Search Results (83)

This study looks at the stability and stabilization issues concerning the nonlinear time-delay systems specified by conformable derivatives. These requirements can be used for many useful applications. Through the construction of appropriate Lyapunov–Krasovskii functionals, we develop novel linear matrix inequality (LMI) conditions for the exponential stability of autonomous systems and practical exponential stability for systems subject to bounded perturbations. Furthermore, we propose state-feedback stabilization strategies that transform the controller design problem into a convex optimization framework solvable via efficient LMI techniques. The theoretical developments are comprehensively validated through numerical examples that demonstrate the effectiveness of the proposed stability and stabilization criteria. The results establish a rigorous framework for analyzing and controlling conformable fractional-order systems with time delays, bridging theoretical advances with practical implementation considerations. Full article

A model of gene regulatory networks with generalized Caputo fractional derivatives with respect to another function is set up in this paper. The main characteristic of the model is the presence of a switching rule, which changes at certain times at both the lower limit of the applied fractional derivative and the right-side part of the equations. This gives the opportunity for better and more adequate modeling of the problem. Mittag–Leffler-type stability is defined for the model and studied with two types of Lyapunov functions. Initially, some properties of absolute value Lyapunov functions and quadratic Lyapunov functions are given, and two types of sufficient conditions are obtained. An example is provided to illustrate our theoretical results and the influences of the type of fractional derivative as well the switching rule on the stability behavior of the equilibrium. Full article

Accurate trajectory control during atmospheric entry is critical for the success of Mars landing missions, where strong non-linearities and uncertain dynamics pose significant challenges to conventional control strategies. This study develops a computational framework that integrates fuzzy parameter-varying models with Lyapunov-based analysis to achieve robust trajectory stabilization of Mars entry vehicles. The non-linear longitudinal dynamics are reformulated via sector-bounded approximation into a Takagi–Sugeno fuzzy parameter-varying model, enabling systematic gain-scheduled controller synthesis. To reduce the conservatism typically associated with quadratic Lyapunov functions, a fuzzy Lyapunov function approach is adopted, in conjunction with the Full-Block S-procedure, to derive less restrictive stability conditions expressed as linear matrix inequalities. Based on this formulation, several controllers are designed to accommodate the variations in atmospheric density and flight conditions. The proposed methodology is validated through numerical simulations, including Monte Carlo dispersion and parametric sensitivity analyses. The results demonstrate improved stability, faster convergence, and enhanced robustness compared to existing fuzzy control schemes. Overall, this work contributes a systematic and less conservative control design methodology for aerospace applications operating under severe non-linearities and uncertainties. Full article

This study examines the extended dissipativity analysis for newly designed mixed traffic systems (MTSs) utilizing the coupling memory sampled-data control (CMSDC) approach. The traffic flow creates a platoon, and the behavior of human-driven vehicles (HDVs) is presumed to adhere to the optimal velocity model, with the acceleration of a single-linked automated vehicle regulated directly by a suggested CMSDC. The ultimate objective of this work is to present a CMSDC approach for optimizing traffic flow amidst disruptions. The primary emphasis is on the proper design of the CMSDC to ensure that the closed-loop MTS is extended dissipative and quadratically stable. A more generalized CMSDC methodology incorporating a time delay effect is created using a Bernoulli-distributed sequence. The existing Lyapunov–Krasovskii functional (LKF) and enhanced integral inequality methods offer sufficient conditions for the suggested system to achieve an extended dissipative performance index. The suggested criteria provide a comprehensive dissipative study, evaluating $L_2-L_{\infty }$, $H_{\infty }$, passivity, and dissipativity performance. A simulation example illustrates the accuracy and superiority of the proposed controller architecture for the MTS. Full article

