Finite-time Performance Research Articles

Prescribed finite-time tracking control with input buffer for a manipulator system

The prescribed finite-time trajectory tracking control problem with input buffer is investigated for a linkage manipulator system. The backstepping method is used to design the prescribed finite-time trajectory tracking controller. A new prescribed finite-time performance function is proposed, which can more easily regulate control performance. With the help of this performance function, a constraint control law is designed for the tracking error, and a better transient performance than the existing prescribed finite-time performance function can be obtained under the same parameter conditions for the trajectory tracking process of the manipulator system. At the same time, a control input buffer function is designed, which solves both the overvoltage problem of control input caused by the overlarge position error of the manipulator and the problem that the manipulator system is difficult to start under heavy load. The simulation experiments verify the effectiveness and superiority of the proposed controller.

Prescribed finite-time safe tracking control based on secure boundary protection method for nonlinear systems with unknown control gains

Aiming to the mutation of the actual output boundary, a prescribed finite-time safe tracking control problem is investigated for a class of nonlinear systems with unknown control gain in this paper. A secure boundary protection method (SBPM) and a new prescribed finite-time performance function (PFTPF) are proposed. The SBPM can construct automatically two adjustable secure boundaries, so that the system meets both the control performance prescribed by the PFTPF and the constraint of the secure boundaries. In order to solve the problem of the excessive jitter of control input caused by the mutation of the output constraint, a bidirectional filtering smoothing mechanism (BFSM) is proposed. The proposed method can effectively deal with the mutation of actual output constraint, and it is not necessary to predict the system output value to adjust the desired output trajectory. Finally, the effectiveness of this proposed method is verified by simulations.

Observer-Based Fault-Tolerant Finite-Time Control of Nonlinear Multiagent Systems.

In this article, an adaptive neural containment control for a class of nonlinear multiagent systems considering actuator faults is introduced. By using the general approximation property of neural networks, a neuro-adaptive observer is designed to estimate unmeasured states. In addition, in order to reduce the computational burden, a novel event-triggered control law is designed. Furthermore, the finite-time performance function is presented to improve the transient and steady-state performance of the synchronization error. Utilizing the Lyapunov stability theory, it will be shown that the closed-loop system is cooperatively semiglobally uniformly ultimately bounded (CSGUUB), and the followers' outputs reach the convex hull constructed by the leaders. Moreover, it is shown that the containment errors are limited to the prescribed level in a finite time. Eventually, a simulation example is presented to corroborate the capability of the proposed scheme.

Event-Triggered Adaptive Preassigned Finite-Time Consensus Control for Multiagent Systems With Nonlinear Faults.

This article investigates a novel neuro-adaptive barrier Lyapunov function (BLF)-based event-triggered preassigned finite-time consensus control with asymptotic tracking for the nonlinear multiagent systems. The proposed approach is designed to broaden the scope of application by considering the high-order nonstrict-feedback dynamics of each agent with dynamic uncertainties subject to external disturbances and nonaffine nonlinear faults. A neural network (NN) is employed to approximate the unknown nonlinear terms. By fusing the NNs and Butterworth low-pass filter technique, the issues arising from the nonaffine nonlinear fault are addressed. To save the communication resources, a novel dynamic event-triggered mechanism based on an enhanced switching threshold is suggested. Additionally, a novel concept called the preassigned finite-time performance function (PFTPF) is defined to improve the transient and steady-state performances as well as providing faster response. The key feature of the proposed adaptive BLF-based control based on the bound estimation method is the introduction of a smooth function with decreasing variable which not only ensures that all the signals remain bounded and the synchronization errors are restricted within the PFTPF but also guarantees that the tracking errors asymptotically converge to zero. Finally, an illustrative example is provided to verify the feasibility of the proposed control approach.

Composite learning prescribed performance control of strict-feedback nonlinear systems with mismatched parametric uncertainties

A composite learning prescribed performance control (CLPPC) approach is presented for strict-feedback nonlinear systems with mismatched parametric uncertainties. A finite-time performance function based on polynomial is introduced to predefined a restriction region with respect to the tracking error. By introducing an error transformation function, the tracking error restriction problem of the original system is transformed into the stability problem of an equivalent transformation system. To guarantee the convergence of unknown parameters, online recording data and instantaneous are used to generate a prediction error, which is used together with filtered tracking errors to update parameter estimations under an interval excitation condition. All signals are proven to be ultimately uniformly stable under the proposed CLPPC strategy. Furthermore, the tracking error is limited within the predefined region after the predefined time. Simulation results verify the effectiveness of the proposed approach.

