Time-varying Barrier Lyapunov Function Research Articles

Composite Neural Learning-Based Nonsingular Terminal Sliding Mode Control of MEMS Gyroscopes.

The efficient driving control of MEMS gyroscopes is an attractive way to improve the precision without hardware redesign. This paper investigates the sliding mode control (SMC) for the dynamics of MEMS gyroscopes using neural networks (NNs). Considering the existence of the dynamics uncertainty, the composite neural learning is constructed to obtain higher tracking precision using the serial-parallel estimation model (SPEM). Furthermore, the nonsingular terminal SMC (NTSMC) is proposed to achieve finite-time convergence. To obtain the prescribed performance, a time-varying barrier Lyapunov function (BLF) is introduced to the control scheme. Through simulation tests, it is observed that under the BLF-based NTSMC with composite learning design, the tracking precision of MEMS gyroscopes is highly improved.

Fuzzy adaptive tracking control for switched nonlinear systems with full time-varying state constraints

In this paper, a novel fuzzy adaptive tracking control scheme is presented for a class of nonstrict-feedback uncertain switched nonlinear systems by taking into account constraint. The considered switched nonlinear system contains unknown nonlinearities. In the design process, firstly, the problem of state constraints is coped with by utilizing the asymmetric time-varying barrier Lyapunov functions (TABLFs), and the problem of “explosion of complexity” is solved by dynamic surface control (DSC) technology. Secondly, fuzzy logic systems (FLSs) are utilized to approximate the unknown nonlinear dynamics. Under the framework of adaptive control design, the switched adaptive state feedback controller is designed, which can guarantee all states cannot violate their constrained sets. Then, based on the Lyapunov function and average dwell time (ADT) approach, the theoretical analysis is provided for the closed-loop systems within constraint performance bounded. Finally, a numerical example is proposed to further elaborate the effectiveness of the presented control scheme.

Fuzzy State Observer-Based Adaptive Dynamic Surface Control of Nonlinear Systems with Time-Varying Output Constraints

In this paper, a new fuzzy dynamic surface control approach based on a state observer is proposed for uncertain nonlinear systems with time-varying output constraints and external disturbances. An adaptive fuzzy state observer is used to estimate the states that cannot be measured in the systems. In our method, a time-varying Barrier Lyapunov Function (BLF) is used to ensure that the output does not violate time-varying constraints. In addition, dynamic surface control (DSC) technology is applied to overcome the problem of “explosion of complexity” in a backstepping control. Finally, the stability and signal boundedness of the system are confirmed by the Lyapunov method. The simulation results show the effectiveness and correctness of the proposed method.

A novel guaranteed tracking performance control for reentry vehicle with actuator constraints and uncertainties

A novel guaranteed tracking performance control scheme is presented for the reentry vehicle encountered in actuator saturation and enormous amount of uncertainties via time-varying barrier Lyapunov function (TVBLF) method. The required stable and transient tracking performance of the reentry attitudes are simultaneously enhanced by the proposed logarithm-type TVBLF and the control design complexity is reduced compared with the prescribed performance technique. Moreover, in order to eliminate the control performance degradation caused by the actuator constraints, an auxiliary error compensation design is inserted into the control law. In addition, the uncertainty rejection capability of the control system is achieved by exploiting the MIMO nonlinear extended disturbance observer. Finally, the uniform ultimately boundedness of the closed-loop system is established and numerical simulations are verified to demonstrate the effectiveness of the proposed control law for the reentry vehicle subject to attitude constraints, actuator saturations and uncertainties.

Adaptive Neural Network Learning Controller Design for a Class of Nonlinear Systems With Time-Varying State Constraints

This paper studies an adaptive neural network (NN) tracking control method for a class of uncertain nonlinear strict-feedback systems with time-varying full-state constraints. As we all know, the states are inevitably constrained in the actual systems because of the safety and performance factors. The main contributions of this paper are that: 1) in order to ensure that the states do not violate the asymmetric time-varying constraint regions, an adaptive NN controller is constructed by introducing the asymmetric time-varying barrier Lyapunov function (TVBLF) and 2) the amount of the learning parameters is reduced by introducing a TVBLF at each step of the backstepping. Based on the Lyapunov stability analysis, it can be proven that all the signals in the closed-loop system are the semiglobal ultimately uniformly bounded and the time-varying full-state constraints are never violated. Finally, a numerical simulation is given, and the effectiveness of this adaptive control method can be verified.

