Barrier Lyapunov Function Research Articles

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.

Disturbance Observer–Based Adaptive Dynamic Event‐Triggered Control for a Class of Nonlinear Systems With Input Saturation

ABSTRACTFor the adaptive tracking control of a class of nonlinear systems with asymmetric input saturation and external disturbances, a novel dynamic event‐triggered neural network control scheme on the foundation of full‐state constraints is proposed. Firstly, by adding a compensation term into the traditional dynamic surface control framework, the filtering error ignored generally is eliminated. Secondly, a nonlinear disturbance observer is constructed to observe the compound interference united by external disturbances and approximation errors based on the approximation ability of neural network. Thirdly, an auxiliary variable is combined with a smooth function used to deal with the saturated input function to offset the influence of input saturation constraints. In addition, for ensuring that all states of the system are constrained by preset time‐varying ranges, the adaptive control method and dynamic event‐triggered condition are posed with the help of barrier Lyapunov function. Then, the tracking performance and the boundness of all signals in the closed‐loop system can be guaranteed by employing the presented adaptive control approach with dynamic event‐triggered mechanism, as well as the Zeno behavior does not appear. Finally, the validity of the designed control method can be demonstrated in simulation examples.

Adaptive Finite‐Time RL Control for Stochastic Non‐Linear Systems With Full State Constraints and Dead Zone Output

ABSTRACTIn this article, the finite‐time control problem of adaptive neural network (NN) reinforcement learning (RL) is investigated for the continuous time stochastic non‐linear systems with full state constraints and dead zone output. Firstly, the adaptive estimation and smooth approximation technique are introduced to solve the difficulty arising from the dead zone non‐linearity. Moreover, to overcome the problem of calculating the explosion caused by the repeated differentiation of the virtual control signals, a finite‐time command filter is constructed. Combining the backstepping technique and the identifier‐actor‐critic RL strategy, an adaptive neural finite‐time RL control scheme is proposed for the considered system by constructing the tangent‐type time‐varying barrier Lyapunov functions (BLFs), which optimizes the tracking performance while ensuring all states do not violate the constraints. Under the proposed control strategy, it is guaranteed that all signals are bounded in probability, and the output of the system can track the reference signal within a finite‐time. Finally, the simulation results verify the effectiveness of the proposed scheme.

Adaptive Impedance Control of a Human–Robotic System Based on Motion Intention Estimation and Output Constraints

The rehabilitation exoskeleton represents a typical human–robot system featuring complex nonlinear dynamics. This paper is devoted to proposing an adaptive impedance control strategy for a rehabilitation exoskelton. The patient’s motion intention is estimated online by the neural network (NN) to cope with the intervention of the patient’s subjective motor awareness in the late stage of rehabilitation training. Due to the differences in impedance parameters for training tasks in individual patients and periods, the least square method was used to learn the impedance parameters of the patient. Considering the uncertainties of the exoskeleton and the safety of rehabilitation training, an adaptive neural network impedance controller with output constraints was designed. The NN was applied to approximate the unknown dynamics and the barrier Lyapunov function was applied to prevent the system from violating the output rules. The feasibility and effectiveness of the proposed strategy were verified by simulation.

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.

Adaptive neural observer-based output feedback anti-actuator fault control of a nonlinear electro-hydraulic system with full state constraints

This paper proposes an adaptive output feedback full state constrain (FSC) controller based on the adaptive neural disturbance observer (ANDO) for a nonlinear electro-hydraulic system (NEHS) with unmodeled dynamics. The Barrier Lyapunov Functions (BLFs) are utilized to ensure that all states of the system are specified within the constraints, and the approximation ability of radial basis function neural networks (RBFNNs) is used to cope with the unknown nonlinear functions. An adaptive neural compensation disturbance observer is elaborated to estimate the compound disturbance and oil leakage fault, effectively addressing these negative effects. Subsequently, observer-based output feedback command filter scheme is developed to diminish the explosion of complexity in the taking derivative procedure and obtain high precise tracking performance. The convergence of tracking errors into a small region around the equilibrium is demonstrated by the Lyapunov stability theory. Ultimately, simulation, experiment, and comparative studies are provided to further validate the effectiveness of the proposed control approach.

