sake of favorable transient and steady-state properties of the system, a prescribed performance function (PPF) is introduced and a transform function is further constructed. Based on the backstepping technique, an asymmetric barrier Lyapunov function is formulated to ensure the tracking errors converge within a human-specified time. On the foundation of this, the occupation of communication channel is effectively reduced by assigning an event-triggered mechanism (ETM) with relative threshold to the process of controller design. By utilizing the proposed control strategy, the NMR is capable of implementing the enemy dislodging mission while the enemy can always be caught by the NMR and the collision would never be presented. Finally, two simulation experiments are given to verify the effectiveness of the proposed scheme.

Vision-based finite-time prescribed performance control for uncooperative UAV target-tracking subject to field of view constraints

Vision-based finite-time prescribed performance control for uncooperative UAV target-tracking subject to field of view constraints

Adaptive neural trajectory tracking non-affine control for a hovercraft subject to multiple safety constraints

ABSTRACT Considering the internal, external uncertainties and robustness decreases, this paper addresses an adaptive neural trajectory tracking non-affine control method for a hovercraft under multiple safety constraints. Firstly, hovercraft’s non-affine model has been built and aim to approximate non-affine formulations, a neural network (NN) is utilized. Secondly, to stabilize the position errors, virtual surge velocity control law is obtained via a log-type barrier Lyapunov function (LBLF). Thirdly, a new asymmetric integral barrier Lyapunov function (AIBLF) is presented to address asymmetric safety constraint problems of hovercraft. Aim to guarantee heading control, the yaw angular velocity is obtained consequently. The proposed adaptive method can guarantee the surge velocity and yaw angular velocity to the inside of asymmetric boundaries with the requirements of safe performance during motion. The total system states are ultimately uniformly bounded (UUB) via Lyapunov stability theories. Finally, obtained simulations results demonstrate the effectiveness of the proposed control scheme.