Lyapunov Stability Theorem Research Articles

Synchronization of Fractional-Order Delayed Neural Networks Using Dynamic-Free Adaptive Sliding Mode Control

In this work, a dynamic-free adaptive sliding mode control (adaptive-SMC) methodology for the synchronization of a specific class of chaotic delayed fractional-order neural network systems in the presence of input saturation is proposed. By incorporating the frequency distributed model (FDM) and the fractional version of the Lyapunov stability theory, a dynamic-free adaptive SMC methodology is designed to effectively overcome the inherent chaotic behavior exhibited by the delayed FONNSs to achieve synchronization. Notably, the decoupling of the control laws from the nonlinear/linear dynamical components of the system is ensured, taking advantage of the norm-boundedness property of the states in chaotic systems. The effectiveness of the suggested adaptive-SMC method for chaos synchronization in delayed fractional-order Hopfield neural network systems is validated through numerical simulations, demonstrating its robustness and efficiency. The proposed dynamic-free adaptive-SMC approach, incorporating the FDM and fractional Lyapunov stability theorem, offers a promising solution for synchronizing chaotic delayed FONNSs with input saturation, with potential applications in various domains requiring synchronization of such systems.

A non‐linear fractional‐order type‐3 fuzzy control for enhanced path‐tracking performance of autonomous cars

AbstractPath‐tracking and lane‐keeping efficiency of driverless cars remain critical characteristics of the efficient and safe deployment of such vehicles in future intelligent transportation systems. This study introduces a robust type‐3 (T3) fuzzy controller implementation for the path‐tracking task of driverless cars during critical driving conditions and subject to exogenous disturbances. Unlike many existing control paradigms, the proposed scheme is independent of the parameter information and assumes the system dynamics are unknown and non‐linear. Control inputs are constructed to improve robustness by eliminating the error bounds while ensuring stability by leveraging the Lyapunov stability theorem and Barbalat's lemma. Also, a predicate scheme based on non‐linear predictive control technique is introduced to enhance the lateral displacement. Based on the obtained results, the schemed controller exhibits competitive effectiveness in path‐tracking tasks, and strong efficiency under various road conditions, parametric uncertainties, and unknown disturbances.

Robust Consensus-based Formation Control of a Group of UAV

Consensus-based formation control (CFC) is one of the most phenomenal formation control methods designed to achieve consensus between any vehicles that using and sharing their position and/or linear velocity with each other in a swarm mission. In this paper, a robust CFC (R-CFC) has been designed and proposed to realize pre-defined formation shapes with a team of unmanned aerial vehicles (UAVs). First, the double integrator dynamics of an UAV is presented. Second, the graph theory is explained briefly to understand any adjacency between UAVs. Then, the proposed R-CFC algorithm has been derived and the stability analysis has been proven via algebraic Riccati stability theory based on Lyapunov stability theorem. After that, the effectiveness of the proposed controller has been tested in real time outdoor tests. The experimental results show that the UAVs have been able to create the desired formation shapes and are less affected by external disturbances such as wind thanks to the proposed control algorithm.

Fixed-Time Synchronization of Complex-Valued Coupled Networks with Hybrid Perturbations via Quantized Control

This paper considers the fixed-time synchronization of complex-valued coupled networks (CVCNs) with hybrid perturbations (nonlinear bounded external perturbations and stochastic perturbations). To accomplish the target of fixed-time synchronization, the CVCNs can be separated into their real and imaginary parts and establish real-valued subsystems, a novel quantized controller is designed to overcome the difficulties induced by complex parameters, variables, and disturbances. By means of the Lyapunov stability theorem and the properties of the Wiener process, some sufficient conditions are presented for the selection of control parameters to guarantee the fixed-time synchronization, and an upper bound of the setting time is also obtained, which is only related to parameters of both systems and the controller, not to the initial conditions of the systems. Finally, a numerical simulation is given to show the correctness of theoretical results and the effectiveness of the control strategy.