Event-Triggered Bipartite Formation Control for Switched Nonlinear Multi-Agent Systems with Function Constraints on States

A distributed adaptive fuzzy event-triggered bipartite formation tracking control scheme is proposed for switched nonlinear multi-agent systems (MASs) with function constraints on states. Fuzzy logic systems (FLSs) are used to identify uncertain items. To improve the transient performance of the system, a fixed-time prescribed performance function (FTPPF) is introduced to make the formation error converge to a prescribed boundary range within a fixed time. Considering that the state constraint boundary is restricted by multiple pieces of information (historical state, topological relationship, neighbor agent output, leader signal and time), a tan-type barrier Lyapunov function (BLF) is constructed to address the challenges brought by the state function constraint. The shortcoming of the “explosion of complexity” is compensated by fusing the backstepping control and command filter. To mitigate the communication burden while ensuring a steady-state performance, a distributed event-triggered fixed-time bipartite formation control scheme is proposed. Finally, the performance of the proposed control method is verified by an MAS consisting of four followers and one leader.

Adaptive neural appointed-time prescribed performance control for the manipulator system via barrier Lyapunov function

Adaptive neural appointed-time prescribed performance control for the manipulator system via barrier Lyapunov function

Fuzzy Adaptive Event-Triggered Consensus Control for Nonlinear Multiagent Systems With Output Constraints and DoS Attacks.

In this article, the fuzzy adaptive event-triggered consensus control issue is addressed for nonlinear multiagent systems (MASs) under output constraints and Denial of Service (DoS) attacks. First of all, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear functions. Then, a novel switching observer is constructed to observe the leader's state and handle DoS attacks. With the help of the exponent-dependent barrier Lyapunov functions (BLFs), the system output can be constrained within a preset region. Based on dynamic surface control (DSC) technique, the issue of computational complexity can be effectively avoided. Combining the designed switching observer and relative thresholds, a robust fuzzy adaptive event-triggered controller is developed, which ensures that the consensus output tracking errors converge to a small neighborhood of zero, and all signals in the closed-loop system keep bounded. Moreover, Zeno behavior can be avoided. Ultimately, simulation results are given to validate the feasibility and effectiveness of the proposed control strategy and theory.

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

This article studies the implementation of practical fixed-time control in stochastic nonlinear systems, implementing event-triggered communication between the controller and the actuator. Firstly, to accomplish the problem of uniform tracking error performance constraints, the improved performance function is investigated, which is combined with the asymmetric barrier Lyapunov function to achieve fast convergence speed and steady state accuracy. Secondly, the practical fixed-time stability is applied in the stochastic nonlinear closed-loop system, which fuses fixed-time command filtering and improved filtering error compensation mechanisms to avoid computational explosion issue. Furthermore, in order to relieve the communication load on the controller and actuator, adjustable trigger thresholds are designed, based on which dynamic event triggering mechanisms are presented for stochastic nonlinear systems. Additionally, the uncertain system behavior is estimated using RBF neuro-networks and the designed controller avoids the singularity problem. Finally, the proposed controller verifies that the system error converges to zero in a fixed time under the Lyapunov stability theory, and that the system output is within the preset boundaries, realizing boundedness of all signals. The superiority of the control method is further demonstrated by three simulation studies including two practical examples.

