Predefined-time Convergence Research Articles

Adaptive anti-unwinding attitude stabilisation with predefined time for rigid spacecraft

In this paper, the problem of attitude stabilisation without unwinding is investigated for rigid spacecraft. To guarantee predefined-time convergence and unwinding-free performance of the closed-loop system, a predefined-time sliding mode function with adjustable parameters is proposed. This sliding mode function contains two equilibrium points. When the states of the closed-loop system are on the sliding mode surface, they converge to the equilibrium point near the initial states. Based on this sliding mode function, an adaptive attitude stabilising control law with tuning parameters is designed to compensate the external disturbances and inertia uncertainty. The presented control law guarantees that the settling time of the closed-loop system and the bounds of the system states can be explicitly determined in advance by adjusting parameters of the sliding mode function and the control law. Finally, numerical simulations are carried out to demonstrate the effectiveness of the presented control law. The simulation results illustrate that the predefined-time convergence and unwinding-free property of the closed-loop system are guaranteed by adopting the presented control law.

Predefined-time controller design for a multiple space transportation robots system based on Lp-Norm-Normalized Sign Function

This paper presents a predefined-time controller for Multiple Space transportation Robots System (MSRS), which can be applied in on-orbit assembly tasks to transport modules to pre-assembly configuration quickly. Firstly, to simplify the analysis and design of predefined-time controller, a Predefined-time Stability Criterion is proposed in the form of Composite Lyapunov Function (CLF-PSC). Besides simplicity, the CLF-PSC also has the advantage of less conservativeness due to utilization of initial state information. Secondly, a concept of Lp-Norm-Normalized Sign Function (LPNNSF) is proposed based on the CLF-PSC. Different from traditional norm-normalized sign function, the Lp-norm of LPNNSF can be selected arbitrarily according to practical control task requirements, which means that the proposed LPNNSF is more generalized and more convenient for calculation. Thirdly, a predefined-time disturbance observer and predefined-time controller are designed based on the LPNNSF. The observer has the property of predefined-time convergence to achieve quicker and more accurate estimation of the lumped disturbance. The controller has less control input and chattering phenomenon than traditional predefined-time controller. In addition, by introducing the observer into the controller, the closed-loop system enjoys high precision and strong robustness. Finally, the effectiveness of the proposed controller is verified by numerical simulations. By employing the controller, the MSRS can carry assembly modules to the desired pre-assembly configuration accurately within predefined time.

Predefined-time convergence strategies for multi-cluster games in hybrid heterogeneous systems

This paper explores the problem of (generalized) Nash equilibrium search in multi-cluster games with heterogeneous dynamics and multiple constraints. Within this research framework, each agent acquires information solely through local interactions with its neighbors and forms clusters based on similarity of interests. These clusters manifest dual relationships of cooperation and competition: agents within the same cluster enhance decision-making capabilities through cooperation, while different clusters compete to maximize their respective benefits. To delve into these complex interactions among clusters and the learning and evolution processes among agents, four distributed control algorithms suitable for various scenario requirements are designed and implemented. These algorithms ensure that each agent converges to a Nash equilibrium (NE) or generalized Nash equilibrium (GNE) of the multi-cluster system within predefined time points. Finally, we apply these algorithms to the connectivity control problem of unmanned aerial vehicle swarms with diverse dynamics, validating the theoretical results through comprehensive simulations.

Disturbance Estimation and Predefined-Time Control Approach to Formation of Multi-Spacecraft Systems.

Accurate sensing and control are important for high-performance formation control of spacecraft systems. This paper presents a strategy of disturbance estimation and distributed predefined-time control for the formation of multi-spacecraft systems with uncertainties based on a disturbance observer. The process begins by formulating a kinematics model for the relative motion of spacecraft, with the formation's communication topology represented by a directed graph for the formation system of the spacecraft. A disturbance observer is then developed to estimate the disturbances, and the estimation errors can be convergent in fixed time. Following this, a disturbance-estimation-based sliding mode control is proposed to guarantee the predefined-time convergence of the multi-spacecraft formation system, regardless of initial conditions. It allows each spacecraft to reach its desired position within a set time frame. The results of the analysis of the multi-spacecraft formation system are also provided. Finally, an example simulation of a five-spacecraft formation flying system is provided to demonstrate the presented formation control method.