Deterministic reinforcement learning for optimized formation control of virtually-coupled trains via performance index monitor

This article presents a deterministic reinforcement learning based optimized formation control for virtually-coupled trains using a novel designed performance index monitor, forming a new paradigm of artificial intelligence-based control for virtually-coupled trains. First, a reinforcement learning-based optimized formation control is designed using backstepping design and neural networks-based actor-critic framework, achieving steady formation separation among multiple trains and providing key theoretical basis to ”moving block with soft wall” (or virtually-coupled) mode, by online approximating the solutions of Hamilton–Jacobi–Bellman equations in both virtual position adjusting and actual speed regulating control signals. Second, a hysteretic-lag performance index monitor is designed to determine the time moments that enough knowledge has been obtained and insufficient knowledge is available in dynamical environments and switch the previously-mentioned reinforcement learning-based optimized formation control to deterministic reinforcement learning manner and vice versa. The idea of deterministic reinforcement learning lies in that as long as the convergences of actor and critic neural networks are observed, speaking equivalently, sufficient knowledge has been obtained provisionally, inner weight vectors of neural networks can be set as deterministic constant ones, achieving the human-like learning and control and reducing the computational amount. Rigorous closed-loop stability using deterministic reinforcement learning is also given using Lyapunov stability theorem. Finally, by utilizing the designed performance index monitor, the switching behavior between reinforcement learning and deterministic reinforcement learning is guaranteed to be finite during finite time of running duration. Simulation examples are given to verify the effectiveness of proposed control.

Second‐order extended state observers‐based adaptive event‐triggered containment control for nonlinear multiagent systems with mismatched stochastic disturbances

SummaryThis article investigates the event‐triggered containment control problem for nonlinear multiagent systems with mismatched stochastic disturbances. A set of second‐order extended state observers (ESOs) is constructed to solve the problem of bounded stochastic disturbances. The observers are able to estimate the disturbances in each control input channel in real‐time and solve the problem of stochastic disturbances path non‐differentiability. Based on backstepping technique, adaptive controllers are designed to ensure that the output of the followers converge to the convex hull formed by the leaders. Moreover, a simplified event‐triggered threshold condition is designed, which effectively reduces the update frequency of the controller and the complexity of threshold condition. Based on the Lyapunov stability theorem, it is proved that all signals in the closed‐loop systems are the practically bounded. Finally, the effectiveness of the proposed control scheme is verified by simulation results.

Passivity-Based Control Method for Three-Level Photovoltaic Inverter to Mitigate Common-Mode Resonant Current

In transformerless three-level photovoltaic inverter systems, the modified LC filter, which directly connects the dc-side neutral point to the common point of filter capacitors, is considered to be an ideal scheme to suppress the troublesome leakage current. However, a new common-mode (CM) resonant current is emerged, which leads to inverter-side current distortion and even system instability. Therefore, a second-order passivity-based controller in time domain featuring with excellent system stability is proposed for the CM resonant current mitigation. First, the reason of CM resonant current generation with the modified LC filter is analysed in detail. Then, the CM current model is derived, which reveals that it is a second-order system. The passivity of this second-order model is strictly proved. Moreover, based on the passive control theory, zero state detectable theory and Lyapunov stability theorem, a second-order passivity-based controller is designed step by step to suppress the CM resonant current, and the system global asymptotic stability is also proved. The proposed controller is based on time domain, which is more intuitive and avoids the error amplification in the conversion from frequency domain to time domain. Finally, the effectiveness and the correctness of theoretical derivation of the passivity-based control method are validated by experiments. Compared with passive damping resistor method, the proposed method not only has better performance, but also avoids the use of real resistor and reduces the cost by using software instead of hardware.

Stability and L∞-Gain of Positive Fractional-Order Singular Systems With Time-Varying Delays

This brief paper investigates the stability and L∞-gain of positive fractional-order singular systems (FOSSs) with time-varying delays. Based on the Drazin inverse of singular matrices, an equivalent auxiliary system is developed to avoid the singularity problem, and a sufficient and necessary criterion ensuring the positivity of delayed FOSSs is established. Furthermore, the asymptotic stability of FOSSs is analyzed using the positivity and monotonicity of system solutions instead of the fractional Lyapunov stability theorem. Finally, a simulation experiment utilizing electrical circuit system is carried out to justify the rationality of the results.

