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In this article, a fault-tolerant tracking control technique is developed for the ascent of hypersonic vehicles (HSV) experiencing wing damage and time-varying state constraints. The difficulty of control problem lies in handling state constraints associated with both state and time, while determining the unknown control directions of the multi-input multi-output (MIMO) nonlinear system. The presence of constraints in both state and time complicates the design of the control algorithm. This paper proposes the construction of a novel state transition function to establish a new unconstrained system, thereby eliminating the conservative feasibility conditions of Barrier Lyapunov Function (BLF) and integral BLF methods when dealing with time-varying constraints. The fusion of time-varying scaling functions and Nussbaum-type functions not only resolves the issue of unknown control directions in the MIMO nonlinear system but also enhances the transient and steady-state performance of the closed-loop system. Neural Networks are employed to approximate the unknown nonlinear functions. Using Lyapunov stability theory, it is proven that state constraints are not violated, and all signals in the closed-loop system are bounded. Simulation results demonstrate the merits of the designed fault-tolerant control (FTC) algorithm. • A unified fault-tolerant control scheme for the ascent hypersonic vehicle is designed. • Wing damage and function constraints on states are considered. • Nonlinear mapping eliminates the feasibility conditions in barrier Lyapunov functions. • The unknown control direction issue in multivariable nonlinear systems is resolved. [ABSTRACT FROM AUTHOR]

The paper presents a new Lyapunov-type predefined-time stabilization control algorithm for stochastic high-order nonlinear systems with asymmetric output constraints. In contrast to stochastic finite-time and fixed-time stabilization, the average value of the settling-time function for stochastic predefined-time stabilization control is independent of both the initial value and the control factors. To mitigate the significant uncertainties arising from the asymmetric output constraint, a tan-type barrier Lyapunov function is formulated. Furthermore, by harnessing the previously mentioned barrier Lyapunov function and integrating the power integrator technique, a controller design strategy is formulated based on the backstepping method. The rigorous analysis in this study proves that the designed controller ensures both the attainment of predefined-time convergence of the system states to the origin in probability and the satisfaction of the output constraint. Finally, an example of a roll angle subsystem for quadrotor UAVs and a numerical illustration are presented to corroborate the theoretical analysis. • A novel Lyapunov-type stochastic predefined-time stable control algorithm is presented in Theorem 1. • Controller design based on the backstepping method is formulated through the power integrator technique. • The tan-type barrier Lyapunov function extends the order range and absorbs the inherent properties of the nonlinear terms. [ABSTRACT FROM AUTHOR]

In this paper, a finite-time convergent continuous action iterated dilemma (CAID) with topological optimization is proposed to overcome the limitations of traditional methods. Asymptotic stability in traditional CAID does not provide information about the rate of convergence or the dynamics of the system in the finite time. There are no effective methods to analyze its convergence time in previous works. We made some efforts to solve these problems. Firstly, CAID is proposed by enriching the players' strategies as continuous, which means the player can choose an intermediate state between cooperation and defection. And discount rate is considered to imitate that players cannot learn accurately based on strategic differences. Then, to analyze the convergence time of CAID, a finite-time convergent analysis based on the Lyapunov function is introduced. Furthermore, the optimal communication topology generation method based on the Deep Q-learning (DQN) is proposed to explore a better game structure. At last, the simulation shows the effectiveness of the proposed method. • The dynamic model of Continuous Action Iterated Dilemma (CAID) with continuous strategy is more realistic. • The convergence time of CAID is analyzed by proposed finite-time convergent analysis method based on the Lyapunov function. • The optimal communication topology generation method based on DQN is proposed to enhance the game structure. [ABSTRACT FROM AUTHOR]

