Asymmetric Barrier Lyapunov Function Research Articles

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

In this paper, an adaptive dynamic surface (DSC) guidance law for missile is designed to intercept the maneuvering target with field-of-view (FOV) and terminal angle constraints in three-dimensional(3D) space, and the missile autopilot dynamics is considered. Firstly, the time-varying transformation function related to line of sight (LOS) is used to replace the FOV constraints, transforming the process-constrained control problem into the output-constrained control problem. Meanwhile, the 3D coupled relative kinematics model considering missile autopilot dynamics and maneuvering target acceleration is established. Secondly, a novel time-varying asymmetric barrier Lyapunov function (TABLF) with dead-zone characteristics is introduced to the adaptive dynamic surface guidance law design process to improve the robustness of parameter debugging. Thirdly, with the help of a nonlinear adaptive filter, the ‘explosion of complexity’ problem can be avoided effectively, which is caused by analytic computation of virtual signal derivatives. Furthermore, aiming at the problem of autopilot dynamic errors, target acceleration disturbances, and unmeasurable parameters in the model, a novel adaptive law is used to evaluate online. Then, the stability of the closed-loop system is rigorously proven using Lyapunov criteria. Ultimately, Numerical simulations with various constraints and comparison studies have been considered to show the feasibility and effectiveness of the proposed missile guidance law.

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

This study focuses on the unresolved control problems pertaining to full-state constrained nonlinear systems within a prescribed time. Initially, two Lyapunov theorems are established using a time-varying scaling function. These theorems facilitate the achievement of prescribed-time stability while ensuring that constraints are not violated. Building upon these theorems and incorporating completely known nonlinear terms, a state-feedback controller is developed and analyzed by employing an asymmetric barrier Lyapunov function (BLF). The analysis demonstrates that the resulting controller enables the tracking error to converge to the origin within a prescribed time while subsequently maintaining it at the origin without violating any constraints. Additionally, as an extension of the proposed prescribed-time control approach, the adaptive control problem for parameterized constrained nonlinear systems is addressed. The designed adaptive controller ensures boundedness of all signals, maintains the states within the specified constraints, and achieves convergence of the tracking error to the origin within an arbitrarily prescribed time. Finally, simulation examples are presented to validate the effectiveness of the proposed control scheme.

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

This paper presents a vision-based finite-time prescribed performance controller for unmanned aerial vehicle (UAV) tracking of uncooperative aerial targets. The relative states between UAV and target are estimated by an onboard monocular camera. The inability of visual measurements to accurately determine the initial state of the target renders conventional prescribed performance controllers ineffective in such situations. As a result, it becomes essential to address the problem of prescribed performance control under conditions of uncertain initial values By utilizing an auxiliary transforming function, an Asymmetric Barrier Lyapunov Function (ABLF) and a finite-time prescribed performance function, a robust adaptive controller based on backstepping framework is proposed to deal with state constraints under unknown initial tracking conditions. It is proved that, the closed-loop relative position is capable of reaching the prescribed performance bound before the preset transforming time and converging to the prescribed steady-state error before a finite setting time. Simulation examples are provided to illustrated the effectiveness of the proposed tracking algorithm.

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.

Adaptive fuzzy control for high-order nonlinear systems with asymmetric time-varying full-state constraints and dead-zone input

The issue of adaptive fuzzy control for a category of high-order uncertain nonlinear systems is discussed in this paper. The time-varying full-state constraints are asymmetric, and the input is subjected to dead-zone. The asymmetric time-varying high-order barrier Lyapunov functions (BLFs) are constructed to depict the constraints characteristic and a controller design strategy is proposed. A dead-zone compensation mechanism is used to eliminate the influence of dead-zone input. Based on adding a power integrator technique and the adaptive control method, an adaptive state feedback controller is designed. As a consequence, all the constraints are not breached and the tracking error converges into a prescribed small region around the origin. Finally, a numerical example and a practical example are given to show the effectiveness of the proposed method.

Event-Triggered Adaptive Fuzzy Neural Network Output Feedback Control for Constrained Stochastic Nonlinear Systems.

This article investigates the problem of command-filtered event-triggered adaptive fuzzy neural network (FNN) output feedback control for stochastic nonlinear systems (SNSs) with time-varying asymmetric constraints and input saturation. By constructing quartic asymmetric time-varying barrier Lyapunov functions (TVBLFs), all the state variables are not to transgress the prescribed dynamic constraints. The command-filtered backstepping method and the error compensation mechanism are combined to eliminate the issue of "computational explosion" and compensate the filtering errors. An FNN observer is developed to estimate the unmeasured states. The event-triggered mechanism is introduced to improve the efficiency in resource utilization. It is shown that the tracking error can converge to a small neighborhood of the origin, and all signals in the closed-loop systems are bounded. Finally, a physical example is used to verify the feasibility of the theoretical 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.

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.

Event-triggered control for [formula omitted]-normal switched stochastic nonlinear systems with asymmetric output constraints

This article focuses on the event-triggered control design for a class of p-normal switched stochastic nonlinear systems(SNS) with asymmetric output constraints. Firstly, in order to handle the pre-specified output constraints, a modified asymmetric tan-type common barrier Lyapunov function(CBLF) is put forward through the idea of piece-wise function. Combining the proposed CBLF with adding a power integrator technique, an event-triggered state-feedback controller is designed to ensure the switched SNS states asymptotically converge to zero in probability. Simultaneously, it is proved that the output will be constrained in the pre-specified bound and Zeno-behavior will not happen. Finally, a simulation of two-tank liquid-level system is given to indicate the effectiveness of the proposed method.

Adaptive Decentralized Control for Interconnected Time-Delay Uncertain Nonlinear Systems With Different Unknown Control Directions and Deferred Full-State Constraints.

In this article, the problem of adaptive decentralized control is investigated for a class of interconnected time-delay uncertain nonlinear systems with different unknown control directions and deferred asymmetric time-varying (DTV) full-state constraints. By constructing the novel time-varying asymmetric integral barrier Lyapunov function (TVAIBLF), the conservative limitation of constant integral barrier Lyapunov function (IBLF) or symmetric IBLF is reduced and the need on the prior knowledge of control gains is also avoided, while the deferred constraints directly imposed on the states of system are achieved by introducing the shifting function into the controller design. Furthermore, based on the Nussbaum-type functions, a new adaptive decentralized control strategy for interconnected time-delay nonlinear systems with subsystems having different control directions is proposed via backstepping method. And it is proven that the proposed control method can guarantee that all signals in closed-loop system are bounded and the transform errors asymptotically converge to zero. Finally, the effectiveness of the proposed control strategy is illustrated through the simulation results.

Collision avoidance and connectivity preservation using asymmetric barrier Lyapunov function with time-varying distance-constraints

Collision avoidance and connectivity preservation are two contrasting issues in multi-agent formation control problems. This paper proposes a distributed control design methodology to stabilize a desired formation shape in a multi-agent system while incorporating these two factors simultaneously. Contrary to a simplifying point mass assumption, we consider that agents in the group are characterized by a circular disk-type structure of different radii. Collision avoidance and connectivity preservation in the group are handled by applying time-varying constraints on the inter-center distances among neighboring agents. The concept of asymmetric time-varying barrier Lyapunov function is exploited to derive the stabilizing distributed control law, under a mild assumption on the initial conditions and a feasibility condition relating dimensions of the desired formation with the lower and upper limits of the barrier functions. We also obtain analytical bounds on the various post-design signals and illustrate the results through a simulation example. Finally, the effect of input saturation is discussed, and a comparison with the sensing-region-dependent potential function-based control design approach from the existing literature is provided.