A robust observer based on the nonlinear descriptor systems application to estimate the state of charge of lithium-ion batteries

A robust observer based on nonlinear descriptor systems is applied to estimate lithium-ion batteries’ state of charge (SOC). We creatively take the relationship between the battery’s open circuit voltage (OCV) and SOC as a nonlinear algebraic constraint, thereby modeling the battery as a nonlinear descriptor system. This model can effectively trade off accuracy and complexity. The robust convergence, even in the presence of uncertainties, is proven through a combination of the Lyapunov stability theorem and linear matrix inequality (LMI) techniques. Experimental results showcase the effectiveness of the proposed SOC estimation technique, offering enhanced convergence speed, estimation accuracy, and robustness compared to conventional sliding mode observers.

Adaptive Neural Network Global Fractional Order Fast Terminal Sliding Mode Model-Free Intelligent PID Control for Hypersonic Vehicle’s Ground Thermal Environment

In this paper, an adaptive neural network global fractional order fast terminal sliding mode model-free intelligent PID control strategy (termed as TDE-ANNGFOFTSMC-MFIPIDC) is proposed for the hypersonic vehicle ground thermal environment simulation test device (GTESTD). Firstly, the mathematical model of the GTESTD is transformed into an ultra-local model to ensure that the control strategy design process does not rely on the potentially inaccurate dynamic GTESTD model. Meanwhile, time delay estimation (TDE) is employed to estimate the unknown terms of the ultra-local model. Next, a global fractional-order fast terminal sliding mode surface (GFOFTSMS) is introduced to effectively reduce the estimation error generated by TDE. It also eliminates arrival time, accelerates the convergence speed of the sliding phase, guarantees finite time arrival, avoids the singularity phenomenon, and bolsters robustness. Then, as the upper bound of the disturbance error is unknown, an adaptive neural network (ANN) control is designed to approximate the upper bound of the estimation error closely and mitigate the chattering phenomenon. Furthermore, the stability of the control system and the convergence time are proven by the Lyapunov stability theorem and are calculated, respectively. Finally, simulation results are conducted to validate the efficacy of the proposed control strategy.

A Fuzzy Control Strategy to Synchronize Fractional-Order Nonlinear Systems Including Input Saturation

One of the most important engineering problems, with numerous uses in the applied sciences, is the synchronization of chaos dynamical systems. This paper introduces a dynamic-free T-S fuzzy sliding mode control (TSFSMC) method for synchronizing the different chaotic fractional-order (FO) systems, when there is input saturation. Using a new definition of fractional calculus and the fractional version of the Lyapunov stability theorem and linear matrix inequality concept, a Takagi–Sugeno fuzzy sliding mode controller is driven to suppress and synchronize the undesired behavior of the FO chaotic systems without any unpleasant chattering phenomenon. Finally, an example of synchronization of complex power grid systems is provided to illustrate the theoretical result of the paper in real-world applications.

Harmonic Analysis of Sliding-Mode-Controlled Buck Converters Imposed by Unmodeled Dynamics of Hall Sensor

DC–DC buck converters have become prominent components for energy optimization in power systems, and how to improve control performances is a challenging issue to be addressed. In this paper, we aim to investigate the harmonic problem of sliding mode (SM) controlled buck converters imposed by the often-ignored unmodeled dynamics of the Hall sensor. The unified mathematical model of the whole system is established by combining the SM controller, the buck converter, and the Hall sensor, where the signal loss in the transmission process of the whole closed-loop control system is considered. Based on the Lyapunov stability theorem, the SM controller is designed to guarantee system stability, as well as to deduce the stable working areas and the tuned controller parameters. Furthermore, we introduce the descriptive function (DF) approach to investigate the influence of the unmodeled dynamics of the Hall sensor on the system harmonics in the frequency domain, which can deduce the relationship between the amplitude-frequency characteristics of the output signal and the Hall sensor. Simulations and experiments validate this paper.