A variable-barrier-function-based prescribed finite-time bounded-[formula omitted] reinforcement learning optimal tracking control strategy without dependence on initial condition

The prescribed finite-time bounded-H∞ optimal tracking control (OTC) problem is investigated for a class of nonlinear systems with unknown initial tracking condition and external disturbances in this paper. A novel variable barrier function is designed to develop a new approach of prescribed performance control (PPC) which is irrelevant to the initial condition of the constrained variable in the system. Meanwhile, the reinforcement learning (RL) method with the actor–critic architecture is used to optimize the control input of the system in order to obtain the least energy consumption. By means of a newly proposed prescribed finite-time performance function (PFTPF), a prescribed finite-time optimal tracking controller is obtained regardless of initial tracking condition of the system. At the same time, the bounded-H∞ control problem is considered for the external disturbances in the system. The designed controller not only ensures the boundedness of all signals in the closed-loop system, but also has a finite-time control performance and an H∞ anti-interference performance. Finally, the effectiveness and the superiority of this proposed method are verified by the simulations.

Data Farming the Parameters of Simulation-Optimization Solvers

The performance of a simulation-optimization algorithm, a.k.a. a solver, depends on its parameter settings. Much of the research to date has focused on how a solver’s parameters affect its convergence and other asymptotic behavior. While these results are important for providing a theoretical understanding of a solver, they can be of limited utility to a user who must set up and run the solver on a particular problem. When running a solver in practice, good finite-time performance is paramount. In this paper, we explore the relationship between a solver’s parameter settings and its finite-time performance by adopting a data farming approach. The approach involves conducting and analyzing the outputs of a designed experiment wherein the factors are the solver’s parameters and the responses are assorted performance metrics measuring the solver’s speed and solution quality over time. We demonstrate this approach with a study of the ASTRO-DF solver when solving a stochastic activity network problem and an inventory control problem. Through these examples, we show that how some of the solver’s parameters are set greatly affects its ability to achieve rapid, reliable progress and gain insights into the solver’s inner workings. We discuss the implications of using this framework for tuning solver parameters, as well as for addressing related questions of interest to solver specialists and generalists.

A novel dynamic finite-time prescribed performance control strategy with constraint and robustness

This paper is devoted to the design of adaptive nonlinear prescribed performance controllers for balancing constraint and robustness. Firstly, a shift function is introduced to enhance robustness in the initial stage. Secondly, a new finite-time performance function and a regulation of dynamic adjustments are developed for the first time. Due to the regulation, it can be prevented by the proposed scheme that tracking errors approach or exceed performance boundaries during operation, which ensures both robustness and constraint, and the performance function is differentiable of order n, which can be used in backstepping design for higher-order systems without approximators. Finally, the designed controller is more robust in both transient and stable states, whose effectiveness and superiority are validated by stability analysis, matlab simulation, and an actual test on a real robotic arm.

Adaptive Neural Network Finite-Time Prescribed Performance Consensus Control for a Class of Second-Order Multi-Agent Systems

This research investigates the semi-global practical finite-time prescribed performance consensus control issue for a class of second-order multi-agent systems with unknown nonlinear functions. Unlike the previous finite-time control set by a finite-time performance function, we give finite-time control by constraining the terminal sliding manifold in a performance function. In addition, an adaptive neural network control scheme is designed, which simplifies the controller and avoids the chattering issue existing in traditional sliding mode control. Eventually, a novel adaptive finite-time prescribed performance consensus control strategy is designed, which ensures that all system variables are semi-globally practical finite-time stable and consensus errors of the multi-agent systems converge within the prescribed region in finite time. The effectiveness and practicality of the presented control strategy are evaluated by conducting simulation cases.

Iteration complexity and finite-time efficiency of adaptive sampling trust-region methods for stochastic derivative-free optimization

ASTRO-DF is a prominent trust-region method using adaptive sampling for stochastic derivative-free optimization of nonconvex problems. Its salient feature is an easy-to-understand-and-implement concept of maintaining “just enough” replications when evaluating points throughout the search to guarantee almost-sure convergence to a first-order critical point. To reduce the dependence of ASTRO-DF on the problem dimension and boost its performance in finite time, we present two key refinements, namely: (i) local models with diagonal Hessians constructed on interpolation points based on a coordinate basis; and (ii) direct search using the interpolation points whenever possible. We demonstrate that the refinements in (i) and (ii) retain the convergence guarantees while matching existing results on iteration complexity. Uniquely, our iteration complexity results match the canonical rates without placing assumptions on iterative models’ quality and their independence from function estimates. Numerical experimentation on a testbed of problems and comparison against existing popular algorithms reveals the computational advantage of ASTRO-DF due to the proposed refinements.

