Lyapunov Stability Principle Research Articles

Research on robust fault-tolerant cooperative control for multi-stage satellites

Abstract The ultra-agile, ultra-stable, and ultra-pointing platform (ASP) is introduced on the basis of the satellite platform by using two-stage control to realize stable control and agile ability of the payload. In order to improve the reliability and attitude control capability of multi-stage satellites with a two-dimensional scanning motion mechanism, a robust fault-tolerant cooperative control algorithm for multi-stage satellites is proposed in this paper when the actuators of the ASP are faulty. Firstly, a dynamic model of a multi-stage satellite and typical fault models of actuators are established. The impact of faults on the multi-stage system is also analyzed in this paper. Secondly, a sliding mode fault observer is proposed for multi-stage satellites aiming at solving the problem of actuator failure. An adaptive sliding mode fault-tolerant control algorithm is designed, and the switch function is also improved which is chattering-free. The stability of the proposed controller is proved by using the Lyapunov stability principle. Finally, the effectiveness of the proposed control algorithm is verified through numerical simulations, and the comparison between four other fault-tolerant control algorithms demonstrates the superiority of the algorithm proposed in this paper.

Seamless Switching Control Strategy for a Power Conversion System in a Microgrid Based on Extended State Observer and Super-Twisting Algorithm

Microgrids can operate stably in both islanded and grid-connected modes, and the transition between these modes enhances system reliability and flexibility, enabling microgrids to adapt to diverse operational requirements and environmental conditions. The switching process, however, may introduce transient voltage and frequency fluctuations, causing voltage and current shocks to the grid and potentially damaging devices and systems connected to the microgrid. To address this issue, this study introduces a novel approach based on the Extended State Observer (ESO) and the Super-Twisting Algorithm (STA). Power conversion systems use Virtual Synchronous Generator (VSG) control and Power-Quality (PQ) control when they are connected to the grid or when the microgrid is not connected to the grid. VSG and PQ share a current loop. Transitioning the reference current generated by the outer loop achieves the switching of control strategies. A real-time observer is designed to estimate and compensate for current fluctuations, disturbances, and variations in id, iq, and system parameters during the switching process to facilitate a smooth transition of control strategies. Furthermore, to enhance the dynamic response and robustness of the system, the Proportional–Integral (PI) controller in the ESO is replaced with a novel super-twisting sliding mode controller based on a boundary layer. The Lyapunov stability principle is applied to ensure asymptotic stability under disturbances. The proposed control strategy is validated through simulation using a seamless switching model of the power conversion system developed on the Matlab/Simulink (R2021b) platform. Simulation results demonstrate that the optimized control strategy enables smooth microgrid transitions, thereby improving the overall reliability of grid operations.

Adaptive Non-singular Fast Terminal Sliding Mode Control for Car-Like Vehicles with Faded Neighborhood Information and Actuator Faults

This study addresses the problem of cooperative control design for a group of car-like vehicles encountering fading channels, actuator faults, and external disturbances. It is presumed that certain followers lack direct access to the states of the leader via a directed graph. This arises challenges in maintaining synchronization and coordination within the network. The proposed control strategy utilizes non-singular fast terminal sliding mode control to accelerate consensus tracking and enhance the convergence of the overall system. This controller is designed to mitigate the impact of actuator faults in the presence of fading channels in the communication network. The effects of such issues on team performance are rigorously analyzed. Based on the Lyapunov stability principle, it has been demonstrated that the controller is capable of providing satisfactory performance for the entire system despite these challenges. Moreover, vehicle synchronization can be effectively maintained. Numerical simulations are conducted to verify the theoretical findings.

Proposed Feedback-Linearized Integral Sliding Mode Control for an Electro-Hydraulic Servo Material Testing Machine

High-precision tracking of an electro-hydraulic servo material testing machine’s force control system was achieved using a proposed integral sliding mode control method based on feedback linearization to improve the machine’s force control performance and anti-interference ability. First, the electro-hydraulic servo system’s nonlinear mathematical model was established, and its input–output linearization was realized using differential geometry theory. Second, integral sliding mode control was introduced into the controller and the feedback-linearized integral sliding mode controller was designed. The controller’s stability was proven based on the Lyapunov stability principle. Finally, a simulation model of the electro-hydraulic servo material testing machine’s force control system was established using AMESim/Simulink software. The designed controller was simulated and verified, and the control effects of the system’s different amplitudes and frequency signals were analyzed. The results showed that the feedback-linearized integral sliding mode control algorithm could effectively improve the system’s force tracking accuracy and parameter adaptability, yielding better robustness and a better control effect.