Time-Varying Tan-Type Barrier Lyapunov Function-Based Adaptive Fuzzy Control for Switched Systems With Unknown Dead Zone

This paper investigates the output constraint problem for switched uncertain nonlinear systems with unknown dead-zone input. The system output is constrained by a time-varying bound, and the time-varying Barrier Lyapunov Function (BLF) is employed to guarantee that the constraint condition is not violated. The parameter of considered dead-zone is unknown but bounded. In order to remove the effectiveness caused by dead-zone, an adaptive scheme is used to adjust the bound of the unknown parameter. In addition, the unknown system dynamic is taken into account, which is modeled by using fuzzy logic systems (FLSs). Combing the backstepping technique, an adaptive controller is constructed such that all the signals in the closed-loop system are bounded under arbitrary switching signal, and the system out can track the reference signal as soon as possible. Moreover, the constraint condition for system output is ensured. Finally, an example is employed to explain the effectiveness of the proposed method.

Observer-Based Adaptive Fuzzy Control for Time-Varying State Constrained Strict-Feedback Nonlinear Systems with Dead-Zone

This paper focuses on the problem of adaptive fuzzy control for a class of time-varying state constrained strict-feedback nonlinear systems with dead-zone. Based on the arbitrary approximation of fuzzy logic systems (FLSs), the unknown nonlinear functions in the system are approximated by FLSs. Time-varying barrier Lyapunov functions and a fuzzy observer are designed to dispose the unmeasured time-varying constrained states in the system. Furthermore, combining with the adaptive backstepping method and Lyapunov stability theory, it is testified that the proposed control strategy can ensure system stability and all the signals in the closed-loop system are semi-global uniformly ultimately bounded. Finally, the simulation results are given to demonstrate the effectiveness of the proposed method.

Adaptive Trajectory Tracking Control of a Fully Actuated Surface Vessel With Asymmetrically Constrained Input and Output

This brief addresses the trajectory tracking control problem of a fully actuated surface vessel subjected to asymmetrically constrained input and output. The controller design process is based on the backstepping technique. An asymmetric time-varying barrier Lyapunov function is proposed to address the output constraint. To overcome the difficulty of nondifferentiable input saturation, a smooth hyperbolic tangent function is employed to approximate the asymmetric saturation function. A Nussbaum function is introduced to compensate for the saturation approximation and ensure the system stability. The command filters and auxiliary systems are integrated with the control law to avoid the complicated calculation of the derivative of the virtual control in backstepping. In addition, the bounds of uncertainties and disturbances are estimated and compensated with an adaptive algorithm. With the proposed control, the constraints will never be violated during operation, and all system states are bounded. Simulation results and comparisons with standard method illustrate the effectiveness and advantages of the proposed controller.

Adaptive fuzzy control for a marine vessel with time‐varying constraints

An adaptive fuzzy neural network (FNN) control scheme is proposed for a marine vessel with time-varying constraints, guaranteed transient response and unknown dynamics. A series of continuous constraint functions are introduced to shape the motion of a marine vessel. To deal with the constraint problems and transient response problems, an asymmetric time-varying barrier Lyapunov function is designed to ensure that the system states are upper bounded by the considered constraint functions. FNNs are constructed to identify the unknown dynamics. Considering existing approximation errors when FNNs approximating the unknown dynamics, an adaptive term is designed to compensate the approximation errors in order to obtain accurate control. Via Lyapunov stability theory, it has been proved that all the states in the closed-loop system are uniformly bounded ultimately without violating the corresponding prescribed constraint region. Two comparative simulations are carried out to verify the effectiveness of the proposed control.