A current-constrained backstepping control method for LC-type three-phase inverters based on integral barrier Lyapunov functions

A current-constrained backstepping control method for LC-type three-phase inverters based on integral barrier Lyapunov functions

Sampled Robust Control for Constrained Unicycle Mobile Robots

The aim of this paper is to design a sampled robust controller for the trajectory tracking problem in constrained unicycle mobile robots. The proposed swithched controller is composed by an aperiodic control law and a periodic control law. The aperiodic control consists on an state–feedback–based event–triggered control wich is designed by means of the attractive ellipsoid method and the barrier Lyapunov function. The periodic sampled control part is designed taking into account a maximum sampling time. A safe set where the state constraints are not violated, and a switching set that determines the region where each part of the controller is active are provided. The proposed strategy guarantees the input–to–state stability of the tracking error dynamics with respect to external disturbances. The feasibility of the proposed approach is demonstrated through simulation results.

Adaptive prescribed-time control for time-varying full-state-constrained nonlinear stochastic systems with actuator failures

In this paper, the problem of prescribed-time adaptive fuzzy tracking control for a class of time-varying full-state-constrained nonlinear stochastic systems with actuator failures is considered. Using a unified barrier function in place of the traditional barrier Lyapunov function (BLF) allows for the transformation of nonlinear stochastic systems with time-varying full-state constraints into equivalent ‘unconstrained’ systems for processing, which can eliminate the feasibility condition required by the virtual controllers generated using the BLF approach. The problem of unknown control gain caused by actuator failures is solved via devising reasonable adaptive laws. At the same time, a prescribed-time tracking controller is devised by using the approximation ability of fuzzy logic systems, which can adapt to the uncertainty of the system and deal with the actuator failures. In addition, the control scheme proposed in this paper can guarantee the performance of the system within prescribed-time and all state variables do not violate the constraint boundaries despite suffering from actuator failures. Finally, the effectiveness of the investigated control strategy is verified through two simulation examples.

BACKSTEPPING STABILIZATION OF NONLINEAR DYNAMICAL SYSTEMS UNDER STATE CONSTRAINTS

The problem of stabilizing the zero value of the state vector of constrained nonlinear dynamical systems written in a special form is solved. The proposed control design accounts for magnitude constraints on the values of state variables and is based on the integrator backstepping approach using logarithmic Lyapunov barrier functions. The obtained stabilizing feedbacks, in contrast to similar known results, are based on the use of linear virtual stabilizing functions that do not grow unbounded as state variables approach the boundary values. As an example, we consider a state constraints aware solution to the control problem of positioning an autonomous underwater vehicle at a given point in space.

Research on composite anti-disturbance adaptive constraint control strategy for quadruped robot

To achieve the stable walking of a quadruped robot, a composite anti-disturbance adaptive constraint control strategy is proposed based on the analysis of the dynamic model. First, the leg control adopts a trajectory tracking constraint control algorithm based on a time-varying tangent-type barrier Lyapunov function, which ensures high-precision control with joint trajectory tracking errors consistently constrained within a time-varying boundary. To further enhance the robustness of the system, an adaptive algorithm is used to compensate for external disturbances and system uncertainties. Second, the body posture control of the quadruped robot adopts the Virtual Model Control algorithm, which achieves stable adjustments of the body posture and soft contact between the foot end and the ground. This further improves its disturbance rejection capability. Finally, a comparative study of control algorithms is being conducted using MATLAB/Simulink. The results show that under this control strategy, the quadruped robot’s motion exhibits good robustness and flexibility.

Fixed‐Time Consensus Control With Event‐Triggered Mechanism for Multi‐Agent Systems Suffered Time‐Varying State Constraints

ABSTRACTA fixed‐time consensus control protocol is proposed for uncertain nonlinear multi‐agent systems (MASs) with time‐varying state constraints. By applying the time‐varying barrier Lyapunov functions (BLFs), an adaptive consensus control protocol is constructed to make certain that all system states maintain within the predetermined time‐varying ranges. Meanwhile, an event‐triggered mechanism (ETM) is established to alleviate the burden of MASs communication. Besides, to guarantee the control performance, a fixed‐time control method based on neural networks (NNs) is developed. It is demonstrated that the MASs can synchronize in a fixed time, and the state constraints are satisfied. Finally, two simulation examples demonstrate the effectiveness of the presented protocol.

