Time-varying Barrier Lyapunov Function Research Articles

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 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.

SDO-Based Command Filtered Adaptive Neural Tracking Control for MIMO Nonlinear Systems With Time-Varying Constraints.

In this article, an adaptive neural tracking control based on saturation disturbance observer (SDO) and command filter is studied for multiple-input-multiple-output nonlinear systems with time-varying constraints and system uncertainties. By employing neural networks (NNs), the system uncertainties are approximated. The SDO is proposed to estimate the composited disturbances which consist of NN approximation errors and the external bounded disturbances. Compared with the traditional disturbance observer, the SDO can reduce the estimation error to some extent. The control requirements are achieved based on the multiconstraints which contain three layers: 1) prescribed performance functions (PPFs); 2) actual constraints; and 3) virtual constraints. The errors remain within the prescribed small neighborhood of zero by using the PPFs, the error constraints ensure that the time-varying constraints are never violated even if the PPFs are not available, and the virtual constraints are applied in a new time-varying barrier Lyapunov function (TVBLF) to design virtual controllers and controller to solve the singularity problem of the traditional TVBLF. In addition, the command filter is introduced to solve the problem of "explosion of complexity." Finally, a numerical simulation verifies the effectiveness of the proposed scheme for a flight control of unmanned aerial vehicle.

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.

Rotation matrix-based finite-time trajectory tracking control of AUV with output constraints and input quantization

This study investigated a rotation-matrix-based finite-time trajectory tracking problem for autonomous underwater vehicles (AUVs) in the presence of output constraints, input quantization, and uncertainties. First, a rotation matrix-based attitude representation is introduced, which allow attitude dynamics to be globally and uniquely represented without unwinding. To satisfy the finite-time stability of AUV tracking control and the output constraints imposed by introducing the new attitude error vector, a novel finite-time command-filtered backstepping controller (FTCFBC) is proposed based on the asymmetrical time-varying barrier Lyapunov function (TVBLF). Subsequently, a second-order auxiliary dynamic system (ADS) is proposed to estimate the negative effects that of input quantization errors. Because the quantized control inputs can be switched at an appropriate earlier or later switching timing depending on the output of the ADS, the negative impact of quantization errors on the control accuracy is reduced. Moreover, an adaptive finite-time disturbance observer (AFTDO) is developed to estimate the lumped uncertainties without prior information on the bounds of the uncertainties. Finally, the results of the theoretical analysis verified that the tracking errors can converge within a finite time. Numerical simulations confirmed the effectiveness of the proposed control scheme.

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.

Lifelong learning‐based multilayer neural network control of nonlinear continuous‐time strict‐feedback systems

AbstractIn this paper, we investigate lifelong learning (LL)‐based tracking control for partially uncertain strict feedback nonlinear systems with state constraints, employing a singular value decomposition (SVD) of the multilayer neural networks (MNNs) activation function based weight tuning scheme. The novel SVD‐based approach extends the MNN weight tuning to layers. A unique online LL method, based on tracking error, is integrated into the MNN weight update laws to counteract catastrophic forgetting. To adeptly address constraints for safety assurances, taking into account the effects caused by disturbances, we utilize a time‐varying barrier Lyapunov function (TBLF) that ensures a uniformly ultimately bounded closed‐loop system. The effectiveness of the proposed safe LL MNN approach is demonstrated through a leader‐follower formation scenario involving unknown kinematics and dynamics. Supporting simulation results of mobile robot formation control are provided, confirming the theoretical findings.

Shifting asymmetric time-varying BLF-based model-free hybrid force/position control for 3-DOF SEA-based manipulator with random initial error

In this work, a shifting asymmetric time-varying barrier Lyapunov function (BLF)-based model-free hybrid force/position controller (SABMHC) is proposed for the endpoint of the 3-DOF series elastic actuator (SEA)-based manipulator which can be used for machining of large curved surfaces. The proposed SABMHC contains a force sub-control loop and a position sub-control loop. The force sub-control loop converts the force control into position control based on the idea of impedance control, and realizes the hybrid force/position control through the position sub-control. Then, in order to achieve accurate trajectory tracking control of the position sub-control loop, a shifting asymmetric time-varying BLF-based model-free controller is proposed, which includes the error shifting function, asymmetric time varying BLF, time-delay estimation (TDE) technique, and adaptive compensation term. To prevent the random initial error from being so large that it exceeds the pre-set boundary and affects the steady-state response, an error shifting function is introduced. The error shifting function can make the shifting error independent of the tracking error before reaching the pre-set shifting time, so as to achieve better control performance by setting a small pre-set boundary for the shifting error. With the Lyapunov function, the designed SABMHC can ensure that the stability and the shifting error converges within the pre-set boundary in a finite time. Finally, the effectiveness and benefits of the proposed SABMHC are analyzed by comparison with the TDE-based intelligent PID (TDE-iPD) and BLF-based sliding-mode controller (BLF-SMC).