Self-organizing interval type-2 function-link fuzzy neural network control for uncertain manipulators under saturation: A predefined-time sliding-mode approach

Robotic manipulators have extensive applications in academic and industrial fields such as grabbing, welding, and machining. Nowadays, better tracking performance and faster transient response have been the fundamental demands in the field of manipulator control. However, robotic manipulators suffer from uncertainties due to various factors in real-world environments. Therefore, achieving satisfactory tracking performance for the manipulator in the presence of uncertainties is a pressing problem. Moreover, most existing control schemes struggle to determine the convergence time of the whole system and rely on specifically designed parameters via experience and prior knowledge, which leads to poor transferability and generalization. To address the abovementioned issues, a predefined-time controller based on a self-organizing interval type-2 function-link fuzzy neural network (IT2FLFNN) is proposed in this paper. Different from most existing fuzzy neural network (FNN) based control schemes, the proposed network starts from an empty rule base and it is constructed by a self-organizing mechanism during the online control process, which provides greater flexibility in terms of network structure and input partition. Also, a function-link network (FLN) is integrated into IT2FLFNN to enhance its convergence speed and rejection of uncertainties. Furthermore, to ensure the predefined-time convergence, a predefined-time sliding-mode control part is merged into the control framework and online learning laws for IT2FLFNN are established via the Lyapunov stability analysis. Finally, a comparative simulation and an experiment demonstrate the superiority of the proposed IT2FLFNN control scheme.

Predefined-Time Zeroing Neural Networks With Independent Prior Parameter for Solving Time-Varying Plural Lyapunov Tensor Equation.

As an extension of the Lyapunov equation, the time-varying plural Lyapunov tensor equation (TV-PLTE) can carry multidimensional data, which can be solved by zeroing neural network (ZNN) models effectively. However, existing ZNN models only focus on time-varying equations in field of real number. Besides, the upper bound of the settling time depends on the value of ZNN model parameters, which is a conservative estimation for existing ZNN models. Therefore, this article proposes a novel design formula for converting the upper bound of the settling time into an independent and directly modifiable prior parameter. On this basis, we design two new ZNN models called strong predefined-time convergence ZNN (SPTC-ZNN) and fast predefined (FP)-time convergence ZNN (FPTC-ZNN) models. The SPTC-ZNN model has a nonconservative upper bound of the settling time, and the FPTC-ZNN model has excellent convergence performance. The upper bound of the settling time and robustness of the SPTC-ZNN and FPTC-ZNN models are verified by theoretical analyses. Then, the effect of noise on the upper bound of settling time is discussed. The simulation results show that the SPTC-ZNN and FPTC-ZNN models have better comprehensive performance than existing ZNN models.

Predefined-time robust adaptive gradient neural network for solving linear time-varying equations and its applications

Adaptive gradient neural networks (AGNN) have been extensively employed as effective models for addressing time-varying problems. However, the existing AGNN are convergent in infinite time and only considered in noiseless environment. Consequently, the AGNN with a certain convergence time and noise tolerance is urgently required. Motivated by the advantages of predefined-time convergence, a novel predefined-time robust adaptive gradient neural network (PRAGNN) is developed for solving linear time-varying equations. It can be concluded that PRAGNN can efficiently obtain real-time solutions of linear time-varying equations within predefined time, independent of initial conditions, by properly selecting parameters. In the process of solving linear time-varying equations, PRAGNN can avoid matrix inversion, which reduces the computing cost compared with zeroing neural networks (ZNN). Furthermore, PRAGNN can completely resist both bounded vanishing noise and bounded non-vanishing noise. Numerical experiments demonstrate the effectiveness of PRAGNN. Finally, PRAGNN has been successfully utilized in 2-D dynamic positioning based on the angle of arrival (AOA) positioning algorithm, as well as in alternating currents (AC) computing.