Technical Note—On the Convergence Rate of Stochastic Approximation for Gradient-Based Stochastic Optimization

Finite-Time Performance of Gradient-Based Stochastic Approximation Algorithms Stochastic approximation (SA) algorithms are among the most commonly used methods for addressing stochastic optimization problems. In “Technical Note: On the Convergence Rate of Stochastic Approximation for Gradient-Based Stochastic Optimization,” J. Hu and M. C. Fu provide a new error bound for SA algorithms when applied to a class of problems with convex differentiable structures. The bound allows a detailed characterization of an algorithm’s finite-time performance through directly analyzing the bias and variance of the employed gradient estimator. The main result is then applied to study and compare the efficiency of traditional Kiefer-Wolfowitz algorithms and those based on random direction finite-difference gradient estimators such as simultaneous perturbation SA. The analysis leads to new insights into when it may be advantageous to use such randomized gradient estimates under various problem and algorithm parameter settings.

A Novel Communication Time-Delay Cooperative Control Method with Switching Event-Triggered Strategy

A novel communication time-delay classification-based method is designed for nonlinear multiagent systems with the finite-time prescribed performance function. The time-delay phenomenon for communication channels between agents is discussed. Then, an improved time-delay classification method is proposed to broaden the standard of classification mechanism by considering the degree of deviation and relative variation of neighbor agents, rather than classifying the delay time into large time-delay and small time-delay. Based on this, the unified Lyapunov-Krasovskii functional and the finite-time performance function are used to solve the large time-delay phenomenon and ensure that the error is within the preset boundary, respectively. Furthermore, a modified switching event-triggered strategy is put forward to reduce the transmission burden, which considers the impact of tracking error to adjust the threshold condition in real-time. Additionally, all signals of the closed-loop systems are bounded. Eventually, two simulation examples verify the validity of the control strategy.

Performance enhancement of quantum Brayton engine via Bose-Einstein condensation.

Bose-Einstein condensation is a quintessential characteristic of Bose systems. We investigate the finite-time performance of an endoreversible quantum Brayton heat engine operating with an ideal Bose gas with a finite number of particles confined in a d-dimensional harmonic trap. The working medium of these engines may work in the condensation, noncondensation, and near-critical point regimes, respectively. We demonstrate that the existence of the phase transition during the cycle leads to enhanced engine performance by increasing power output and efficiencies corresponding to maximum power and maximum efficient power. We also show that the quantum engine working across the Bose-Einstein condensation in N-particle Bose gas outperforms an ensemble of independent single-particle heat engines. The difference in the machine performance can be explained in terms of the behavior of specific heat at constant pressure near the critical point regime.

Safe tracking control based on a secure boundary protection method for nonlinear systems with unknown initial tracking condition

Aiming to the sudden change of the system actual output constraint, a novel safe tracking control strategy is investigated for a class of non-strict feedback nonlinear systems with unknown initial tracking condition in this paper. A secure boundary protection method (SBPM) based on prescribed performance and a new prescribed finite-time performance function (PFTPF) are proposed. The SBPM can automatically construct two adjustable secure boundaries, so that the system output meets both the control performance prescribed by the PFTPF and the secure boundary constraint. In order to solve the problem of the excessive control input jitter caused by the sudden change of output constraint, a bidirectional filtering smoothing mechanism (BFSM) is proposed. The proposed SBPM can effectively ensure the safe tracking control of the system with unknown initial tracking condition when the actual output constraint changes suddenly, and ensure that the system has the prescribed finite-time control performance given by the PFTPF. Differently from the existing works, the system output will be strictly constrained into the actual output constraint without the prediction for the system output value. Finally, the effectiveness of this proposed method is verified by simulations.

Fuzzy wavelet neural adaptive finite-time self-triggered fault-tolerant control for a quadrotor unmanned aerial vehicle with scheduled performance

This paper focuses on fuzzy wavelet neural networks-based adaptive finite-time self-triggered fault-tolerant control design with assured tracking performance for a quadrotor unmanned aerial vehicle subject to unknown actuator faults. First, an improved finite-time performance function is integrated with the command-filtered backstepping control framework to assure the scheduled tracking performance, which can effectively constrain the transient fluctuations of the tracking error at fault occurrence. Then, two compensation mechanisms are developed to weaken the adverse impact induced by actuator faults and filter errors. Further, a fuzzy wavelet neural adaptive self-triggered fault-tolerant controller with guaranteed performance is designed to improve the fault insensitivity and tracking accuracy of the controlled vehicle, where the fuzzy wavelet neural networks are employed to approximate the unknown nonlinearities and the control signals are allowed to achieve irregular updating only when the pre-specified trigger protocol is violated. Stability analysis proves that the designed controller guarantees the attitude and position subsystems are practical finite-time stable, and the tracking errors are strictly confined to a preassigned region and never cross its allowed bounds. Finally, the validity of the developed control scheme is confirmed by the simulation results.