Residual evaluation of fault detection in discrete‐time systems

AbstractThis paper studies residual evaluation of fault detection in discrete‐time systems considering unknown‐but‐bounded disturbance. By applying Lyapunov stability principle and zonotopic technique, respectively, two dynamic threshold estimation methods are proposed to detect fault of discrete‐time systems. The proposed methods are extended to systems with time‐delay to improve the applicability in practical systems. The effectiveness and comparison of the proposed methods are illustrated by numerical examples.

Stability Study of Event Dynamic Systems Based on Discrete Mathematical Random Variable Modeling

This project intends to consider the stability of a nonlinear control system with unknown dynamics. The system is controlled systematically by using the reverse step method based on Lyapunov's stability principle. This paper also gives the conclusion that when the control law is in a steady state, the output signal in this state will reach uniform boundedness or asymptotic convergence. Finally, a numerical simulation is carried out through an example, and the results show that the algorithm is effective.

Event‐based reduced‐order H∞$H_{\infty }$ estimation for switched complex networks based on T‐S fuzzy model

AbstractThis paper investigates the design of a reduced‐order filter for a specific class of switched complex network systems with time‐varying delays. To handle the nonlinear components of the complex network, a T‐S fuzzy model is employed to convert them into a set of linear components. To tackle the issue of heavy network load, a memory‐based adaptive trigger mechanism is proposed. In this study, a reduced‐order state estimator is designed using the T‐S fuzzy model. To demonstrate the exponential stability of the error system, a suitable Lyapunov function is constructed based on the Lyapunov stability principle. The parameter matrix of the reduced‐order estimator is determined using the linear matrix inequality and convex linearization method. Additionally, a sufficient condition for the exponential stability of the error system at the suppression level is provided. Finally, the feasibility of the proposed scheme is validated through a simulation experiment.

An adaptive impedance control method for polishing system of an optical mirror processing robot

AbstractTo solve the constant contact force control problem between the end tool of a 5 degrees of freedom hybrid optical mirror processing robot and a workpiece, an adaptive impedance control method for the pneumatic servo-polishing system of the robot is designed. Firstly, the pneumatic servo-polishing control system at the end of the robot is set up. Secondly, the impedance control method for contact force is investigated based on the mathematical model of the pneumatic servo-polishing control system. Additionally, the causes of steady-state error of impedance control are analyzed theoretically, and the calculation method for steady-state error of impedance control is deduced. Finally, an indirect adaptive impedance controller based on Lyapunov Stability Principle is developed to estimate the environmental stiffness and position online, so as to reduce steady-state error and realize the tracking of polishing contact force. The simulation and experimental results suggest that the adaptive impedance control method not only recognizes that the contact force of the robot is relatively constant during the polishing process but also has high control accuracy for the force, fast-tracking response for the abrupt force, and considerable adaptability to the variable environmental stiffness.

Neural network-based direct robust adaptive non-fragile fault-tolerant control of amorphous flattened air-ground wireless self-assembly system

PurposeIn this paper, the authors take an amorphous flattened air-ground wireless self-assembling network system as the research object and focus on solving the wireless self-assembling network topology instability problem caused by unknown control communication faults during the operation of this system.Design/methodology/approachIn the paper, the authors propose a neural network-based direct robust adaptive non-fragile fault-tolerant control algorithm suitable for the air-ground integrated wireless ad hoc network integrated system.FindingsThe simulation results show that the system eventually tends to be asymptotically stable, and the estimation error asymptotically tends to zero with the feedback adjustment of the designed controller. The system as a whole has good fault tolerance performance and autonomous learning approximation performance. The experimental results show that the wireless self-assembled network topology has good stability performance and can change flexibly and adaptively with scene changes. The stability performance of the wireless self-assembled network topology is improved by 66.7% at maximum.Research limitations/implicationsThe research results may lack generalisability because of the chosen research approach. Therefore, researchers are encouraged to test the proposed propositions further.Originality/valueThis paper designs a direct, robust, non-fragile adaptive neural network fault-tolerant controller based on the Lyapunov stability principle and neural network learning capability. By directly optimizing the feedback matrix K to approximate the robust fault-tolerant correction factor, the neural network adaptive adjustment factor enables the system as a whole to resist unknown control and communication failures during operation, thus achieving the goal of stable wireless self-assembled network topology.

Neural Network-Based Adaptive Sliding-Mode Control for Fractional Order Fuzzy System With Unmatched Disturbances and Time-Varying Delays

This article concentrates on the neural network (NN)-based adaptive sliding-mode control (SMC) for fuzzy fractional-order system (FOS), <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\alpha\in(0,1).$</tex-math> </inline-formula> First of all, a novel method of optimal SMC approach is developed for fuzzy FOSs by using the adaptive dynamic program (ADP), integral sliding mode, and NN with unmatched disturbances and time-varying delays. Next, to weaken the influence of the nonlinearities, the SMC strategy is proposed for the specific system, which is established on the corresponding SMD to ensure that the FOS reach the SMS in a finite time. Moreover, it shows that the matrix of SMS can be described by the linear matrix inequality (LMI). Furthermore, the Hamilton–Jacobi–Bell man (HJB) equation can be approximated by a single NN method, and the Lyapunov stability principle proves that the weight errors are convergent, further guaranteeing the asymptotically stability of the fuzzy FOS. Finally, to display that the above-presented policy is effective, simulation results are presented.