Adaptive NN Tracking Control for Uncertain MIMO Nonlinear System With Time-Varying State Constraints and Disturbances.

In this article, an adaptive neural network (NN) tracking control scheme is proposed for uncertain multi-input-multi-output (MIMO) nonlinear system in strict-feedback form subject to system uncertainties, time-varying state constraints, and bounded disturbances. The radial basis function NNs (RBFNNs) are adopted to approximate the system uncertainties. By constructing the intermediate variables, the external disturbances that cannot be directly measured are approximated by the disturbance observers. The time-varying barrier Lyapunov function (TVBLF) is constructed to guarantee the boundedness of the errors lie in the sets. To overcome the potential singularity problem that the denominator of the barrier function term approaches zero in controller design, the adaptive NN tracking control scheme with time-varying state constraints is proposed. Based on the TVBLF, the controller will be designed to guarantee tracking performance without violating the appropriate error constraints. The analysis of TVBLF shows that all closed-loop signals remain semiglobally uniformly ultimately bounded (SGUUB). The simulation results are performed to validate the validity of the proposed scheme.

Event-Triggered Adaptive Fuzzy Finite-Time Output Feedback Control for Stochastic Nonlinear Systems With Input and Output Constraints

This paper focuses on the problem of designing an adaptive fuzzy event-triggered finite-time output feedback control for stochastic nonlinear systems with input and output constraints. A fuzzy observer is designed to estimate the unmeasured states. The quartic asymmetric time-varying barrier Lyapunov function is established to ensure constraint satisfaction. By utilizing the stochastic theory, finite-time command filtered backstepping method and event-triggered mechanism, a finite-time event-triggered controller is recursively designed, which can not only guarantee finite-time convergent property, but also reduce communication pressure. Meanwhile, the matter of “explosion of complexity” is removed by introducing the finite-time command filter and the effect of filtered errors is offset by constructing error compensation signals. Moreover, an auxiliary system is introduced to handle the input constraint. Finally, the effectiveness of the theoretical results is demonstrated by the simulation example.

Event-triggered adaptive control for stochastic nonlinear systems with time-varying full state constraints and output dead-zone

This paper studies the problem of event-triggered adaptive control for a class of strictly-feedback stochastic nonlinear systems. The output dead zone and time-varying full-state constraints are considered in the controller. Firstly, time-varying barrier Lyapunov functions (TVBLFs) are introduced to address problems of time-varying state constraints. Then, the Nussbaum-type function is used to compensate for the influence of the output dead zone. The problem of state constraint is well solved when the system’s output signal is affected by the dead zone, which satisfies a wider application space. In addition, a new relative threshold of the event-triggered control (ETC) scheme is considered to save communication resources, and the Zeno behavior is excluded. This scheme makes the trigger interval more flexible and optimizes the performance of the controller. Moreover, the error compensation signals reduce the filtered errors and simplify the algorithm. Simultaneously, an adaptive tracking controller with the backstepping technique is designed so that all signals in the closed-loop system are bounded and the tracking error converges to a small residual set of the origin. Finally, two simulation examples are given to demonstrate the effectiveness of the control method.

Adaptive finite-time fault-tolerant control for Robot trajectory tracking systems under a novel smooth event-triggered mechanism

The problem of adaptive finite-time fault-tolerant control with smooth event-triggered mechanism is addressed for quadrotor trajectory tracking systems. In light of recent studies on fault-tolerant control in the field of nonlinear systems, this article focuses on quadrotor trajectory tracking systems with actuator faults and disturbances. Different from the previous works, an ingenious smooth event-triggered mechanism is proposed to circumvent the discontinuous triggered signal and alleviate the communication burden simultaneously, which is of great significance to increase the operation life of the quadrotor. Subsequently, the finite-time performance function is designed to guarantee the prescribed tracking performance. Furthermore, a novel finite-time convergent adaptive fault-tolerant controller is proposed via the time-varying barrier Lyapunov function technique. The radial basis function neural networks are utilized to deal with the nonlinear approximation, and the adaptive laws are developed to accurately estimate the unknown model uncertainty, thus effectively handling the challenge of the controller design caused by the actuator faults and disturbances. Under the developed adaptive fault-tolerant controller, all the closed-loop system signals are bounded and the tracking errors are convergent within finite time. Meanwhile, the Zone behavior can be excluded by the positive sampling intervals. Finally, two examples are employed to verify the effectiveness and advantages of the suggested control scheme.

