Lyapunov Approach Research Articles

Prescribed Performance Control for PEM Fuel Cell Air Supply System Based on Fully Actuated Approach With Fixed Regulation Time

ABSTRACTThe problem of air feed system control with guaranteed prescribed performance and fixed time control is investigated for proton exchange membrane fuel cell (PEMFC). First of all, the original model of PEMFC air feed system is converted to fully actuated system using higher order fully actuated system (HOFAS) approach. A fixed time extended state observer (ESO) is employed to approximate the cathode pressure. The parameter uncertainty is compensated by an adaptive radial basis function neural network (RBFNN). Then a prescribed performance sliding mode controller is designed with fixed convergence time. The proposed control law could guarantee the prescribed transient response for oxygen excess ratio (OER) error under stack current changing and bounded uncertainty. Lyapunov approach is utilized to proof fixed‐time stability of proposed controller. Simulation results of the study tests illustrate that the presented controller is efficient under constant OER tracking control, constant OER tracking control with parameter perturbation, and variable OER tracking control, respectively.

Adaptive control of magnetic levitation system based on fuzzy inversion

A novel adaptive tracking controller for magnetic levitation systems (MLS) is developed. The controller is based on a special adaptive control scheme incorporating fuzzy model of electromagnetic acceleration enabling fast and accurate fuzzy inversion. The controller ensures accurate tracking of any smooth desired position signal, despite unknown MLS parameters. The closed-loop system stability, in the sense of uniform ultimate boundedness (UUB) of error trajectories, is proved using Lyapunov approach. The closed-loop system performance is investigated during numerical experiments. Finally the proposed controller is verified by successful implementation on a DSP board controlling a typical magnetic levitation ball system. Performed tests and experiments demonstrate that the proposed control technique is robust against discretization and unknown MLS model parameters, provides high tracking accuracy, is easily implementable, and simple to tune.

Control strategies for mitigating torsional and axial vibrations in rotary oilwell drilling systems

Abstract This paper examines a nonlinear dynamics model to explore the significant factors influencing the coupled torsional-axial vibrations of a drill string. The primary focus lies in effectively modeling, analyzing, and controlling both torsional and axial vibrations occurring in a rotary oil well drilling system. The model employed incorporates a wave equation with a damping term (PDE) connected to an ordinary differential equation (ODE) through a nonlinear function representing the interaction between the drill bit and the rock. We proceed to establish the well-posedness of the coupled PDE-ODE in an appropriate functional space. As a PDE-ODE coupled system, we specifically investigate the stability problem concerning the velocity at the bottom extremity, considering both the presence and absence of the damping term in the wave PDE. To address this, we propose a systematic method based on a Lyapunov approach for designing feedback controllers. These controllers ensure system stability and effectively suppress harmful vibrations.

A Novel Parallel Control Method for Optimal Consensus of Nonlinear Multiagent Systems.

This work concentrates on the initial introduction of parallel control to investigate an optimal consensus control strategy for continuous-time nonlinear multiagent systems (MASs) via adaptive dynamic programming (ADP). First, the control input is integrated into the feedback system for parallel control, facilitating an augmented system's optimal consensus control with an appropriate augmented performance index function to be established, which is identical to the original system's suboptimal control with a conventional performance index. Second, the feasibility of the proposed control scheme is evaluated based on the policy iteration algorithm, and the convergence of the algorithm is demonstrated. Then, an online learning algorithm becomes available to implement the ADP-based optimal parallel consensus control protocol without prior knowledge of the system. The Lyapunov approach is employed to indicate that the signals are convergent. Ultimately, the experimental data support the theoretical results.

Robust Fuzzy Adaptive Fault‐Tolerant Control for a Class of Second‐Order Nonlinear Systems

ABSTRACTIn this brief, an optimal active fuzzy fault‐tolerant control (OAFFTC) scheme is proposed for a class of unknown perturbed multi‐input multi‐output (MIMO) nonlinear systems with nonaffine nonlinear actuator faults and time‐varying sensor faults. The control strategy can handle automatically (online updating) with three additives (bias, drift, and loss of accuracy) along with one multiplicative (loss of effectiveness) sensor faults and nonlinear state‐dependent actuator faults. In order to deal with uncertain system dynamics, sensor and actuator faults, and external disturbances, fuzzy systems (FSs) and backstepping techniques were combined to provide the adaptive control term as well as a robust control term. Butterworth filter is used to get rid the algebraic loop problem. The suggested robust term, can deal with approximation errors of the fuzzy systems (FSs). To automatically optimize the adaptive parameters and the starting conditions, particle swarm optimization (PSO) approach is introduced. The Lyapunov approach is employed to demonstrate the closed‐loop system's stability. To assess the efficacy and correctness of the suggested scheme, quadrotor dynamic model is performed on the simulation part.