Gliding Vehicle Controller Based on Neural Network Compensating Dynamic Inversion Error

Aiming at the attitude control problem of the gliding vehicle with uncertainty and strong coupling, a dynamic inversion control method based on RBF neural network compensated inversion error is discussed. Firstly, based on the double time scale separation hypothesis, the controlled aircraft model is divided into a fast and slow state subsystem. Then the dynamic inversion control laws are designed for each of the two subsystems. The weight update rule of the RBF neural network is derived online based on the Lyapunov stability principle to compensate for the inversion error caused by the modeling error and uncertainty. The simulation verifies the effectiveness of the control law. The robustness of the control system after neural network compensation is significantly improved.

Periodically Intermittent Control of Memristor-Based Hyper-Chaotic Bao-like System

In this paper, based on a three-dimensional Bao system, a memristor-based hyper-chaotic Bao-like system is successfully constructed, and a simulated equivalent circuit is designed, which is used to verify the chaotic behaviors of the system. Meanwhile, a control method called periodically intermittent control with variable control width is proposed. The control width sequence in the proposed method is not only variable, but also monotonically decreasing, and the method can effectively stabilize most existing nonlinear systems. Moreover, the memristor-based hyper-chaotic Bao-like system is controlled by combining the proposed method with the Lyapunov stability principle. Finally, we should that the proposed method can effectively control and stabilize not only the proposed hyper-chaotic system, but also the Chua’s oscillator.

Three-Stage-Impulse Control of Memristor-Based Chen Hyper-Chaotic System

In this paper, on the basis of the three-dimensional Chen system, a smooth continuous nonlinear flux-controlled memristor model is used as the positive feedback term of this system, a hyper-chaotic circuit system is successfully constructed, and a simulated equivalent circuit is built for simulation using Multisim software, which agrees with the numerical simulation results by comparison. Meanwhile, a new impulsive control mode called the three-stage-impulse is put forward. It is a cyclic system with three components: continuous inputs are exerted in the first and third parts of the cycle while giving no input in the second part of the cycle, an impulse is exerted at the end of each continuous subsystem, the controller is simple in structure and effective in stabilizing most existing nonlinear systems. The Chen hyper-chaotic system will be controlled based on the three-stage-impulse control method combined with the Lyapunov stability principle. At the end of this paper, we have employed and simulated a numerical example; the experimental results show that the controller is effective for controlling and stabilizing the newly designed hyper-chaotic system.

Adaptive neural network–based trajectory tracking non-affine control of hovercraft with double-loop constraint performance

This study investigates the design of a trajectory tracking constraint control method for hovercraft non-affine formulations via neural network approximation. The tracking scheme comprises an outer closed-loop of attitude and an inner closed-loop of velocity (double-loop). First, a performance function is devised to constrain the attitude errors and then a transformed error function is introduced to simplify it into an equivalent unconstrained control system. Next, an improved asymmetric integral barrier Lyapunov function is designed to address asymmetric velocity constraint problems, which can guarantee the safe turning motion or performance required at high speed. Furthermore, neural networks are employed to estimate the unknown terms of each subsystem, which solve system uncertainties and non-affine dynamics problems. The double closed-loop control system is ultimately uniformly bounded by utilizing the Lyapunov stability principle. Finally, simulation results are presented to verify the tracking performance and effectiveness of the proposed control strategy.

Adaptive Chattering-Free PID Sliding Mode Control for Tracking Problem of Uncertain Dynamical Systems

Aiming at the trajectory tracking problem with unknown uncertainties, a novel controller composed of proportional-integral-differential sliding mode surface (PIDSM) and variable gain hyperbolic reaching law is proposed. A PID-type sliding mode surface with an inverse hyperbolic integral terminal sliding mode term is proposed, which has the advantages of global convergence of integral sliding mode (ISM) and finite time convergence of terminal sliding mode (TSM), and the control effect is significantly improved. Then, a variable gain hyperbolic approach law is proposed to solve the sliding mode approaching velocity problem. The variable gain term can guarantee different approaching velocities at different distances from the sliding mode surface, and the chattering problem is eliminated by using a hyperbolic function instead of the switching function. The redesign of the sliding mode surface and the reaching law ensures the robustness and tracking accuracy of the uncertain system. Adaptive estimation can compensate for uncertain disturbance terms in nonlinear systems, and the combination with sliding mode control further improves the tracking accuracy and robustness of the system. Finally, the Lyapunov stability principle is used for stability analysis, and the simulation study verifies that the proposed control scheme has the advantages of fast response, strong robustness, and high tracking accuracy.

