Asymmetric Time-varying Barrier Lyapunov Function Research Articles

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.

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).

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.

Quaternion based Three-Dimensional Impact Time and Field-of-View Constrained Guidance

In this paper, an impact time-constrained guidance scheme against stationary targets, considering the bounds on the seeker's look angle, is proposed. The guidance strategy is developed within a nonlinear and coupled three-dimensional framework using quaternion-based dynamics to avoid possible singularities. The guidance approach first obtains the bounds on the time-to-go values corresponding to the bounds on the interceptor's field-of-view. These bounds on time-to-go are then utilized to derive interceptor lateral acceleration using asymmetric time-varying barrier Lyapunov function to intercept a target at a pre-defined time of impact without violating the prescribed bounds on the field-of-view. Furthermore, a way to achieve larger impact times with a multi-phase guidance structure was devised. The effectiveness of the proposed guidance law is validated with numerical simulations, the results of which are found to be satisfactory.

Finite-time adaptive neural network command filtered controller design for nonlinear system with time-varying full-state constraints and input quantization

In this paper, an adaptive finite-time command filtered control scheme is investigated for a class of nonlinear systems with asymmetric time-varying full state constraints and input quantization. Firstly, by fusing the backstepping control method and command filter technique, a novel adaptive neural networks (NNs) command filtered control approach is proposed. Moreover, a modified error compensation mechanism is constructed to compensate for the filtering error. Secondly, a smooth nonlinear transformation is constructed to eliminate the influence brought by the actuator subject to input quantization. Based on the constructed asymmetric time-varying barrier Lyapunov function (TVBLF), the strict constraints are guaranteed not to be violated and the stability of the closed-loop system is achieved in finite-time. Finally, simulations are carried out to illustrate the effectiveness of the theoretical results.

Predefined-time tracking of nonlinear strict-feedback systems with time-varying output constraints

In this paper, the problem of the predefined-time tracking with time-varying output constraints (TVOC) is investigated for a class of nonlinear strict-feedback systems. First, the sufficient conditions for the studied problem are presented. Then, a recursive design algorithm of the controller is proposed by backstepping technique. A novel stabilizing function is constructed by adding a fractional term, which is capable of decreasing the asymmetric time-varying Barrier Lyapunov Function (BLF) to the origin within any desired settling time. After that, it is shown that under our proposed control, all the closed-loop signals are bounded, and the tracking error converges to zero within any desired settling time and remains zero thereafter without the violation of the output constraint. The settling time in this paper is not only independent of the design parameters, nor does it depend on the initial conditions, and can be set according to per our will. Finally, two examples are given to illustrate the effectiveness of the proposed method.

Fuzzy adaptive event-triggered control for a class of nonlinear systems with time-varying full state constraints

This paper proposes a fuzzy adaptive event-triggered control (ETC) design method for nonlinear systems with time-varying state constraints. Fuzzy logic systems (FLSs) is adopted to approximate the unknown smooth functions and the constraints are satisfied by using an appropriate asymmetric time-varying barrier Lyapunov function (BLF). The communication burden from the controller to the actuator is reduced by designing an appropriate ETC scheme. Finally, it is shown that the full-state constraints are not violated at any step of the backstepping design and the signals in the closed-loop system are bounded. The effectiveness of the proposed adaptive ETC scheme is verified by two simulation examples.

Adaptive output feedback control for a class of uncertain non-strict feedback systems with asymmetric time-varying output constraints

This study investigated a novel adaptive output feedback control scheme for non-strict feedback nonlinear systems with uncertainties, disturbances, and asymmetric time-varying output constraints. Because that the states of the system are unmeasurable, we used an adaptive fuzzy state observer to obtain the estimated values of the states. To make the output and tracking error satisfy their asymmetric time-varying constraints, an asymmetric time-varying barrier Lyapunov function was adopted. To overcome the “explosion of complexity” problem, we also adopted the dynamic surface control technology. The stability of the closed-loop system was proved by the Lyapunov method, and we give two simulation examples to show the effectiveness of the proposed control method.

Variable-Structure Near-Space Vehicles with Time-Varying State Constraints Attitude Control Based on Switched Nonlinear System.

This study is concerned with the attitude control problem of variable-structure near-space vehicles (VSNSVs) with time-varying state constraints based on switched nonlinear system. The full states of vehicles are constrained in the bounded sets with asymmetric time-varying boundaries. Firstly, considering modeling uncertainties and external disturbances, an extended state observer (ESO), including two distinct linear regions, is proposed with the advantage of avoiding the peaking value problem. The disturbance observer is utilized to estimate the total disturbances of the attitude angle and angular rate subsystems, which are described in switched nonlinear systems. Then, based on the estimation values, the asymmetric time-varying barrier Lyapunov function (BLF) is employed to construct the active disturbance rejection controller, which can ensure the full state constraints are not violated. Furthermore, to resolve the ‘explosion of complexity’ problem in backstepping control, a modified dynamic surface control is proposed. Rigorous stability analysis is given to prove that all signals of the closed-loop system are bounded. Numerical simulations are carried out to demonstrate the effectiveness of the proposed control scheme.

Adaptive neural dynamic surface control of MIMO uncertain nonlinear systems with time-varying full state constraints and disturbances

In order to stabilize multiple-input–multiple-output uncertain strict feedback nonlinear systems with time-varying full-state constraints and external disturbances, an adaptive neural dynamic surface control method is investigated in this paper. A new compensator is proposed, which combines approximation error based adaptive radial basis function neural networks (RBFNNs) and nonlinear disturbance observer (NDOB) to improve the compensate performance of unmodeled dynamics and external disturbances. To prevent that the time-varying full state constraints are violated, the controller is designed via asymmetric time-varying barrier Lyapunov function (ATBLF). Meanwhile, the dynamic surface control is established to avoid the problem of “explosion of complexity” in traditional backstepping design. All closed-loop signals are proved to be semiglobally uniformly ultimate bounded through stability analysis. Finally, the simulation for six degrees of freedom (6-DOF) model unmanned airship are given to illustrate the effectiveness of the proposed control method.

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.

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.

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.

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 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.