Global Tracking Control for High-Order Odd-Rational-Powers Systems with Unknown Nonlinearities and Powers

The global control problem of high-order nonlinear systems with unknown odd rational powers and nonlinearities has been solved in this paper for the first time. Barrier functions were introduced into the controller to set the controller free from rational powers, which solved the problem caused by unknown odd rational powers. In utilizing barrier functions and their inverse functions, two transformations were constructed for the state and tracking errors, which resulted in the global tracking controller for the high-order odd-rational-powers nonlinear systems with unknown system nonlinearities. No knowledge of system nonlinearities and odd rational powers is required to construct the controller in this paper, and only control gains are assumed to be positive to guarantee the controllability of the system, which implies that the proposed method is model-free and has much more relaxed conditions than all the existing methods for high-order nonlinear systems. The global boundedness of all closed-loop signals was proved based on the Lyapunov stability theorem. Finally, simulation results were given to demonstrate the effectiveness of the proposed method.

Adaptive Robust Terminal Sliding Mode Control with Integral Backstepping Synthesized Method for Autonomous Ground Vehicle Control

Autonomous ground vehicles (AGVs) operating in complex environments face the challenge of accurately following desired paths while accounting for uncertainties, external disturbances, and initial conditions, necessitating robust and adaptive control strategies. This paper addresses the critical path-tracking task in AGVs through a novel control framework for multilevel speed AGVs, considering both structured and unstructured uncertainties. The control system introduced in this study utilizes a nonlinear adaptive approach by integrating integral backstepping with terminal sliding mode control (IBTSMC). By incorporating integral action, IBTSMC continuously adjusts the control input to minimize tracking errors, improving tracking performance. The hybridization of the terminal sliding mode method enables finite time convergence, robustness, and a chatter-free response with reduced sensitivity to initial conditions. Furthermore, adaptive control compensators are developed to ensure robustness against unknown but bounded external disturbances. The Lyapunov stability theorem is employed to guarantee the global asymptotic stability of the closed-loop system and the convergence of tracking errors to the origin within finite time. To validate the effectiveness of the proposed control scheme, high-fidelity cosimulations are conducted using CarSim and MATLAB. Comparative analysis is performed with other methods reported in the literature. The results confirm that the proposed controller demonstrates competitive effectiveness in path-tracking tasks and exhibits strong efficiency under various road conditions, parametric uncertainties, and unknown disturbances.

Simplified adaptive backstepping control for uncertain nonlinear systems with unknown input saturation and its application

The calculation complex problem is one of the significant obstacles in the real-time implementation of traditional backstepping controllers. In this paper, we consider the simplification problem of the adaptive backstepping tracking controller for uncertain nonlinear systems with unknown input saturation. Compared with traditional backstepping controllers, virtual stabilizing functions and their derivatives are needless in our controller, which effectively reduces the computation burden. And then the one-order compensation subsystem is employed to eliminate the effect of nonlinear uncertainties based on the adaptive control scheme and the congelation of variables technique. Next, the performance of the closed-loop nonlinear system is analyzed based on the Lyapunov stability theorem. In the final, simulation and experimental results are given to show the effectiveness of our controller.

Command Filter AILC for Finite Time Accurate Tracking of Aircraft Track Angle System Based on Fuzzy Logic

In this paper, the longitudinal model of an uncertain aircraft is taken as the research object, and the aircraft path inclination is controlled by controlling the input rudder deflection angle. An adaptive iterative learning control (AILC) scheme is proposed to solve the accurate tracking control problem of the flight path inclination on a finite time interval. The aircraft track angle system is abstractly modeled to obtain a triangular model in the form of strict feedback. For the abstracted strict feedback model, the fuzzy logic is used to approximate the uncertain part of the model. A command filter and an error compensation mechanism are introduced to prevent the computational bloat problem caused by excessive system order, and a convergent series sequence is used to deal with the truncation error caused by the approximation of the fuzzy logic. Based on the Lyapunov stability theorem, all signals of the closed-loop system are bounded on the finite time interval 0 , T , and the output of the system can track the desired trajectory accurately. Finally, the feasibility and effectiveness of the method are verified by MATLAB simulation results.