Automatic Control of Food Machinery Based on Neural Network and Computational Torque Compounding

In order to improve the effect of automatic control of food machinery, this paper combines neural network and computational torque compounding to study the automatic control system of food machinery to improve the effect of automatic control of food machinery. Moreover, this paper studies the problem of strong time-varying nonlinear friction disturbance in the servo motion system, and analyzes the friction nonlinearity at low speed and commutation motion of the system. In addition, this paper introduces the application requirements for the nonlinear friction compensation control method, and proves that the designed controller can maintain the stability of the system under the condition of strong nonlinear time-varying friction through the Lyapunov stability principle. The experimental study shows that the control strategy given in this paper can not only effectively improve the tracking speed of the joints, but also effectively alleviate the later tremor, and the automatic control effect of food machinery based on neural network and computational torque compounding has certain effects.

A novel synchronization control with index adjuster for stochastic neural networks via trace similarity

Based on the stability of the error system, we focus on the synchronization control of Stochastic Neural Networks (SNNs) with Time-Varying Delays (TVD). In order to observe the effect of the slave system following the drive system, we carry out the output result analysis of networks based on logic framework for the drive-follow systems. The constructive method and extremum theory are utilized to prove that the sample traces are similar to the state traces of the systems. For achieving the efficient control of the error system, the gain matrix of the controller with index regulator is designed to adjust the intensity of the parameters. Through one contrast analysis, the proposed control method is superior to the control approach given by comparative literature. Employing rigorous derivation, the exponential synchronous conditions are obtained based on trace similarity and the Lyapunov stability principle. In particular, one numerical example with three neurons fully validates the obtained results.

Model‐based online efficiency control of induction motor drives based on nonlinear technique

To accomplish benefits such as high accuracy and fast response, the model-based loss minimisation algorithms (LMAs) are introduced in the literature, as one of the main available techniques for minimising power losses in electrical motors. They are appropriate for dynamic applications, which necessitate very fast update of the control variable. This study proposes a novel real-time LMA based on super-twisting sliding mode controller (SMC) for induction motor (IM) drives, while keeping a good dynamic response. In this regard, a loss minimisation criterion for the efficiency optimisation is proposed and scrutinised. It is shown analytically that LMA will be realised if the nonlinear controller forces this criterion to zero. Moreover, a super-twisting SMC integrated with the iron loss is proposed which directly regulates both the power loss-minimising criterion and the electromagnetic torque by choosing those as control outputs. The stability of the super-twisting SMC is also verified through the Lyapunov's stability principle. The complete closed-loop control of the proposed LMA-based IM drive is successfully implemented in real-time using a digital signal processor board TMS320F28335 for a laboratory 3-phase IM drive of 2.2 kW. The performance and functionality of the proposed scheme are assessed through experimental results.

Research on Takagi-Sugeno Fuzzy-Model-Based Vehicle Stability Control for Autonomous Vehicles

Human–machine cooperative driving is an important stage in the development of autonomous driving technology. However, in emergencies, the problem of vehicle stability control for human–computer cooperative autonomous vehicles is still worthy of attention. This paper mainly realizes the stability control of the human–machine cooperative driving vehicle through active steering and considers the influence of the change of vehicle speed on the vehicle stability control performance. Therefore, a vehicle stability control method based on the superposition of steering torque is proposed, in which the Takagi-Sugeno fuzzy model is used to solve the variable parameter problem. Firstly, a vehicle system model with steering moment as input is established to ensure that the driver can participate in the steering control. Secondly, the nonlinear T-S fuzzy model is established by fuzzifying the local linear model. Then, the parallel-distributed-compensation (PDC) method is used to design the vehicle stability controller, and the asymptotic stability of the system in the range of variable parameters is proved by using the Lyapunov stability principle. Finally, the simulation and experimental results show that the control method can improve the handling stability of the human–machine cooperative driving vehicle under the condition of vehicle speed variation.

Trajectory tracking control based on memory data for robots with imprecise dynamic properties and interference

AbstractIn this article, a new controller design method is proposed for the trajectory tracking problem of robots with imprecise dynamic properties and interference. By using the tracking error memory data of state variables to construct control law, the tracking errors caused by the system interference and inaccurate system modeling can be eliminated, and interference compensation can be realized, so that the system has the desired dynamic performance. The proposed method comes from the tracking control design of an affine nonlinear system. The controller is based on the error function of the control input in the ideal state and the actual state. According to the Lyapunov stability principle, it is proved that the proposed controller has good robustness under the conditions of bounded interference and inaccurate modeling. MATLAB was used to establish the controller and dynamic equation of the two‐joint planar robot for trajectory tracking simulation. Simulation results are presented to illustrate the performance of the proposed controller.