Observer‐based control for nonlinear Hadamard fractional‐order systems via SOS approach

AbstractPractical stability refers to the notion that the origin is not an equilibrium point (EP) and that the system states tend to converge toward a sphere centered at the origin. The first goal of this paper is to analyze the concept of “practical stability” in Caputo–Hadamard fractional‐order derivative (CHFOD) systems. Then, using the Lyapunov approach, a polynomial fuzzy (PF) observer‐based controller for stabilizing CHFOD PF systems is created. The observer‐based control is innovative since it was created and proven using the sum‐of‐squares (SOS) method. In conclusion, a numerical illustration is provided to corroborate the theoretical findings.

Event-triggered cascade predictor for a class of nonlinear MIMO systems with large communication delays

The event-triggered predictor design problem for a class of nonlinear MIMO systems with large time delays is investigated in this paper. A periodic event-triggered mechanism is designed to avoid unnecessary data transmission and save communication energy. The triggering condition is only determined by sampled outputs of the system, such that it is applicable in case of the communication delay. Then a novel observer-based cascade predictor is proposed to reconstruct the original system state based on the delayed and event-triggered measurements, which is composed of a continuous-discrete observer and several sub-predictors in a chain structure. The stability of proposed predictor is analyzed through the Lyapunov approach. By using a sufficient number of sub-predictors and applying appropriate parameters, the prediction errors converge to bounded regions exponentially under large time delays. Finally, simulations are performed to verify the effectiveness of the proposed predictor and the event-triggered communication mechanism.

Novel adaptive fuzzy control for pendubot with actuator faults and uncertainties: Design and experiments

Pendubot has been widely applied as a benchmark platform for control research and education. In this paper, a novel adaptive fuzzy hierarchical sliding mode controller (AFHSMC) is proposed for the pendubot under actuator faults and uncertainties. The proposed controller is designed by combining hierarchical sliding mode control (HSMC), fuzzy logic control (FLC), and balancing composite motion optimization. The proposed controller preserves many advantages such as having a straightforward structure, simple implementation, chattering reduction, and high precision and robustness. The stability of the proposed controller is ensured by using the Lyapunov approach. To verify the control performance, various numerical simulations and experiments are conducted on a pendubot under conditions that involve actuator faults and uncertainties. Compared to the conventional HSMC and FHSMC controllers, the proposed AFHSMC improves by 0.43% and 0.38% for tracking precision of the first link's angle estimate, 3.26% and 0.08% for the second link's angle estimate when influenced by uncertainties, as well as 65.23% and 12.24% for the first link, 83.95% and 16.15% for the second link when influenced by faults.

Fixed-Time Fault-Tolerant Adaptive Neural Network Control for a Twin-Rotor UAV System with Sensor Faults and Disturbances

This paper presents a fixed-time fault-tolerant adaptive neural network control scheme for the Twin-Rotor Multi-Input Multi-Output System (TRMS), which is challenging due to its complex, unstable dynamics and helicopter-like behavior with two degrees of freedom (DOFs). The control objective is to stabilize the TRMS in trajectory tracking in the presence of unknown nonlinear dynamics, external disturbances, and sensor faults. The proposed approach employs the backstepping technique combined with adaptive neural network estimators to achieve fixed-time convergence. The unknown nonlinear functions and disturbances of the system are processed via an adaptive radial basis function neural network (RBFNN), while the sensor faults are actively estimated using robust terms. The developed controller is applied to the TRMS using a decentralized structure where each DOF is controlled independently to simplify the control scheme. Moreover, the parameters of the proposed controller are optimized by the gray-wolf optimization algorithm to ensure high flight performance. The system’s stability analysis is proven using a Lyapunov approach, and simulation results demonstrate the effectiveness of the proposed controller.

Fixed-time consensus and finite-time flocking of second-order nonlinear multi-agent systems under false data injection attacks

This paper focuses on addressing consensus and flocking issues in second-order nonlinear multi-agent systems (MASs) under the false data injection attacks. Novel adaptive control protocols are proposed to effectively mitigate the impact of these attacks by updating adaptive parameters. Based on algebraic graph theory, matrix theory and the Lyapunov approach, various sufficient conditions are established, which show the fixed-time consensus and finite-time flocking can be achieved for the MASs. Moreover, some upper bounds for the settling time are derived in terms of the parameters of the model. Finally, three simulation examples are presented to validate the efficacy of our proposed theoretical results.