• Proposed a new switched epidemic model arising from changes in contact rates in an infected society. • Considering vulnerable individuals as vaccination frontiers along with the possibility of vaccine failure. • Qualitative analysis of the model using two theorems on positive invariance set and positivity of solutions. • Global stability analysis of equilibria, with a focus on the basic reproduction number (R 0) as a bifurcation value. • Manipulating the contact rates between subsystems through the contact-rate-dependent average dwell time to control a disease. This paper introduces a switched SQWVEAIR (Susceptible, Quarantined, Weak, Vaccinated, Exposed, Asymptomatic, Infected, and Recovered) epidemic model considering changing contact rates in an infected society. It also takes into account the presence of vulnerable individuals as frontiers in vaccination, recognizing their societal importance. The qualitative analysis of the model involves two theorems on the positive invariance set and the positivity of the solutions. Additionally, it calculates the equilibria of the proposed model and analyzes their global stabilities using the Lyapunov functional technique, focusing on the basic reproduction number (R 0) as a bifurcation value. To achieve globally uniformly exponential stability, it calculates the contact-rate-dependent average dwell time (CRDADT) for each stable and unstable subsystem, developing a Lyapunov function. It also derives sufficient conditions, expressed as linear matrix inequalities (LMIs), to ensure stability. A numerical example is provided to demonstrate the effectiveness of the theoretical analysis and validate our research findings. [ABSTRACT FROM AUTHOR]

In this paper, the safety control problem for spacecraft inspection mission is investigated, which means that there is no position and attitude obstacle collisions between the inspection spacecraft and the defined forbidden zones. We propose a control strategy that ensures safety, utilizing the control barrier function to address multiple safety constraints with logical relationships among them. Firstly, the position and attitude constraints are defined, and the hybrid logical relationship among different attitude constraints is analyzed. To handle complex position and attitude constraints, the Kreisselmeier-Steinhauser function is introduced to approximate the max/min function, thereby expressing them as continuous and differentiable functions. Subsequently, the control barrier function-based quadratic programming (CBF-QP) problems are solved to generate safe velocity and angular velocity. These problems have explicit solutions and do not require extensive computational resources. The safe position and attitude are then obtained by integrating the safe velocity and angular velocity. Notably, the forbidden regions are expanded by a constant in the construction of CBF-QP problems, which acts as a margin for the tracking controller's performance. Finally, attitude and position tracking controllers based on the control Lyapunov barrier function (CLBF) are designed respectively, taking into account the lumped disturbance in the system, which means that the attitude and position control are computed independently. Numerical simulation results demonstrate that the proposed control strategy effectively handles complex constraints in inspection missions, ensuring system stability and safety, even under severe conditions. [ABSTRACT FROM AUTHOR]

An adaptive neural network energy-based control approach is proposed in this paper to address the issue of stabilizing a partial space elevator during cargo transportation. The method handles the challenges presented by external disturbances and model uncertainties. The dynamic model of the partial space elevator, with a typical multi-input and multi-output underactuated system, is presented. A control scheme using energy-based techniques is proposed to guarantee the stable configuration of the system, and auxiliary kinematic vector variables are designed to incorporate the uncontrollable variables to constitute controllable state subsets. Under these frameworks, adaptive control schemes are formulated using multi-layer neural networks to mitigate model uncertainty. Robust compensators are designed to effectively counteract the unknown boundaries of external disturbances and approximation errors. The stability of the closed control system is rigorously demonstrated through the application of the Lyapunov function and LaSalle's invariance principle. Numerical simulations demonstrate that the proposed control method is highly effective in suppressing oscillations during the transfer period of a partial space elevator. [ABSTRACT FROM AUTHOR]

