Adaptive Finite-time Tracking Control Research Articles

Adaptive Finite-Time Tracking Control of Fractional Microgrids Against Time-Delay Attacks

Adaptive Finite-Time Tracking Control of Fractional Microgrids Against Time-Delay Attacks

Finite-time adaptive prescribed performance DSC for pure feedback nonlinear systems with input quantization and unmodeled dynamics

<abstract><p>This paper presents a new prescribed performance-based finite-time adaptive tracking control scheme for a class of pure-feedback nonlinear systems with input quantization and dynamical uncertainties. To process the input signal, a new quantizer combining the advantages of a hysteresis quantizer and uniform quantizer has been used. Radial basis function neural networks have been utilized to approximate unknown nonlinear smooth functions. An auxiliary system has been employed to estimate unmodeled dynamics by producing a dynamic signal. By introducing a hyperbolic tangent function and performance function, the tracking error was made to fall within the prescribed time-varying constraints. Using modified dynamic surface control (DSC) technology and a finite-time control method, a novel finite-time controller has been designed, and the singularity problem of differentiating each virtual control scheme in the existing finite-time control scheme has been removed. Theoretical analysis shows that all signals in the closed-loop system are semi-globally practically finite-time stable, and that the tracking error converges to a prescribed time-varying region. Simulation results for two numerical examples have been provided to illustrate the validity of the proposed control method.</p></abstract>

Finite-Time Adaptive Neural Control for a Class of Nonlinear Systems With Asymmetric Time-Varying Full-State Constraints.

In this article, an adaptive finite-time tracking control scheme is developed for a category of uncertain nonlinear systems with asymmetric time-varying full-state constraints and actuator failures. First, in the control design process, the original constrained nonlinear system is transformed into an equivalent "unconstrained" one by using the uniform barrier function (UBF). Then, by introducing a new coordinate transformation and incorporating it into each recursive step of adaptive finite-time control design based on the backstepping technique, more general state constraints can be handled. In addition, since the nonlinear function in the system is unknown, neural network is employed to approximate it. Considering singularity, the virtual control signal is designed as a piecewise function to guarantee the performance of the system within a finite time. The developed finite-time control method ensures that all signals in the closed-loop system are bounded, and the output tracking error converges to a small neighborhood of the origin. At last, the simulation example illustrates the feasibility and superiority of the presented control method.

Fuzzy Adaptive Finite-Time Tracking Control for a Class of Nonlinear Systems: An Event-Triggered Quantized Control Scheme

This brief proposes a fuzzy adaptive event-triggered quantized finite-time control (ETQFTC) scheme for uncertain strict-feedback nonlinear systems with full-state constraints. By means of state transformation, filtered backstepping technique and fuzzy adaptive control with the idea of minimum learning parameter (MLP), a <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$C^{1}$</tex-math></inline-formula> ETQFTC scheme with low differential calculation and few parameter updates is developed. In the proposed scheme, the feasibility condition generally required in the existing state-constrained control, and the control chattering and singularity problem which are common in the existing FTC schemes are removed and avoided respectively. Finally, complete stability analysis and a set of comparative simulations are presented.

An Observer-Based Adaptive Neural Network Finite-Time Tracking Control for Autonomous Underwater Vehicles via Command Filters

Due to the hostile marine environment, there will inevitably be unpredictable factors during the operation of unmanned underwater vehicles, including changes in ocean currents, hull dimensions, and velocity measurement uncertainties. An improved finite-time adaptive tracking control issue is considered for autonomous underwater vehicles (AUVs) with uncertain dynamics, unknown external disturbances, and unavailable speed information. A state observer is designed to estimate the position and velocity of the vehicle via a neural network (NN) approach. The NN is used to estimate uncertainties and external disturbances. A finite-time controller is designed via backstepping and command filter techniques. A multi-input multi-output (MIMO) filter for AUVs is established, and the corresponding MIMO filter compensation signal is constructed to eliminate the effect of filtering error. All the signals of the closed-loop system are proved to be finite-time bounded. An example with comparison is given to show the effectiveness of our method.

Adaptive Finite-Time Tracking Control of Nonlinear Systems With Dynamics Uncertainties

In this paper, the problem of adaptive backstepping finite-time tracking control is investigated for a class of strict-feedback nonlinear systems with unmodeled dynamics and dynamic disturbances. A modified finite-time dynamic signal is first introduced to dominate the dynamic disturbance. By using the adaptive control, backstepping technique, and finite-time stability theory, an adaptive finite-time tracking controller is developed. Under the proposed control scheme, the finite-time tracking performance and the boundedness property of all signals in the closed-loop system are ensured. Finally, simulation results check the effectiveness of the suggested approach.