A Dynamic Parameter Noise-Tolerant Zeroing Neural Network for Time-Varying Quaternion Matrix Equation With Applications.

As a common and significant problem in the field of industrial information, the time-varying quaternion matrix equation (TV-QME) is considered in this article and addressed by an improved zeroing neural network (ZNN) method based on the real representation of the quaternion. In the light of an improved dynamic parameter (IDP) and an innovative activation function (IAF), a dynamic parameter noise-tolerant ZNN (DPNTZNN) model is put forward for solving the TV-QME. The presented IDP with the character of changing with the residual error and the proposed IAF with the remarkable performance can strongly enhance the convergence and robustness of the DPNTZNN model. Therefore, the DPNTZNN model possesses fast predefined-time convergence and superior robustness under different noise environments, which are theoretically analyzed in detail. Besides, the provided simulative experiments verify the advantages of the DPNTZNN model for solving the TV-QME, especially compared with other ZNN models. Finally, the DPNTZNN model is applied to image restoration, which further illustrates the practicality of the DPNTZNN model.

Adaptive neural network-based practical predefined-time nonsingular terminal sliding mode control for upper limb rehabilitation robots

This article investigates the predefined time trajectory tracking control problem of upper limb rehabilitation robots in the presence of the model uncertainty and external disturbances. An adaptive neural network-based practical predefined-time fast nonsingular terminal sliding-mode control (PPT-FNTSMC) strategy is proposed, in which a novel sliding mode surface is constructed to achieve predefined-time convergence and avoid the singularity problem as well. Additionally, a neural network is employed to approximate the lumped disturbances, and the estimated values are utilized in the controller for compensation, thereby reducing the required switching gain and mitigating chattering phenomenon. A rigorous theoretical analysis is provided to illustrate that the tracking errors can converge to a vicinity of the origin in a predefined time. Finally, simulations on a two-joint single-arm robot and a 5-DOF upper-limb exoskeleton are conducted and compared with an existing control method to demonstrate the effectiveness and superiority of the proposed control strategy.

Predefined-Time Tracking Control of Unmanned Surface Vehicle under Complex Time-Varying Disturbances

Aiming at the unmanned surface vehicle (USV) trajectory tracking control under complex time-varying environment, a predefined-time convergence sliding mode disturbance observer (PTC-SMO) is introduced to effectively handle the internal parameter uncertainties and external environmental disturbances, thereby guaranteeing precise compensation of the lumped disturbance term within a set time. Then, in order to achieve precise tracking of the desired trajectory using USV under a predetermined time constraint, a novel fast trajectory tracking control strategy with predefined-time convergence (PTC-FTTCS) is established to improve tracking performance and ensure that the trajectory tracking error converges quickly in the predefined time. Through rigorous comparative simulation under ideal conditions and time-varying disturbances, the results demonstrate reliable trajectory tracking and disturbance handling effects, and the tracking performance and disturbance observation performance are significantly better than state-of-the-art methods.

Predefined-time stabilization of stochastic nonlinear systems with application to UAVs

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis.

Design and Analysis of a Novel Distributed Gradient Neural Network for Solving Consensus Problems in a Predefined Time.

In this article, a novel distributed gradient neural network (DGNN) with predefined-time convergence (PTC) is proposed to solve consensus problems widely existing in multiagent systems (MASs). Compared with previous gradient neural networks (GNNs) for optimization and computation, the proposed DGNN model works in a nonfully connected way, in which each neuron only needs the information of neighbor neurons to converge to the equilibrium point. The convergence and asymptotic stability of the DGNN model are proved according to the Lyapunov theory. In addition, based on a relatively loose condition, three novel nonlinear activation functions are designed to speedup the DGNN model to PTC, which is proved by rigorous theory. Computer numerical results further verify the effectiveness, especially the PTC, of the proposed nonlinearly activated DGNN model to solve various consensus problems of MASs. Finally, a practical case of the directional consensus is presented to show the feasibility of the DGNN model and a corresponding connectivity-testing example is given to verify the influence on the convergence speed.