This paper addresses the mean-square quasi-consensus problem for a class of heterogeneous multi-agent systems (MASs) with cascade-type two-layer structure subject to discrete-time deception attacks. A two-layer distributed hybrid controller is proposed based on the structural characteristics of the considered MASs. The deception attacks are supposed to occur in the upper-layer communication channel and their occurrences are modeled by a Bernoulli process. The discrete-time deception signal is considered as a bounded external disturbance sequence, so the mean-square quasi-consensus problem can be reduced to a mean-square exponential input-to-state stability (MSEISS) problem. A novel MSEISS analysis method combined with the use of a weighted discontinuous Lyapunov function is developed to establish a MSEISS criterion of the consensus error system, where the robustness performance of the mean-square quasi-consensus with respect to the randomly occurring deception attacks is quantified by the MSEISS gain. The effectiveness of the proposed resilient distributed hybrid control algorithm is verified through numerical simulations. Specifically, the proposed resilient control algorithm is applied to the secondary control of DC microgrid with discrete interaction. Several case studies show that the resulting resilient distributed hybrid secondary control algorithm has a good robustness performance on resisting the deception attacks. • A hybrid control framework for heterogeneous multi-agent systems under discrete-time deception attacks is developed. • A separate principle is proposed to decouple the design of lower- and upper-layer controllers. • The effect of deception attacks on consensus performance is analyzed in terms of mean-square input-to-state stability. • A resilient secondary control algorithm is proposed for DC microgrids subject to deception attacks. [ABSTRACT FROM AUTHOR]

This paper is concerned with the input-to-state stability (ISS) for a kind of delayed memristor-based inertial neural networks (DMINNs). Based on the nonsmooth analysis and stability theory, novel delay-dependent and delay-independent criteria on the ISS of DMINNs are obtained by constructing different Lyapunov functions. Moreover, compared with the reduced order approach used in the previous works, this paper consider the ISS of DMINNs via non-reduced order approach. Directly analysis the model of DMINNs can better maintain its physical backgrounds, which reduces the complexity of calculations and is more rigorous in practical application. Additionally, the novel proposed results on the ISS of DMINNs here incorporate and complement the existing studies on memristive neural network dynamical systems. Lastly, a numerical example is provided to show that the obtained criteria are reliable. [ABSTRACT FROM AUTHOR]

This paper is concerned with the fixed-time consensus control problem for non-strict feedback multi-agent systems with asymmetric output constraints and full state constraints. Considering the feasibility of controlling execution, a novel practical virtual control signal is developed utilizing both saturation function and hyperbolic tangent function to ensure that this signal can remain within the same restricted range as the corresponding state variable throughout entire operation process. In backstepping steps, the design of ideal virtual control signal also adopts a different form of piecewise function than before, introducing high-order polynomial functions to avoid singularity problems in the derivation process. In addition, function approximation ability of radial basis function neural networks technique is applied to estimate uncertainties derived from the system functions and controller design procedure. Moreover, universal barrier Lyapunov function approach is improved for constructing an adaptive constrained synchronization control scheme. By fixed-time stability theory, it is shown that the tracking errors of the MAS converge to an adjustable region around the origin in a fixed time and the state variables always obey their constraints. And the upper bound of the settling time is merely dependent on design parameters, which is not affected by the initial states of MAS. The effectiveness of the proposed control strategy is shown by a numerical simulation example at last. Two scenarios are provided to demonstrate the advantages of the control protocol proposed in this paper. [ABSTRACT FROM AUTHOR]

Different from the existing multiple Mittag-Leffler stability or multiple asymptotic stability, the multiple exponential stability, which has explicit and faster convergence rate, is investigated in this paper for fractional-order impulsive control Cohen–Grossberg neural networks. First, by using the definition of Dirac delta function, the fractional-order control Cohen–Grossberg neural networks are translated into fractional-order impulsive neural networks, in which pulse effect relies on the fractional order of the addressed system. Then, based on maximum norm, 1 − norm and general q − norm (q = 2 n) , a series of novel criteria are obtained respectively to ensure that such n − neuron neural networks can have ∏ i = 1 n (2 L i + 1) total equilibrium points and ∏ i = 1 n (L i + 1) locally exponentially stable equilibrium points, by utilizing the known fixed point theorem, the method of average impulsive interval, the theory of fractional-order differential equations, and the method of Lyapunov function. This paper's investigation reveals the effects of impulsive function, impulsive interval, and fractional order on the dynamic behaviors. Finally, theoretical results are shown to be effective by four illustrative examples. [ABSTRACT FROM AUTHOR]