Finite-Time Performance Mask Function-Based Distributed Privacy-Preserving Consensus: Case Study on Optimal Dispatch of Energy System

Finite-Time Performance Mask Function-Based Distributed Privacy-Preserving Consensus: Case Study on Optimal Dispatch of Energy System

Dynamic Threshold Finite-Time Prescribed Performance Control for Nonlinear Systems With Dead-Zone Output.

This article investigates the tracking control problem for nonlinear systems. An adaptive model is proposed to represent the dead-zone phenomenon and solve its control challenge with a Nussbaum function in conjunction. Drawing inspiration from the existing prescribed performance control schemes, a novel dynamic threshold scheme is developed that fuses a proposed continuous function with a finite-time performance function. A dynamic event-triggered strategy is applied to reduce the redundant transmission. The proposed time-varying threshold control strategy has fewer updates than the traditional fixed threshold and improves the efficiency of resource utilization. A command filter backstepping approach is employed to prevent the complexity explosion faced by the computation. The suggested control strategy ensures that all system signals are bounded. The validity of the simulation results has been verified.

Distributed adaptive sliding-mode control for 2-D plane vehicle platoon with prescribed performance and angle constraint

This paper focuses on the distributed adaptive sliding-mode control problem for two-dimensional (2-D) plane vehicle platoon with prescribed performance, angle constraints, and actuator faults. The quadratic spacing policy (QSP) is first adopted for the 2-D plane vehicle platoon to adjust the inter-vehicle spacing. The spacing error can converge within a finite time to the small region predetermined by a new finite-time performance function (FTPF). Meanwhile, a new transformed error function is introduced to convert the FTPF-constrained spacing errors into equivalent unconstrained ones. Besides, the property of the invertible nonlinear mapping function is used for the original system with the angle constraint to get a new unconstrained system. Moreover, a new controller based on hyperbolic tangent function is designed to handle actuator faults occurring multiple times over a period. Furthermore, the stability and string stability of the 2-D plane vehicle platoon are achieved through sliding-mode control. Finally, the simulation results validate the effectiveness of the proposed techniques.

Adaptive finite-time prescribed performance tracking control for hydraulic servo systems with friction compensation

Hydraulic systems present numerous challenges in the development of high-performance tracking controllers due to their highly nonlinear characteristics and heavy modeling uncertainties. Addressing this issue, this paper presents a friction compensation-based finite-time tracking control strategy with prescribed performance constraints. The system model is first derived, taking into consideration the nonlinear behaviors and potential uncertainties encountered in practical scenarios. Then, an adaptive finite-time prescribed performance controller is synthesized based on the backstepping framework. A novel form of finite-time performance function is introduced to constrain the tracking error, which provides the closed-loop system with a less complex guarantee of finite-time convergence and can also deliver the required transient performance and steady-state accuracy. Additionally, given the impact of uncertainty terms and the difficulty in obtaining the virtual command derivative, we employ neural networks (NNs) to estimate unknown dynamics and introduce command filters to acquire the intermediate signals, simplifying the backstepping control design process. Theoretical analysis indicates that the proposed control strategy can achieve the desired tracking performance and ensure the stability of the entire closed-loop system. Comparative numerical simulations are presented to confirm the usefulness of the suggested approach.

Improved finite-time prescribed performance super-twisting sliding mode united control framework for underwater vehicle-manipulator system

This paper investigates the trajectory tracking control problem for underwater vehicle-manipulator system (UVMS) with model uncertainties, dynamic coupling effects and external disturbances. Firstly, an improved finite-time performance function (IFTPF) is proposed to ensure the prescribed tracking accuracy with predefined convergence time while avoiding singularities in the system and enhancing robustness. Additionally, to reduce the controller’s dependence on the system model and compensate for unknown external disturbances, a neural network (NN) estimator is proposed to estimate the combination of system uncertainties and dynamic coupling effects, while a neural network-based nonlinear disturbance observer (NNDO) addresses the unknown external disturbances. Furthermore, an improved finite-time prescribed performance super-twisting sliding mode control framework using neural network-based disturbance observer (NNDO-IFTPPSTSMC) is proposed to ensure control accuracy and robustness while reducing chattering phenomenon. Theoretical analysis demonstrates that corresponding error variables of the system are bounded, and the trajectory tracking errors satisfy the prescribed performance constraints. Finally, simulation results validate the effectiveness and feasibility of the proposed method.