Adaptive robust backstepping attitude control for a multi-rotor unmanned aerial vehicle with time-varying output constraints

Output constraints and uncertainties are the main factors that degrade the control performance of the multi-rotor unmanned aerial vehicle (MUAV). In this paper, an adaptive neural network backstepping dynamic surface control algorithm based on asymmetric time-varying Barrier Lyapunov Function is proposed for the attitude system of a novel MUAV under asymmetric time-varying output constraints, model uncertainties and external disturbances. The asymmetric time-varying Barrier Lyapunov Function, which will grow infinite when its arguments approach some limit, is introduced to keep the output under time-varying asymmetric constraints. Considering the derivation problem of the virtual control function in backstepping, the dynamic surface control is applied to simplify the algorithm. The adaptive neural network is used to approximate the dynamic model of the attitude system, and the minimal learning parameters are employed at the same time to reduce online computation burden. In order to balance out the external disturbance and further reduce the approximate error of the adaptive neural network, a robust term is designed to compensate the above negative impacts. The proposed algorithm guarantees that all the signals of the closed-loop system bounded by Lyapunov theory. Finally, some contrast simulation experiments are given to illustrate the effectiveness and superiority of the control scheme.

Finite-Time Stabilization for a Class of Non-Affine Nonlinear Systems With Input Saturation and Time-Varying Output Constraints

This paper investigates finite-time stabilization of a class of non-affine nonlinear systems with time-varying output constraints, input saturation, and unknown disturbance. Without loss of accuracy, an approximation method is employed to convert the non-affine nonlinear system to an affine-like expression. A novel adaptive terminal sliding mode disturbance observer is proposed to enhance system robustness by estimating unknown compound disturbances in finite time, including external disturbances and system uncertainties. A time-varying barrier Lyapunov function is applied to ensure that constraints are not violated. Backstepping-based controllers are designed to drive tracking errors to zero in finite time. Simulation results demonstrated the effectiveness of the proposed control technique.

Robust Nonlinear Path Following Control of Underactuated MSV With Time-Varying Sideslip Compensation in the Presence of Actuator Saturation and Error Constraint

A robust nonlinear path following control scheme is proposed for the underactuated marine surface vehicle (MSV) under the condition of the unknown time-varying sideslip, time-varying error constraint, actuator saturation, and unknown compound disturbances including external environment disturbance and model uncertainties in this paper. First, integrating the time-varying barrier Lyapunov function and sideslip observer, an error-constrained and sideslip observer based line-of-sight (ECS-LOS) guidance law is established. The ECS-LOS guidance law can calculate the desired heading angle, estimate the time-varying sideslip angle, and deal with the error constraint problem. Second, the robust path following controller is developed via dynamic surface control technique to achieve attitude tracking and velocity tracking control. The unknown compound disturbances are estimated by means of disturbance observer and the actuator saturation is compensated by the auxiliary function. Stability analysis proves that the tracking error of MSV can converge into a small neighborhood around zero and the constraint requirements on the vessel position are not violated during operation, while guaranteeing all states in the closed-loop control system are uniformly ultimately bounded. In the end, simulation studies and comparisons are carried out to demonstrate the validity of the proposed control approach.

Adaptive Neural Networks Control Using Barrier Lyapunov Functions for DC Motor System with Time-Varying State Constraints

This paper proposes an adaptive neural network (NN) control approach for a direct-current (DC) system with full state constraints. To guarantee that state constraints always remain in the asymmetric time-varying constraint regions, the asymmetric time-varying Barrier Lyapunov Function (BLF) is employed to structure an adaptive NN controller. As we all know that the constant constraint is only a special case of the time-varying constraint, hence, the proposed control method is more general for dealing with constraint problem as compared with the existing works on DC systems. As far as we know, this system is the first studied situations with time-varying constraints. Using Lyapunov analysis, all signals in the closed-loop system are proved to be bounded and the constraints are not violated. In this paper, the effectiveness of the control method is demonstrated by simulation results.

Robust state-constrained control design for nonlinear systems with uncertainties using a new barrier Lyapunov function

In this paper, a robust state-constrained control algorithm is proposed by introducing time-varying barrier Lyapunov functions (BLF) for nonlinear systems with uncertainties. Novel time-varying symmetric/asymmetric forms of error barrier functions are investigated in order to relax the requirements of the initial state compared with existing BLF-based literatures. By integrating the proposed time-varying BLF method with the backstepping technique, constraint satisfaction is achieved and signals in closed-loop are uniform asymptotically stable. In addition, the extended state observer technique is utilized to prevent the constraint violation during the transient phase and strengthen the robustness of the control system in the presence of uncertainties. Numerical simulations are implemented to illustrate the attitude tracking performance obtained from the proposed method for a homing missile with angle of attack constraint, parametric uncertainties and external disturbances.