The current paper investigates the path following control problem for marine vehicles with multiple disturbances and input saturation. First, considering that marine vehicles exposed to the marine environment always contain stochastic components, which were ignored in most of the previous studies, the multiple disturbances in this paper are decomposed into complex nonlinear terms, slow-varying disturbances, and stochastic disturbances. Accordingly, an appropriate stochastic differential model is constructed. Second, a new stochastic path following control strategy based on the fuzzy logic system, the stochastic disturbance observer, and the auxiliary dynamic compensators is established. The fuzzy logic system is adopted for approximating the complex nonlinear terms, the stochastic disturbance observer is constructed to estimate the slow-varying disturbances in stochastic situation, and the auxiliary dynamic compensators are designed to tackle input saturation. In the end, the stability of the entire system is proven through linear matrix inequalities and Lyapunov functions. The simulation results demonstrate the proposed controller's effectiveness and robustness. • The multiple disturbances are divided into three categories, and astochastic differential model is proposed. • The fuzzy logic system is adopted for approximating the marine vehicle model's complex nonlinear terms. • The stochastic disturbance observer is constructed to estimate the slow-varying disturbances in stochastic situation. • The auxiliary dynamic compensators are adopted to overcome the input saturation. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the finite region stability (FRS) and networked predictive control (NPC) problems for two-dimensional (2-D) networked control systems (NCS) with time delays, quantization errors, packet losses and random disturbances described by the Roesser model. The random packet dropouts and disturbances are modeled as Bernoulli process, and the sufficient conditions of FRS and finite region boundedness (FRB) for 2-D NCS are obtained by using the expectation to process the Lyapunov function difference, so as to better study the transient performance of the systems. According to the recursive formula, an active compensation scheme for time delays of NPC is proposed, which takes into account quantization errors, packet losses, nonlinearity and interferences. Introducing FRS and FRB into 2-D NCS and considering the above factors in NPC scheme are new attempts made in this paper. An example is used to demonstrate the validity of the conclusions in the end. • For nonlinear 2-D NCS, sufficient conditions for FRS and FRB are established. • A new NPC scheme including nonlinearity and random disturbances is introduced. • A state feedback controller with packet losses and quantization errors is proposed. [ABSTRACT FROM AUTHOR]

The hybrid integrator-gain system (HIGS) has been introduced recently with the aim to overcome fundamental limitations of linear time-invariant (LTI) control systems. To support the analysis and design of HIGS-based controllers, in this paper a novel frequency-domain condition for stability analysis of the feedback interconnection of an LTI system and HIGS is presented. Compared to existing frequency-domain stability conditions such as the one extending the circle-criterion, the condition presented in this paper exploits explicit knowledge regarding HIGS' switching strategy, thereby potentially providing a significantly less conservative condition. In particular, the novel condition in this paper guarantees the existence of a quadratic Lyapunov function that does not need to be positive definite within the full state space. The proposed condition can be verified graphically in a manner that is reminiscent of the classical Popov plot, as will be illustrated in an experimental case-study. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of time-varying formation control for heterogeneous unmanned swarm systems (USSs) consisting of multiple unmanned aerial vehicles (UASs) and unmanned surface vehicles (USVs) based on a directional switching topology. Firstly, a novel USSs model is established, involving the effect of multiple network attacks, network bandwidth constraints and input saturation. In particular, a scaling attack model is proposed to account for denial-of-service (DoS) and deception attacks. Secondly, a distributed controller based on a dynamic event triggering mechanism is designed to reduce the communication load by adjusting the communication frequency between individuals, and the Zeno phenomenon is effectively avoided. Finally, the Lyapunov function is used to obtain sufficient conditions for system stability and bounds on the frequency and duration of network attacks. The experiments and comparison results verify the proposed strategy's effectiveness and superiority. • A novel heterogeneous USS model consisting of UAVs and USVs is constructed. • A new scaling attack model is established that integrates the DoS attacks and deception attacks. • A novel controller based on a dynamic event triggering scheme is designed. [ABSTRACT FROM AUTHOR]