Fault tolerant control of uncertain hydraulic system against actuator fault based on redesign Lyapunov approach

The design of stabilizing controller for uncertain nonlinear systems with control constraints is a challenging problem. This paper proposes the design of fault tolerant control for a class of uncertain nonlinear systems with actuator faults based on Lyapunov redesign principle. First, an assumption is introduced to design the control of the nominal system. Then, a new control law has been introduced to handle the difficulty caused by actuator failures. It is shown that the actuator faults can be completely compensated by the proposed nonlinear controller. Finally, the method will be applied to a hydraulic system to show its effectiveness.

Neuro‐adaptive prescribed performance control for spacecraft rendezvous based on the fully‐actuated system approach

AbstractThis paper investigates the control problem of spacecraft rendezvous with obstacle constraint, considering the external disturbance forces caused by orbit perturbation. Firstly, the translational dynamic model of spacecraft rendezvous is given and then rewritten into a second‐order fully‐actuated system form. Then, by employing the prescribed performance control method, the performance function and error transformation are determined, pre‐defining the prescribed performance bounds. Moreover, the fully‐actuated system approach is used to linearize the original nonlinear system, which simplifies the processes of control law design and ensures model accuracy. After that, to ensure that the spacecraft could avoid the dangerous zone during its manoeuvre, the artificial potential function is introduced, based on which a sliding mode surface is designed. Finally, the prescribed performance control–artificial potential function‐based control law is derived, further adopting the neuro‐adaptive method to deal with external interferences. The stability of the close‐loop control system is analysed through the Lyapunov approach and the effectiveness of the proposed control scheme is verified by carrying out a numerical simulation.

Nonlinear Enhanced Control for Wind Energy Generation System-Based Permanent Magnet Synchronous Generator

This paper proposes a Nonlinear Backstepping Approach (NBA) to improve the control performance of a Permanent Magnet Synchronous Generator (PMSG)-based Wind Energy Generation System (WEGS) under parameter uncertainties and short circuits with fluctuations in the grid voltage. Both the rectifier and the three-phase inverter are controlled using the NBA scheme; this method ensures Maximum Power Point Tracking (MPPT), which is a very appealing control objective with unpredictable scenarios of wind speed, and regulates the active and reactive power flows to the electrical network under varying wind speeds. Also, an inverter was employed to control voltage of the DC bus and the powers. The regulator’s stability is achieving using the Lyapunov approach. Simulation results with Matlab/Simulink confirm the efficiency of the presented scheme. The comparative analysis of the NBA with conventional Vector Controllers (VCs), under parameter deviations and for low voltage drop conditions, demonstrates the efficiency of the studied method.

A resilient event-triggered control strategy for truck platooning cyber–physical systems against denial-of-service attacks

With the deployment of vehicle-to-everything(V2X) communication technology, Denial-of-Service(DoS) attacks gradually pose potential threats for the truck platooning cyber–physical systems(TPCPS) due to disruption of information exchange in vehicular networks, resulting in instability of truck platooning and even traffic accidents. Motivated by this, the study proposes a resilient event-triggered control strategy to maintain the performance or stability of the TPCPS when DoS attacks happen. First, a resilient event-triggered mechanism is proposed to ensure that the onboard controller can receive and update status information in time after attack intervals, mitigating effect of the vehicle-to-vehicle(V2V) communication disruptions. Subsequently, the sufficient condition is derived which is to confine DoS attacks and makes a key role in maintaining the platoon’s internal stability. To guarantee the consensus control performance of the TPCPS, the switched event-triggered controller is designed by the Lyapunov approach. The controller is expected to output corresponding control based on the updated status information in communication interval. Ultimately, the proposed strategy’s effectiveness is validated through simulations. The proposed resilient event-triggered control strategy is shown to be able to effectively mitigate abnormalities in the TPCPS under DoS attacks, thus ensuring safe and comfortable driving. Compared with event-triggered sliding mode control, the proposed method achieves smaller inter-vehicle distances while ensuring stability, enhancing traffic efficiency.

On the local quadratic stability of T–S fuzzy systems in the vicinity of the origin

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. Discussions on the inherent limitations associated with fuzzy Lyapunov approaches are also given. To illustrate the theoretical results, we provide comprehensive examples that demonstrate the core concepts and validate the efficacy of the proposed conditions.