Prescribed-time observer-based output feedback stabilisation of switched uncertain planar systems with asymmetric output constraints

This paper presents an observer-based output feedback control strategy to solve the prescribed-time stabilisation of uncertain planar switched nonlinear systems with asymmetric output constraints. Based on adding a power integrator technique, prescribed-time switched state feedback controllers and a common fractional-type barrier Lyapunov function are developed. Then, deliberately constructed prescribed-time switched reduced-order observers are presented to estimate the unmeasurable state. Combing the switched state feedback controllers and reduced-order observers proposed in this note, the closed-loop switched planar systems achieve prescribed-time stability. Meanwhile, the violation of asymmetric output constraints is prevented implicitly by the developed barrier Lyapunov function. The novelty of this approach lies in the ingenious construction of prescribed-time switched observers and the unified design characteristics of the method, which enable the accomplishment of prescribed-time output feedback stabilisation for switched systems with/without output constraints without necessitating any structure modifications to the switched controllers and observers.

Finite-time stabilisation for a class of high-order uncertain planar systems with an output constraint via output feedback

This article is concerned with the output-feedback finite-time stabilisation problem for a class of high-order planar systems with unknown control coefficients, unknown measurement sensitivity and output constraint. The bounds of the unknown control coefficients and unknown measurement sensitivity are unknown, which prevent the construction of conventional constrained output-feedback finite-time controllers. Based on homogeneous systems theory, a simple constrained output-feedback finite-time controller is successfully constructed by utilising a new type of barrier Lyapunov function. Rigorous theoretical analysis suggests that the considered system under the proposed output-feedback controller is finite-time stable, and the requirement of output constraint is achieved. The innovative aspect of this control approach is its unification of the output-feedback finite-time stabilisation problem for high-order uncertain planar systems, addressing both scenarios with and without output constraints, all within a unified framework, without altering the established control structure. Finally, two examples are given to illustrate the effectiveness of the proposed control scheme.

Finite‐Time Decentralized Adaptive Fuzzy Control for Non‐Triangular Form Large‐Scale Time‐Delay Systems With Full State Constraints

ABSTRACTThis paper is concerned with the problem of finite‐time decentralized adaptive fuzzy fault tolerant control for a class of non‐triangular form large‐scale time delay systems with full state constraints. By using the fuzzy logic systems and domination approach, the unknown nonlinear functions are approximated and the non‐triangular form structure is tackled, respectively. The time‐varying barrier Lyapunov function (TBLF) is used to ensure that the full state constraints are satisfied. Based on the proposed TBLF and backstepping technique, an adaptive fuzzy fault‐tolerant control protocol is presented. It can assure that the errors converge to a small neighborhood of the origin in a finite time, the signals of the whole closed‐loop systems are bounded and the full state constraints are satisfied. Simulation example is presented to further demonstrate the effectiveness of the proposed approach.

Adaptive Neural Control of Constrained MIMO Nonlinear Systems With Asymmetric Input Saturation and Dead Zone.

In this article, the adaptive neural control is studied for multiple-input-multiple-output (MIMO) nonlinear systems with asymmetric input saturation, dead zone, and full state-function constraints. A suitable transformation is introduced to overcome the dead zone and saturation nonlinearity, and radial basis function (RBF) neural networks (NNs) are used to approximate the unknown nonlinear functions. What is more, we apply the Nussbaum function and time-varying barrier Lyapunov function (BLF) to deal with the unknown control gains and full state-function constraints, respectively. Based on the backstepping method, a universal adaptive neural control scheme is presented such that not only the state-function constraints of the closed-loop system cannot be violated and all signals of the closed-loop systems are bounded, but also the tracking error converges to a small neighborhood containing the origin. The effectiveness of the proposed control scheme is verified by an application to the mass-spring-damper system and a numerical example.