Neural Network Controller Design for an Uncertain Robot With Time-Varying Output Constraint

An adaptive control-based neural network for a ${n}$ -link robot is studied and the considered robot can be transformed as a class of multi-input–multioutput systems. The position of the robot or the output of the transformed systems is constrained in a time-varying compact set. It is commonly known that the constant constraint belongs to a special case of the time-varying constraint, and thus, it can be more general for handling practical problem as compared with the existing methods for robot. The neural approximation is used to estimate the unknown functions of systems and the time-varying barrier Lyapunov function is used to overcome the violation of constraints. It can prove the stability of the closed-loop systems by using Lyapunov analysis. The feasibility of the approach is demonstrated by performing a simulation example.

Adaptive fuzzy dynamic surface control of nonlinear systems with input saturation and time-varying output constraints

Abstract This paper deals with the design of adaptive fuzzy dynamic surface control for uncertain strict-feedback nonlinear systems with asymmetric time-varying output constraints in the presence of input saturation. To approximate the unknown nonlinear functions and overcome the problem of explosion of complexity , a Fuzzy logic system is combined with the dynamic surface control in the backstepping design technique. To ensure the output constraints satisfaction, an asymmetric time-varying Barrier Lyapunov Function (BLF) is used. Moreover, by applying the minimal learning parameter technique, the number of the online parameters update for each subsystem is reduced to 2. Hence, the semi-globally uniformly ultimately boundedness (SGUUB) of all the closed-loop signals with appropriate tracking error convergence is guaranteed. The effectiveness of the proposed control is demonstrated by two simulation examples.

Adaptive Neural Network Control for Nonlinear Hydraulic Servo-System with Time-Varying State Constraints

An adaptive neural network control problem is addressed for a class of nonlinear hydraulic servo-systems with time-varying state constraints. In view of the low precision problem of the traditional hydraulic servo-system which is caused by the tracking errors surpassing appropriate bound, the previous works have shown that the constraint for the system is a good way to solve the low precision problem. Meanwhile, compared with constant constraints, the time-varying state constraints are more general in the actual systems. Therefore, when the states of the system are forced to obey bounded time-varying constraint conditions, the high precision tracking performance of the system can be easily realized. In order to achieve this goal, the time-varying barrier Lyapunov function (TVBLF) is used to prevent the states from violating time-varying constraints. By the backstepping design, the adaptive controller will be obtained. A radial basis function neural network (RBFNN) is used to estimate the uncertainties. Based on analyzing the stability of the hydraulic servo-system, we show that the error signals are bounded in the compacts sets; the time-varying state constrains are never violated and all singles of the hydraulic servo-system are bounded. The simulation and experimental results show that the tracking accuracy of system is improved and the controller has fast tracking ability and strong robustness.

Adaptive Control of Input Delayed Uncertain Nonlinear Systems With Time-Varying Output Constraints

This paper focuses on the tracking control of a class of uncertain nonlinear systems with consideration of both time-varying input delay and output constraints. By introducing an auxiliary signal, which is based on the finite integral of the past control values in the design procedure, an adaptive controller is proposed to compensate for the effect of input delay and to handle various uncertainties. Meanwhile, an asymmetric time-varying barrier Lyapunov function is employed in the controller design to ensure the output constraint satisfaction. The stability analysis utilizing Lyapunov-Krasovskii functionals reveals that the proposed adaptive controller guarantees a uniformly ultimately bounded tracking performance and the time-varying output constraints are never violated. Two simulation examples are given to verify the effectiveness of the proposed control scheme.

Control of nonlinear systems with time-varying output constraints

This paper presents control design for strict feedback nonlinear systems with time-varying output constraints. An asymmetric time-varying Barrier Lyapunov Function (BLF) is employed to ensure constraint satisfaction. By allowing the barriers to vary with the desired trajectory in time, the initial condition requirements are relaxed. Through a change of tracking error coordinates, we eliminate the explicit dependence of the BLF on time, thereby simplifying the analysis of constraint satisfaction. We show that asymptotic output tracking is achieved without violation of the output constraint, and also quantify the transient performance bound as a function of time that converges to zero. To handle parametric model uncertainty, we present an adaptive controller that ensures constraint satisfaction during the transient phase of online parameter adaptation. The performance of the proposed control is illustrated through a simulation example.