Multi-agent flocking control with complex obstacles and adaptive distributed convex optimization

The optimization issue involving flocking control and obstacle avoidance behavior in continuous-time multi-agent systems is the main topic of this work. When an agent encounters an obstacle, a virtual agent is introduced to generate repulsive force, enabling the multi-agent system to navigate around obstacles smoothly. Under the local interaction between agents, a multi-agent flocking control and obstacle avoidance algorithm is proposed with utilizing adaptive distributed convex optimization. This algorithm can minimize the sum of local costs of the system. A symbolic function-based estimation method is introduced to effectively relax the constraints of the cost function. The Lyapunov approach is employed to show the stability of the multi-agent system. With the proposed algorithm, each agent can achieve flocking behavior for convex optimization in complex obstacle environments by interacting with their neighbors, virtual agents, and virtual leaders. Last but not least, simulation examples are given to further illustrate the effectiveness and efficiency of the suggested control algorithm.

Online optimal tracking control of unknown nonlinear singularly perturbed systems using single network adaptive critic with improved learning

This study is the first time devoted to seek an online optimal tracking solution for unknown nonlinear singularly perturbed systems based on single network adaptive critic (SNAC) design. Firstly, a novel identifier with more efficient parametric multi-time scales differential neural network (PMTSDNN) is developed to obtain the unknown system dynamics. Then, based on the identification results, the online optimal tracking controller consists of an adaptive steady control term and an optimal feedback control term is developed by using SNAC to solve the Hamilton–Jacobi–Bellman (HJB) equation online. New learning law considering filtered parameter identification error is developed for the PMTSDNN identifier and the SNAC, which can realize online synchronous learning and fast convergence. The Lyapunov approach is synthesized to ensure the convergence characteristics of the overall closed loop system consisting of the PMTSDNN identifier, the SNAC and the optimal tracking control policy. Three examples are provided to illustrate the effectiveness of the investigated method.

Semi-decentralized Lyapunov-based formation control of multiple omnidirectional mobile robots

<p>This paper introduces an advanced formation control algorithm based on a Lyapunov approach for coordinating multiple omnidirectional mobile robots in collaborative object transport tasks. The semi-decentralized strategy ensures that the robots maintain a predefined geometric formation, crucial for stability during material transportation, and dynamically adapt to avoid collisions using onboard sensors. Experimental with a physical robot simulator demonstrates successful maintenance of line and triangle formations achieving an average side length maintenance of 1.00 meters with minimal deviation. Quantitative analysis across 30 experimental runs reveals consistent performance, with a maximum side length fluctuation of only 2 centimeters, validating the effectiveness of maintaining formation within a multi-robot system (MRS) framework. The Lyapunov-based approach proves to be an efficient method for cooperative object transport, achieving consistent performance with minimal deviation.</p>

Observer‐based optimal fault‐tolerant tracking control for input‐constrained interconnected nonlinear systems with mismatched disturbances

SummaryThis paper investigates an observer‐based optimal fault‐tolerant tracking control problem for interconnected nonlinear systems with input constraints and mismatched disturbances via adaptive dynamic programming (ADP). Firstly, an augmented system consisting of tracking error and the reference trajectory is constructed, and then the original optimal tracking control problem is transformed into the optimal regulation control problem of the augmented system. An integral sliding‐mode‐based optimal fault‐tolerant control scheme is developed to eliminate the effect of actuator faults and guarantee the optimal control performance. Furthermore, a neural network‐based observer is designed to identify the completely unknown system dynamics based on the input‐output data, thereby relaxing the restriction on system dynamics. Subsequently, the modified Hamilton‐Jacobi‐Bellman equations are solved by using the ADP algorithm under a critic network framework. According to the Lyapunov approach, all signals in the closed‐loop augmented system are uniformly ultimately bounded. Finally, the effectiveness of the developed control scheme is demonstrated via simulation results.

Decentralized adaptive tracking control for interconnected nonlinear systems with unmodeled dynamics and input delays

This paper focuses on the decentralised adaptive tracking control problem for nonstrict-feedback interconnected nonlinear systems with unmodeled dynamics and input delays. To identify the unstructured uncertainties, a novel broad learning system (BLS) approximation technique is introduced in this study to solve it. On this basis, a nonlinear state observer is designed to estimate the unmeasurable state variables. A dynamic signal is introduced to deal with the effect of unmodeled dynamics, and the appropriate error transformation is utilised to handle the effect of input delays. The decentralised adaptive tracking control strategy is proposed to the considered interconnected nonlinear systems using the design procedures of backstepping control with command filter. The semi-globally uniformly ultimately boundedness (SGUUB) stability and the tracking performance of the whole closed-loop systems could be guaranteed by using the Lyapunov approach. Finally, simulation results are provided to validate the present theoretical claims.