The issue of a novel finite-time stability and stabilization design for a class of nonlinear impulsive systems is discussed in this paper. In previous finite-time control designs for impulsive systems, the convergence rate of these control strategies is even less rapid than the exponential convergence rate when the initial state is distant from the origin. To overcome this problem, two sufficient conditions for the novel finite-time stability of impulsive systems are presented, in which the stabilizing impulses and the destabilizing impulses are considered, respectively. Meanwhile, the upper bound of the settling-time is evaluated. In addition, combining Lyapunov functions theory with impulsive control, we design a controller for impulsive dynamical systems to satisfy the novel finite-time stability. Finally, two simulation examples are given, in which the first example demonstrates the superiority of the proposed finite-time stability criterion for nonlinear impulsive systems by comparing it with traditional finite-time stability, and the second example verifies the effectiveness of the presented controller. • A novel finite-time stability criterion for nonlinear impulsive systems is established for the first time. • The upper bounds of settling-time were estimated for systems with stabilizing and destabilizing impulses, respectively. • Combining Lyapunov functions and impulse control theory, a fast finite-time controller is constructed. [ABSTRACT FROM AUTHOR]

• An on-orbit assembly mission of heterogenous spacecraft clusters containing rigid and flexible spacecraft is presented. • The relative dynamics and neural network (NN)-based pose control laws for both rigid and flexible spacecraft are presented. • The effectiveness of the proposed control methods is demonstrated at multiple levels through simulations of typical working conditions as well as comparative analysis and a large number of simulation statistics. • Vicsek fractal is innovatively applied to large space structures. The large space structure designed is not only suitable for large space antennas, but also has a wider range of applications, such as distributed telescopes. On-orbit assembly is a highly effective technique for building large space structures. This paper presents the dynamics and control of an on-orbit assembly of a large space structure based on a heterogenous spacecraft cluster comprising both rigid and flexible spacecraft. The topology of the large space structure is inspired by the Vicsek fractal. A distributed assembly strategy is proposed for the spacecraft team. Radial Basis Function neural networks (RBFNNs) are utilized to approximate the bounded uncertain terms in translational and attitude dynamics. To avoid collisions during the pre-assembly phase, a neural network (NN)-based controller with collision avoidance force is designed for relative position motion. During the assembly phase, only proportional-derivative (PD) law is employed for relative position control. In addition, an NN-based controller is designed for relative attitude control for both rigid and flexible spacecraft. To estimate the unmeasured flexible vibrations, modal coordinate observers are introduced for the flexible spacecraft. The stability of the closed-loop system is proved via Lyapunov functions. Moreover, numerical results are presented to validate the effectiveness of the proposed controllers and assembly strategy. [ABSTRACT FROM AUTHOR]

This paper considers the fixed-time stability of Filippov systems and discontinuous networks described by the Filippov systems. Firstly, the more generalized and economical inequality condition on Lyapunov function is proposed, which can not only improve the previous negative definite conditions, but also the indefinite conditions. Based on the definition of the Lyapunov stability and finite-time convergence, new fixed-time stability lemmas are proposed and the settling-time is also estimated. In order to apply the new fixed-time stability lemmas to the neural networks, fixed-time stabilization of a class of fuzzy leakage-delayed neural networks with discontinuous activations is considered which is rarely studied since the delay is leakage and activations are discontinuous and they are not easy to deal with simultaneously. By means of the Filippov regularization and differential inclusions theory, new criteria on the stabilization of the considered networks are derived via the new modified non-chattering controller, which can improve the previous ones with parameter and symbolic function. Finally, example and numerical simulations further examine the correctness of the main results. [ABSTRACT FROM AUTHOR]