Adaptive practical predefined-time leader-follower consensus for second-order multiagent systems with uncertain disturbances

This article investigates the predefined-time consensus tracking problem for second-order multiagent systems (MASs) with uncertain disturbances. First, a distributed estimator is proposed to estimate the leader's states within predefined time. Then, a novel sliding mode surface is constructed and an adaptive sliding mode observer is established to estimate the uncertain disturbances within predefined time. Subsequently, by employing the predefined-time sliding surface and the adaptive technique, a novel adaptive sliding mode consensus protocol is proposed to overcome the singularity problem and achieve practical predefined-time convergence of the tracking errors to the neighborhood of origin. The Lyapunov approach is employed to prove the practical predefined-time stability of second-order MAS and the settling time is only determined by a single parameter, which facilitates the control protocol design according to the convergence time requirement. Simulation results illustrate the effectiveness of the proposed control scheme.

Predefined-Time Stability-Based Zeroing Neural Networks and Their Application in Solving the Lyapunov Equation

Lyapunov equation is extensively applied in engineering areas, and zeroing neural networks (ZNN) are very effective in solving this kind of equation. In this paper, two predefined-time stability theorems are used to devise new activation functions. Then, we obtain two new ZNN models, which are applied in solving the Lyapunov equation. This type of model is called the predefined-time stability-based zeroing neural network model. Compared with the ZNN models which have existed, the proposed model retains the noise-tolerant virtue and gains a new advantage: predefined-time convergence. Lastly, we verify that the model developed in this paper is superior to the known models in solving the time-variant Lyapunov equation via numerical simulations.

Nonlinear Polytopic Systems With Predefined Time Convergence

This paper deals with predefined time control for nonlinear polytopic systems. With such a control, the settling time function is uniform with respect to initial conditions of the system and can be chosen by the designer. By using the control Lyapunov function, a sufficient condition is investigated for the existence of a continuous and predefined time stable state feedback controller. The obtained sufficient condition is also necessary, such that the closed-loop nonlinear polytopic system has a robust control Lyapunov function (RCLF) for all possible parametric uncertainties. Finally, a practical system shows the efficacy of the proposed approach.

Predefined-time sliding mode control based on exact time disturbance observer for second-order systems with matched and mismatched disturbances

This paper’s primary motivation is to present a globally predefined-time sliding mode control (PtSMC) strategy to stabilize a class of second-order systems subjected to matched and mismatched disturbances. To achieve this, the paper proposes a new exact time disturbance observer (DOB) based on a terminal time regulator, which accurately estimates the disturbances within a prescribed time, effectively preventing the system state from escaping to infinity due to high gains and overestimation. In addition, a new predefined-time sliding mode variable with the estimation of DOB is developed to ensure a predefined-time convergence on the sliding mode phase against mismatched disturbances. The proposed DOB-based technique can alleviate the chattering resulting from the use of an overestimated gain, in contrast to the controller without employing a DOB. Furthermore, a predefined-time reaching law is introduced to guarantee a global predefined-time convergence. This paper establishes the stability of the disturbed second-order system under the proposed controller through strict Lyapunov analysis. The novelty of the proposed method lies in its global predefined-time convergence, chattering-reduced properties and robustness against matched and mismatched disturbances. Finally, numerical simulations and application examples validate the proposed methodology’s effectiveness.

Predefined-Time Convergent Kinematic Control of Robotic Manipulators With Unknown Models Based on Hybrid Neural Dynamics and Human Behaviors.