Path planning and collision avoidance are essential components of an autonomous driving system (ADS), ensuring safe navigation in complex environments shared with other road users. High-quality planning and reliable obstacle avoidance strategies are essential for advancing the SAE autonomy level of autonomous vehicles, which can largely reduce the risk of traffic accidents. In daily driving scenarios, lane changing is a common maneuver used to avoid unexpected obstacles such as parked vehicles or suddenly appearing pedestrians. Notably, lane-changing behavior is also widely regarded as a key evaluation criterion in driver license examinations, highlighting its practical importance in real-world driving. Motivated by this observation, this paper aims to develop an autonomous lane-changing system capable of dynamically avoiding obstacles in multi-lane traffic environments. To achieve this objective, we propose a hierarchical decision-making and control framework in which a Double Deep Q-Network (DDQN) agent operates as the high-level planner to select lane-level maneuvers, while a High-Order Control Lyapunov Function–High-Order Control Barrier Function–based Quadratic Program (HOCLF-HOCBF-QP) serves as the low-level controller to ensure safe and stable trajectory tracking under dynamic constraints. Simulation studies are used to evaluate the planning efficiency and overall collision avoidance performance of the proposed hierarchical control framework. The results demonstrate that the system is capable of autonomously executing appropriate lane-changing maneuvers to avoid multiple obstacles in complex multi-lane traffic environments. In computational cost tests, the low-level controller operates at 100 Hz with an average solve time of 0.66 ms per step, and the high-level policy operates at 5 Hz with an average solve time of 0.60 ms per step. The results demonstrate real-time capability in autonomous driving systems. Full article

This study presents advanced control and energy management strategies for uncertain wind energy systems using a Takagi–Sugeno (T-S) fuzzy modeling framework. To address key challenges, such as system uncertainties, external disturbances, and input delays, the study integrates a fuzzy H∞ robust control approach with a neural network-based delay compensation mechanism. A fuzzy observer-based H∞ tracking controller is developed to enhance robustness and minimize the impact of disturbances. The stability conditions are rigorously derived using a quadratic Lyapunov function, H∞ performance criteria, and Young’s inequality and are expressed as Linear Matrix Inequalities (LMIs) for computational efficiency. In parallel, a neural network-based controller is employed to compensate for the input delays introduced by online learning processes. Furthermore, an energy management layer is incorporated to regulate the power flow and optimize energy utilization under varying operating conditions. The proposed framework effectively combines control and energy coordination to improve the systems’ performance. The simulation results confirm the effectiveness of the proposed strategies, demonstrating enhanced stability, robustness, delay tolerance, and energy efficiency in wind energy systems. Full article

This paper is concerned with the event-based synchronization control for chaotic neural networks by using a refined discontinuous trigger scheme. To get rid of the Zeno phenomenon and decrease the triggering times, a refined discontinuous event-trigger (RDET) scheme is employed by designing a new threshold function. The proposed threshold function consists of two parts, i.e., quadratic term and exponential decay term, which makes the derivative of the Lyapunov function possibly not less than zero. On this basis, an important lemma is derived, which contributes to performing a stability analysis. Then, the corresponding closed-loop system model is established in the presence of a trigger scheme. Then, a time-dependent Lyapunov function (TLF) method is established based on the features of an RDET. In view of inequality estimation techniques and stability theory, some synchronization criteria are developed to guarantee that the synchronization of chaotic neural networks can be realized by using the novel discontinuous event-trigger schemes. Finally, a Hopfield neural network is displayed to demonstrate the advantages and effectiveness of the derived results. Full article

In this paper, we develop new necessary and sufficient Lyapunov conditions for fixed-time stability that refine the classical fixed-time stability results presented in the literature by providing an optimized estimate of the settling time bound that is less conservative than the existing results. Then, building on our new fixed-time stability results, we introduce the notion of uniformly strongly dissipative dynamical systems and show that for a closed dynamical system (i.e., a system with the inputs and outputs set to zero) this notion implies fixed-time stability. Specifically, we construct a stronger version of the dissipation inequality that implies system dissipativity and generalizes the notions of strict dissipativity and strong dissipativity while ensuring that the closed system is fixed-time stable. The results are then used to derive new Kalman–Yakubovich–Popov conditions for characterizing necessary and sufficient conditions for uniform strong dissipativity in terms of the system drift, input, and output functions using continuously differentiable storage functions and quadratic supply rates. Furthermore, using uniform strong dissipativity concepts, we present several stability results for nonlinear feedback systems that guarantee finite-time and fixed-time stability. For specific supply rates, these results provide generalizations of the feedback passivity and nonexpansivity theorems that additionally guarantee finite-time and fixed-time stability. Finally, several illustrative numerical examples are provided to demonstrate the proposed fixed-time stability and uniform strong dissipativity frameworks. Full article