Finite-time adaptive neural control of uncertain constrained nonlinear systems with actuator fault

This article investigates the finite-time adaptive tracking control for a class of nonlinear systems, which are affected by unknown control coefficients, full state constraints of asymmetric functions and actuator fault. In order to overcome the full-state-function constraints, we present the barrier Lyapunov function (BLF) dependent of state and time. Meanwhile, the Nussbaum function and the radial basis function (RBF) neural networks (NNs) are introduced to handle unknown control coefficients and unknown nonlinear functions respectively. Then, a fault-tolerant tracking controller is established to pledge that all states do not violate the asymmetric state-function-constraint boundary, all signals of the closed-loop system are bounded, and the tracking error converges to a small neighborhood including the origin within finite time. The feasibility of the proposed control scheme is illustrated by two examples.

A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.

Finite-Time Adaptive Fuzzy Event-Triggered Control of Constrained Nonlinear Systems via Bounded Command Filter

In this note, finite-time adaptive tracking control is studied for nonlinear systems with unmodeled dynamics, asymmetric time-varying output constraints, and uncertain disturbances. Without any growth conditions, fuzzy logic systems are applied to tackle the unknown complicated functions. A novel backstepping approach is developed by combining barrier Lyapunov functions and bounded finite-time command filter. By regulating the threshold parameters online, a new dynamic event-triggered controller is established to ensure that all the signals of the closed-loop system are bounded and the output can follows the preset signal in finite time. Meanwhile, the output is always staying in an asymmetric time-varying interval all the time. The feasibility of the proposed control algorithm is verified with a numerical example and a practical application.

Robust adaptive finite-time tracking control for Intervention-AUV with input saturation and output constraints using high-order control barrier function

The Intervention-Autonomous Vehicle (I-AUV) as the effective operation equipment in the deep sea is suppressed to the external and physical constraints, which makes it challenging to achieve underwater missions. Aiming at the trajectory tracking control of I-AUV with input saturation and output constraints, a higher-order control barrier function-quadratic program (HoCBF-QP) based control scheme is proposed in this paper considering the uncertainties, disturbance and dynamic interaction. Firstly, a robust adaptive control is presented to track the desired trajectory in a finite time, where a feedback control term, based on the continuous terminal sliding mode (TSM) technique, is designed to improve the tracking performance under the uncertainties, disturbance and dynamic interaction. Secondly, a time-varying HoCBF is further developed to handle the high relative degree time-varying output constraints, then the multiple high-order control barrier functions can bring a family of safety-critical control input to preserve the reachability of AUV posture and joints motion. Thirdly, a convex quadratic program (QP)-based separation control frame is designed to conduct the tracking problem and output satisfaction separately. Due to its globally optimal advantage, the proposed control design provides a flexible frame to track objectives for the constrained I-AUV systems. Comparable simulation results demonstrate the fast convergence, robustness and high tracking accuracy of the proposed HoCBF-QP control for I-AUV systems with constraints.

Event-based decentralized adaptive finite-time tracking control of interconnected nonlinear time-varying systems

Event-based decentralized adaptive finite-time tracking control of interconnected nonlinear time-varying systems

Dynamic Event-Based Adaptive Finite-Time Tracking Control for Nonlinear Stochastic Systems Under State Constraints

This article focuses on the problem of adaptive finite-time tracking control for nonlinear stochastic systems under asymmetric constraints based on dynamic event-triggering control. Different from the existing works, a novel adaptive tracking control algorithm is proposed with asymmetric time-varying constraints and dynamic event-triggering mechanism. First, to constrain the state variable within given time-varying boundaries, a novel predefined-time performance function is constructed. Second, a novel barrier function related to state variable is constructed, by means of which the state variable is directly constrained within the asymmetric time-varying boundaries without the virtual controller. In addition, by establishing a novel dynamic function, we propose a dynamic event-triggering mechanism, and then design controller accordingly, which can reduce computation burdens and save the network resources. By the aid of the Lyapunov stability theory, it is proved that the system tracking error converges to an adjustable bounded set in probability in a finite time and all state variables are successfully constrained into the asymmetric time-varying boundaries. Finally, the effectiveness of the proposed control algorithm is verified by a simulation example.

Fuzzy Approximation-Based Adaptive Finite-Time Tracking Control for a Quadrotor UAV with Actuator Faults

Fuzzy Approximation-Based Adaptive Finite-Time Tracking Control for a Quadrotor UAV with Actuator Faults

Finite time adaptive neural tracking control for non-strict-feedback uncertain non-linear systems with disturbance and input delay

In this paper, based on neural networks (NNs), we consider finite time adaptive tracking control scheme for non-strict-feedback uncertain non-linear systems with time-variant external disturbance and input delay. A novel auxiliary system has been introduced to degrade the design difficulty caused by input delay. For the unknown non-linear functions and uncertainties in each step, radial basis function NNs are introduced to approximate them such that the control objective can be obtained. Furthermore, based on the idea of backstepping technique, an effective finite time adaptive neural tracking controller has been obtained in the presence of finite time Lyapunov theory, and the singularity problem that may occur in the design process has been overcome using the piecewise functions method. Using the Lyapunov stability theorem, which shows that all the signals of the closed-loop systems are finite time bounded, and the tracking error fluctuates around the origin. Consequently, the proposed scheme not only solves the tracking problem of non-strict-feedback systems with input delay but also realizes the finite time stability performance constraint. Finally, the simulations of two examples show the superiority of the proposed scheme.