This article proposes a model-free kinematic control method with predefined-time convergence for robotic manipulators with unknown models. The predefined-time convergence property guarantees that the regulation task can be finished by robotic manipulators in a preset time, in spite of the initial state of manipulators. This feature will facilitate the scheduling of a series of tasks in industrial applications. To this end, a varying-parameter predefined-time convergent zeroing neural dynamics (ZND) model is first proposed and employed to solve the regulation problem. As well as the primary task, a conventional ZND model is utilized to achieve the avoidance of obstacle. The stability of the proposed controller is analyzed based on the Lyapunov stability theory. For the sake of dealing with the unknown kinematic model of robotic manipulators, gradient neural dynamics (GND) models are exploited to adapt the Jacobian matrices just relying on the control signal and sensory output, which enables us to control robotic manipulators in a model-free manner. Finally, the efficacy and merits of the proposed control method are verified by simulations and experiments, including a comparison with the existing method.

A Strictly Predefined-Time Convergent and Noise-Tolerant Neural Model for Solving Linear Equations With Robotic Applications

Nowadays, there are time-critical applications involving linear equations, such as the fault reconstruction problem, where hard response time constraints and robustness to external disturbances are expected. Zeroing neural network (ZNN) is one of the effective solutions to time-variant problems including time-variant linear equations. This paper proposes a strictly predefined-time convergent and noise-tolerant ZNN (SPTC-NT-ZNN) to solve time-variant linear equations. Differing from the existing ZNN models, the designed SPTC-NT-ZNN is enhanced to be convergent in strictly predefined time while exhibiting noise tolerance. This guarantees the desirable timely convergence and robustness for time-critical applications. In theory, the strictly predefined-time convergence and noise-tolerance properties of the proposed SPTC-NT-ZNN are mathematically proved in a rigorous manner. Comparative validations are performed to verify that the SPTC-NT-ZNN outperforms existing typical ZNNs, regarding the convergence and robustness performance. To demonstrate potential applications, the SPTC-NT-ZNN is applied to 3D stereo reconstruction and motion control of a Franka Emika Panda robot, showing the efficacy of the proposed method.

Neural Network-Based Nonconservative Predefined-Time Backstepping Control for Uncertain Strict-Feedback Nonlinear Systems.

To handle the tracking problem of uncertain strict-feedback nonlinear systems with matched and mismatched composite disturbances, this article studies a predefined-time backstepping controller by resorting to a Lyapunov-based predefined-time dynamic paradigm, a regulation function, and neural networks (NNs). Moreover, an adding-absolute-value (ADV) technique is adopted in the design process to remove the control singularity. Theoretical analyses prove the boundedness of all closed-loop system signals and the predefined-time convergence of the tracking error into an arbitrarily small vicinity of the origin. The proposed controller exhibits four advantages: 1) the actual convergence time is precisely predefined by only one design parameter irrespective of the initial conditions, and the control energy is economized; 2) no unbounded terms are adopted for predefining the actual convergence time, thus avoiding numerical overflow problem under limited memory space and gaining strong noise-tolerant ability; 3) the peaking tracking error and control input magnitude can be effectively reduced by appropriately setting parameters of the regulation function; and 4) the controller is continuous and nonsingular everywhere. Finally, a practical example of a single-link manipulator is presented to validate the efficacy and superiority of our predefined-time controller.

Efficient Predefined-Time Adaptive Neural Networks for Computing Time-Varying Tensor Moore-Penrose Inverse.

This article proposes predefined-time adaptive neural network (PTANN) and event-triggered PTANN (ET-PTANN) models to efficiently compute the time-varying tensor Moore-Penrose (MP) inverse. The PTANN model incorporates a novel adaptive parameter and activation function, enabling it to achieve strongly predefined-time convergence. Unlike traditional time-varying parameters that increase over time, the adaptive parameter is proportional to the error norm, thereby better allocating computational resources and improving efficiency. To further enhance efficiency, the ET-PTANN model combines an event trigger with the evolution formula, resulting in the adjustment of step size and reduction of computation frequency compared to the PTANN model. By conducting mathematical derivations, the article derives the upper bound of convergence time for the proposed neural network models and determines the minimum execution interval for the event trigger. A simulation example demonstrates that the PTANN and ET-PTANN models outperform other related neural network models in terms of computational efficiency and convergence rate. Finally, the practicality of the PTANN and ET-PTANN models is demonstrated through their application for mobile sound source localization.