This paper presents a zeroing neural networks (ZNN)-based gait optimization strategy for humanoid robots. First, the algorithm converts the angular momentum linear inverted pendulum (ALIP)-based gait planning problem into a time-varying quadratic programming (TVQP) problem by adding adaptive adjustment factors and physical limits as inequality constraints to avoid system oscillations or instability caused by large fluctuations in the robot’s angular momentum. Secondly, This paper proposes a real-time and efficient solution for TVQP based on an integral strong predefined time activation function zeroing neural networks (ISPTAF-ZNN). Unlike existing ZNN approaches, the proposed ISPTAF-ZNN is enhanced to achieve convergence within a strong predefined-time while exhibiting noise tolerance. This ensures the desired rapid convergence and resilience for applications requiring strict time efficiency. The theoretical analysis is conducted using Lyapunov stability theory. Finally, the comparative experiments verify the convergence, robustness, and real-time performance of the ISPTAF-ZNN in comparison with existing ZNN approaches. Moreover, comparative gait planning experiments are conducted on the self-built humanoid robot X02. The results demonstrate that, compared to the absence of an optimization strategy, the proposed algorithm can effectively prevent overshoot and approximate energy-efficient responses caused by large variations in angular momentum. Full article

Collision avoidance and path planning are critical topics in autonomous vehicle development. This paper presents the progressive development of an optimization-based controller for autonomous vehicles using the Control Lyapunov Function–Control Barrier Function–Quadratic Programming (CLF-CBF-QP) approach. This framework enables a vehicle to navigate to its destination while avoiding obstacles. A unicycle model is utilized to incorporate vehicle dynamics. A series of simulations were conducted, starting with basic model-in-the-loop (MIL) non-real-time simulations, followed by real-time simulations. Multiple scenarios with different controller configurations and obstacle setups were tested, demonstrating the effectiveness of the proposed controllers in avoiding collisions. Real-time simulations in Simulink were used to demonstrate that the proposed controller could compute control actions for each state within a very short timestep, highlighting its computational efficiency. This efficiency underscores the potential for deploying the controller in real-world vehicle autonomous driving systems. Furthermore, we explored the feasibility of a hierarchical control framework comprising deep reinforcement learning (DRL), specifically a Deep Q-Network (DQN)-based high-level controller and a CLF-CBF-QP-based low-level controller. Simulation results show that the vehicle could effectively respond to obstacles and generate a successful trajectory towards its goal. Full article

This paper investigates a novel reinforcement learning (RL)-based quadratic programming (QP) method for the safety-critical trajectory tracking control of autonomous underwater vehicles (AUVs). The proposed approach addresses the substantial challenge posed by model uncertainty, which may hinder the safety and performance of AUVs operating in complex underwater environments. The RL framework can learn the inherent model uncertainties that affect the constraints in Control Barrier Functions (CBFs) and Control Lyapunov Functions (CLFs). These learned uncertainties are subsequently integrated for formulating a novel RL-CBF-CLF Quadratic Programming (RL-CBF-CLF-QP) controller. Corresponding simulations are demonstrated under diverse trajectory tracking scenarios with high levels of model uncertainties. The simulation results show that the proposed RL-CBF-CLF-QP controller can significantly improve the safety and accuracy of the AUV’s tracking performance. Full article