Event-Based Design of Finite-Time Adaptive Control of Uncertain Nonlinear Systems.

The problem of finite-time adaptive tracking control against event-trigger error is investigated in this article for a type of uncertain nonlinear systems. By fusing the techniques of command filter backstepping technical and event-triggered control (ETC), an adaptive event-triggered design method is proposed to construct the controller, under which the effect of event-triggered error can be compensated completely. Moreover, the proposed controller can increase robustness against uncertainties and event error in the backstepping design framework. In particular, we establish the finite-time convergence condition under which the tracking error asymptotically converges to zero in finite time with the aid of a scaling function. Detailed and rigorous stability proofs are given by making use of the improved finite time stability criterion. Two simulation examples are provided to exhibit the validity of the designed adaptive ETC approach.

Neural network-based adaptive finite-time tracking control of switched nonlinear systems with time-varying delay

This work investigates the adaptive finite-time tracking control problem for switched nonlinear systems, in which backlash-like hysteresis and time-varying delay are taken into account. The nonlinear estimation ability of radial basis function neural networks is employed to relax the restriction on unknown nonlinear functions. The dynamic surface technology and the finite-time control approach avoid the “curse of dimensionality” and “singularity” problems existing in the backstepping design procedure, separately. By Lyapunov–Razumikhin function scheme, the proposed finite-time signal guarantees superior tracking performance under the average dwell time switching. Finally, to testify the practicability of the presented strategy, two simulation examples are shown.

Adaptive finite-time tracking control of robot manipulators with multiple uncertainties based on a low-cost neural approximator

Benefiting from a newly designed switching function in terminal sliding manifold and novel uncertainty handling solutions, this article presents a low-cost neuroadaptive control scheme that can not only achieve the finite time tracking control of robot system with multiple uncertainties also circumvent the possible singularity. Specifically, for the kinematics parameter uncertainties involved, the proposed terminal sliding mode observer can ensure the actual position of end-effector be accurately estimated within a finite time. And then, a neural approximator is designed to handle the non-parameterizable lumped dynamics uncertainty, and a new low-cost neural adaptive mechanism is constructed to reduce the computational burden. Furthermore, it is proved that all closed-loop signals are bounded and the tracking error converges to an arbitrarily small adjustable neighborhood of the origin within a finite time. The comparison simulation example also confirms the effectiveness and superiority of the proposed control scheme.

Adaptive neural finite-time hierarchical sliding mode control of uncertain under-actuated switched nonlinear systems with backlash-like hysteresis

This article investigates an adaptive finite-time tracking control for under-actuated nonlinear systems with unknown backlash-like hysteresis and arbitrary switchings. A hierarchical sliding mode (HSM) control scheme is developed considering external disturbances and hysteresis nonlinearity. In addition, unknown functions of the considered system are handled based on neural networks (NNs) approximation, and a projection algorithm is introduced to solve the singularity of the denominator. To avoid the case in which the error is repeatedly magnified, the sum of the upper bounds of the approximation error, the external disturbance and the backlash-like hysteresis model nonlinear parts are estimated.By resorting to the Lyapunov stability theory, the boundedness of all signals can be proved under arbitrary switchings. At last, two simulation examples are presented to demonstrate the validity of the proposed approach.

Observer-based adaptive fuzzy finite-time tracking control of switched nonlinear systems

In this article, we investigate the finite-time output feedback control issue for switched nonlinear systems. In the design procedure, fuzzy logic systems are used for identifying the unknown functions in switched nonlinear systems. A common state observer is constructed such that the unmeasured states can be measured. Based on the framework of the backstepping algorithm, an observer-based finite-time adaptive tracking control strategy is proposed via the common Lyapunov function approach. The stability analysis process confirms in detail that all the closed-loop signals are bounded under arbitrary switchings and the tracking error can converge to a small neighbourhood of the origin after a finite period of time. In order to verify the feasibility of the proposed control scheme, a numerical simulation example is shown in this paper.

Adaptive finite-time control for nonlinear multi-agent high-order systems with actuator faults

This paper addresses the adaptive finite-time tracking control problem for a class of multi-agent high-order systems with actuator faults. By adding a power integrator and taking advantage of the approximation capabilities of radial basis function in neural networks, an adaptive backstepping controller is developed to overcome difficulties associated with the positive odd integer terms of nonlinear multi-agent high-order systems. Moreover, fault-tolerant control is used to tackle the impact of actuator failures. The developed adaptive finite-time control scheme ensures that the outputs of all followers track synchronously the reference signal quickly in finite time, and all signals of the controlled system are semi-globally uniformly finite-time stable. Simulation results demonstrate the feasibility of the proposed scheme.