Dynamic Output Feedback and Neural Network Control of a Non-Holonomic Mobile Robot.

This paper presents the design and synthesis of a dynamic output feedback neural network controller for a non-holonomic mobile robot. First, the dynamic model of a non-holonomic mobile robot is presented, in which these constraints are considered for the mathematical derivation of a feasible representation of this kind of robot. Then, two control strategies are provided based on kinematic control for this kind of robot. The first control strategy is based on driftless control; this means that considering that the velocity vector of the mobile robot is orthogonal to its restriction, a dynamic output feedback and neural network controller is designed so that the control action would be zero only when the velocity of the mobile robot is zero. The Lyapunov stability theorem is implemented in order to find a suitable control law. Then, another control strategy is designed for trajectory-tracking purposes, in which similar to the driftless controller, a kinematic control scheme is provided that is suitable to implement in more sophisticated hardware. In both control strategies, a dynamic control law is provided along with a feedforward neural network controller, so in this way, by the Lyapunov theory, the stability and convergence to the origin of the mobile robot position coordinates are ensured. Finally, two numerical experiments are presented in order to validate the theoretical results synthesized in this research study. Discussions and conclusions are provided in order to analyze the results found in this research study.

Adaptive Dynamic Programming-Based Event-Triggered Robust Control for Multiplayer Nonzero-Sum Games With Unknown Dynamics1-4mmPlease verify and confirm the term "Multi-Player" has been changed to "Multiplayer" in the title of this article.

In this article, the event-triggered robust control of unknown multiplayer nonlinear systems with constrained inputs and uncertainties is investigated by using adaptive dynamic programming. To relax the requirement of system dynamics, a neural network-based identifier is constructed by using the system input-output data. Subsequently, by designing a nonquadratic value function, which contains the bounded functions, the system states, and the control inputs of all players, the event-triggered robust stabilization problem is converted into an event-triggered constrained optimal control problem. To obtain the approximate solution of the event-triggered Hamilton-Jacobi (HJ) equation, a critic network for each player is established with a novel weight updating law to relax the persistence of excitation condition based on the experience replay technique. Furthermore, according to the Lyapunov stability theorem, the present event-triggered robust optimal control ensures the multiplayer system to be uniformly ultimately bounded. Finally, two simulation examples are employed to show the effectiveness of the present method.

Global Feedback Regulation for a Class of Uncertain Nonlinear Systems via Integral Control: A Gain Control Technique

This paper studies the global feedback regulation problems for triangular nonlinear systems perturbed by matched disturbances and modeling uncertainties with unknown system parameters. Instead of constructing extended state observers, new integral controllers composed of an integral dynamic are constructed to make all states of the uncertain systems bounded and asymptotically converge to zero. Firstly, an integral dynamic is constructed and a new state transformation is introduced, which transforms the triangular nonlinear systems into a class of auxiliary intermediate systems. Secondly, by using the time-varying gain technique, designing regulating controllers for the auxiliary intermediate systems is converted into designing a dynamic parameter for a class of new systems. Thirdly, with the help of the Lyapunov stability theorem and the characteristics of designed dynamic parameter, it is provided that the boundness of the new systems yields the regulation of the auxiliary intermediate systems, which further indicates the global feedback regulation of the considered systems. Two physical system examples are given to demonstrate the effectiveness of the proposed controllers.

Boundary Control Design of Three-Dimensional Vibrating Marine Riser System With Barrier Term

Abstract In this paper, a boundary control with barrier term is proposed for a typical three-dimensional flexible riser system by integrating backstepping technique with barrier Lyapunov functions. The proposed boundary control does not depend on the exact value of interference and can effectively restrain the vibration of the riser and constrain the angle between the riser and the platform. The proposed control has a small amount of calculation and strong robustness, and can effectively restrain the riser vibration when the environmental disturbance changes. In addition, based on the proposed boundary control method, the stability of the closed-loop system in space and time is proved by Lyapunov stability theorem when the initial conditions are satisfied. Numerical simulation shows the effectiveness and superiority of the controller.