This paper presents a synthesis of higher-order control Lyapunov functions (HOCLFs) and higher-order control barrier functions (HOCBFs) capable of controlling nonlinear dynamic systems while maintaining safety. Building on previous Lyapunov and barrier formulations, we first investigate the feasibility of the Lyapunov and barrier function approach in controlling a non-affine dynamic system under certain convexity conditions. Then we propose an HOCLF form that ensures convergence of non-convex dynamics with convex control inputs to target states. We combine the HOCLF with the HOCBF to ensure forward invariance of admissible sets and guarantee safety. This online non-convex optimal control problem is then formulated as a convex Quadratic Program (QP) that can be efficiently solved on board for real-time applications. Lastly, we determine the HOCLBF coefficients using a heuristic approach where the parameters are tuned and automatically decided to ensure the feasibility of the QPs, an inherent major limitation of high-order CBFs. The efficacy of the suggested algorithm is demonstrated on the real-time six-degree-of-freedom powered descent optimal control problem, where simulation results were run efficiently on a standard laptop. Full article

In this paper, we investigated a three-dimensional chaotic system that models key aspects of a monetary system, including interest rates, investment demand, and price levels. The proposed system is described by a set of autonomous quadratic ordinary differential equations. We analyze the dynamic behavior of this system through equilibrium points and their stability, Lyapunov exponents (LEs), and bifurcation diagrams. The system demonstrates a variety of behaviors, including chaotic, periodic, and equilibrium states depending on parameter values. Additionally, we explore the multistability of the system and present a radial basis function neural network (RBFNN) controller design to stabilize the chaotic behavior. The effectiveness of the controller is validated through numerical simulations, highlighting its potential applications in economic and financial modeling. Full article

The marine environment is highly complex and variable, featuring obstacles such as islands, buoys, and vessels. Safe navigation of the surface agent (SA) fleet is crucial for ensuring the safety of the SA fleet, enhancing operational efficiency, and guaranteeing the smooth execution of the fleet’s mission. Regarding the problem of formation obstacle avoidance for SA fleets encountering complex obstacles during navigation, this chapter presents a fixed-time-based safe navigation algorithm for the SA fleet based on streamline traction. Firstly, to precisely position each SA at the designated location within the formation, a highly malleable leader–follower formation mode is introduced. Based on an enhanced interfered fluid dynamical system (EIFDS) obstacle avoidance algorithm, the virtual Leader is guided to evade static obstacles and determine a trajectory of the designated position. Secondly, a first-order fixed-time control Lyapunov function (FTCLF) is designed based on the EIFDS obstacle avoidance algorithm to guide the angular velocity constraint. The optimal guiding angular velocity signal is obtained through quadratic programming, ensuring that the SA steers towards the designated position while avoiding obstacles. Next, for the guiding velocity amplitude signal, a first-order fixed-time control barrier function (FTCBF) is designed based on the streamline formation scheme and the inter-boat safety distance to guide the velocity amplitude constraint. The optimal guiding velocity amplitude signal is obtained through quadratic programming, guaranteeing that each SA maintains the formation while avoiding collisions with adjacent vessels. Finally, the simulation results indicate the effectiveness, superiority, and stability of the proposed fixed-time-based safe navigation guidance algorithm for the SA fleet based on streamline traction. Full article

The auxiliary unmanned ground vehicle (AUGV) for physical education can significantly enhance the continuity and safety of training and competitions. However, obstacles and area boundary constraints present substantial challenges to the efficiency of the AUGV. This paper proposes an anti-disturbance target tracking control strategy for AUGV, enabling rapid tracking of out-of-bounds balls. In the guidance layer, we design safety constraints based on the exponentially stabilizing control Lyapunov function (ES-CLF) position constraint and control barrier function (CBF), and solve the expected convergence velocity guidance law through quadratic programming. Additionally, the expected motion direction of AUGV is determined using the expected combined velocity. In the control layer, we employ a nonlinear tracking differentiators (NLTD) to achieve finite-time estimation of the derivative of the guidance velocity signal, and observed the model parameter uncertainty and external environmental disturbances through a fixed time disturbance observer. Finally, a fixed-time control strategy is developed to achieve precise target tracking. Stability analysis and simulation results confirm the effectiveness of the proposed AUGV target tracking control strategy and the safety collision avoidance method. Full article