Event-trigger-based composite adaptive fuzzy control for nonlinear time-varying state constraint systems with asymmetric input saturation

In this paper, a novel composite adaptive fuzzy control (AFC) based on the command filtered backstepping and event-triggered mechanism is proposed for nonstrict-feedback nonlinear systems with input saturation and time-varying full-state constraints. A fuzzy observer is designed to estimate the unmeasured states. Simultaneously, by introducing a serial-parallel estimation model, a fuzzy control tactic with the composite adaptive law of parameters is established which greatly increases the precision of unknown term estimation. In addition, the command filtering technique is employed to solve the issue of “explosion of complexity” and compensate for the errors caused by the command filters. The event-triggered mechanism is utilized to effectively decrease the data redundancy. By using the time-varying barrier Lyapunov functions (BLFs), all the states can remain within a prescribed time-varying interval. The designed controller can guarantee the convergence of the tracking error at the origin and the boundedness of all closed-loop signals. Finally, two simulation examples are carried out to validate the effectiveness of the proposed control scheme.

Time-Varying BLFs-Based Adaptive Neural Network Finite-Time Command-Filtered Control for Nonlinear Systems

This article deals with the adaptive neural network (NN) finite-time (FT) command-filtered tracking control problem for a class of nonlinear systems with time-varying full-state constraints. Based on the asymmetric time-varying barrier Lyapunov functions (TVBLFs), the issue of time-varying full-state constraints is settled. The influence of unknown items in the system can be eliminated by the adaptive NN control method. Moreover, the improved FT command filter is introduced to relax the restriction on the input signal and solve the explosion of complexity (EOC) problem. Meanwhile, the FT error compensation mechanism is developed to eliminate the influence of filtering error. It is shown that the proposed strategy can guarantee FT boundedness of all the signals in the closed-loop system and FT convergence of the tracking error. An example verifies the effectiveness of the proposed control method.

Predefined–Time Adaptive Control of a Piezoelectric–Driven Motion System With Time–Varying Output Constraint

This brief investigates the output feedback adaptive tracking control of a piezoelectric-driven motion (PDM) system with time-varying output constraint. The key features of the developed predefined-time adaptive neural control (PTANC) method are as follows. i) A broad learning system with recurrent enhancement node (RENBLS) is used to construct an RENBLS-based observer such that state information can be estimated; ii) we incorporate a performance regulator and time-varying barrier Lyapunov function (TVBLF) into the controller design. The proposed method can then achieve the control effect in a predefined time without violating the output constraint. Stability analysis of the PTANC strategy is demonstrated in theory. Furthermore, the effectiveness of the proposed control scheme is experimentally verified via the PDM system.

Adaptive Neural Control for Nonlinear MIMO Function Constraint Systems

Dear Editor, In this letter, a novel adaptive control design problem for uncertain nonlinear multi-input-multi-output (MIMO) systems with time-varying full state constraints is proposed, where the considered systems consist of various subsystems, and the states of each subsystem are interconnected tightly. It is universally acknowledged that in the existing researches with state constraints, system constraint bounds are always constants or time-varying functions. Different from previous methods, the constraint boundary of this letter is regarded as a special function of not only time but of state variables. In order to handle time-varying full state constraints, the tangent type time-varying barrier Lyapunov functions (tan-TVBLFs) are introduced. By combining neural networks (NNs) and backstepping technique, an intelligent controller is developed. Meanwhile, we introduce an even function to guarantee the feasibility of NN approximation of unknown functions over practical compact sets. The feasibility of the mentioned control strategy is certified through the simulation results.

Quasi-synchronous control of uncertain multiple electrohydraulic systems with prescribed performance constraint and input saturation

This article focuses on the high accuracy quasi-synchronous control issue of multiple electrohydraulic systems (MEHS). In order to overcome the negative effects of parameter uncertainty and external load interference of MEHS, a kind of finite-time disturbance observer (FTDO) via terminal sliding mode method is constructed based on the MEHS model to achieve fast and accuracy estimation and compensation ability. To avoid the differential explosion in backstepping iteration, the dynamic surface control is used in this paper to guarantee the follower electrohydraulic nodes synchronize to the leader motion with a better performance. Furthermore, a time-varying barrier Lyapunov function (tvBLF) is adopted during the controller design process to constraint the output tracking error of MEHS in a prescribed performance with time-varying exponential function. As the initial state condition is relax by tvBLF, the input saturation law is also adopted during the controller design process in this paper to restrain the surges of input signals, which can avoid the circuit and mechanical structure damage caused by the volatile input signal. An MEHS experimental bench is constructed to verify the effectiveness of the theoretical conclusions proposed in this paper and the advantages of the proposed conclusions in this paper are illustrated by a series of contradistinctive experimental results.

Fixed-Time Neural Control of Robot Manipulator With Global Stability and Guaranteed Transient Performance

Nowadays, due to many limitations in reality, the optimization of tracking precision and convergence time has attracted the attention of researchers in robotics community. In this article, a fixed-time adaptive neural network (NN) controller is proposed for unknown robot manipulators. A switching mechanism is integrated into the control design such that the semiglobal stability of the conventional NN control systems can be extended to global stability. The time-varying barrier Lyapunov function and the fixed-time control technique are incorporated into the controller design to guarantee the prescribed motion constraints and the fixed-time convergence simultaneously. Compared with some existing fixed-time NN control algorithms, the assumption that NN weight should be upper bounded can be relaxed in our work. Finally, the simulation and experiment studies are respectively carried out based on an unknown 2-degree of freedom robot and a Baxter robot to demonstrate the effectiveness and superiority of the proposed control scheme.

Appointed-Time Control for Flexible Hypersonic Vehicles with Conditional Disturbance Negation

This paper investigates the anti-disturbance control design for flexible air-breathing hypersonic vehicles (FAHVs) with appointed-time prescribed tracking performances. The challenging issues include multisource disturbances, cross-coupling effects of the vehicle dynamics, and asymmetric amplitude and rate saturations. To address these issues, we propose an appointed-time prescribed performance control scheme for FAHVs via conditional disturbance negation technique. In contrast to existing disturbance rejection approaches, the proposed control scheme not only estimates the disturbances first in a fixed time, but also evaluates the estimated disturbances and selectively conducts compensation actions according to the insight of the FAHV dynamic characteristics. To further enhance convergence rate, the composite appointed-time prescribed performance controllers are designed for FAHVs via time-varying barrier Lyapunov function and nonsmooth backstepping technique, which ensure satisfactory transient response and steady-state performances. In addition, the asymmetric amplitude and rate saturation problem of actuators are dealt with by introducing unified approximation dynamics. It is rigorously proved that the practical appointed-time convergence of the tracking errors and the fixed-time convergence of all signals in the resultant FAHV closed-loop system can be achieved under the proposed control scheme. Finally, extensive comparative simulations are provided to demonstrate the feasibility and superiority of the proposed approach.

A Barrier Neuroadaptive Dynamic Surface Control Approach for Tank Gun Control Systems With Input Saturation

In harsh battlefield environments, tanks have to encounter some nonlinear characteristics including frictional moment, gear backlash and parameter drifts, etc. The existence of such nonlinear characteristics makes the controller design of tank gun control systems (TGCSs) challenging. In this paper, a barrier neuroadaptive control approach is proposed to handle the uncertainties and nonlinearities, so as to achieve satisfactory tracking performance for TGCSs. With a time-varying barrier Lyapunov function employed in controller design, the output error of TGCS is restricted within the preset bound during the control process. A radial basis function (RBF) neural network is built to approximate the uncertainties in tank gun control systems. An anti-windup control strategy is developed to deal with the input saturation nonlinearity, with a Nussbaum function used to compensate for the nonlinear term arising from input saturation. By reasonably applying filtering error into output-constrained adaptive backstepping control design, the three steps in the traditional backstepping control design are reduced to two steps. The asymptotic stability of the closed-loop TGCSs is proven by Lyapunov theory. Finally, a simulation example is presented to verify the effectiveness of the proposed control scheme.