In this paper, the robust digital stabilization problem of nonlinear systems is investigated. In particular, a methodology for the design of robust quantized sampled-data stabilizers updated via an event-triggered mechanism is provided for time-varying control-affine nonlinear systems affected by actuation disturbances and measurement noises. The notion of time-varying steepest descent feedback (TSDF), continuous or not, and the Input-to-State Stability (ISS) redesign methodology are used for the development of the proposed robust event-based digital controller. Under the assumption that the actuation disturbances and measurement noises are bounded with a-priori known bounds and that the amplitude of the measurement noises satisfies a certain condition related to the new added robustification term, the following result is proved: there exist a suitably fast sampling and an accurate quantization of the input/output channels such that the digital implementation of robustified TSDF controllers, updated through a proposed event-triggered mechanism, ensures semi-global practical stability of the related closed-loop system regardless of the above uncertainties. In the methodology here proposed, time-varying sampling periods and the non-uniform quantization of the input/output channels are allowed. Moreover, the theory here developed includes the analysis of the intersampling system behaviour. Possible discontinuities in the function describing the TSDF at hand are also managed. The provided results are validated through a numerical example. [ABSTRACT FROM AUTHOR]

In this paper, the boundary control problem for a class of flexible riser control systems with input quantization and boundary position constraints is studied. Since quantization errors can adversely affect the performance of the control system, input quantization is an unavoidable issue for maintaining the high accuracy of the system. Partial differential equations are utilized to model the dynamics of the flexible riser system. Based on the partial differential equation model, a new auxiliary term is introduced to compensate for the effects of quantization, and a boundary controller is constructed using the barrier Lyapunov function, which guarantees the stability of the considered system. Moreover, the boundary position of the system satisfies its constraints. Furthermore, the simulation results verify the effectiveness of the proposed control method. [ABSTRACT FROM AUTHOR]

This paper focuses on non-instantaneous impulsive systems with double state-dependent delays. The finite-time stability criteria of such systems are obtained via impulsive control theory and Lyapunov function method, and the effects of destabilizing impulse and stabilizing impulse on the finite-time stability are considered, respectively. Meanwhile, the obtained results are applied to finite-time stability of genetic regulatory networks with state-dependent delays and non-instantaneous impulses as an example. • The relationship between state-dependent delay and non-instantaneous impulse is revealed. • The restrictions of state-dependent delays are reduced in order to make the conditions more applicable. • The effects of destabilizing and stabilizing impulse on the finite-time stability are considered. • The obtained results are applied to genetic regulatory networks. [ABSTRACT FROM AUTHOR]

This paper specializes in exponential output synchronization of reaction-diffusion neural networks (RDNNs) for two different cases of output couplings. The proposed model is novel for incorporating multiple output couplings related to their own output states as well as output spatial diffusion couplings in the absence of ordinary differential equations (ODE) systems. Generalized intermittent control based on spatial sampled-data is adopted for the first time to handle error systems consisting of the states of RDNNs with different output couplings scenarios and the average of the sum of their output states to achieve exponential stability. Some sufficient conditions for determining the proposed network models are established by control protocols based on the Lyapunov functional method. Finally, the obtained theoretical results are demonstrated to be valid by numerical simulations. • A novel RDNNs with multiple output spatial diffusion coupling is proposed. • The method of intermittent spatial sampled-data control is first employed in the output-coupled model. • The output synchronization criterion is established by means of Lyapunov functions and intermittent control. [ABSTRACT FROM AUTHOR]

This paper studies the neural network adaptive fault-tolerant control (NNAFTC) for a class of uncertain nonlinear systems with full state constraints. It is the first time to introduce switched adaptive fault compensation strategy for the controller design process. On the one hand, the proposed method overcomes the limitation needed to be given a prescribed local restriction region of the traditional state constraint schemes, such as log-type, tan-type and integral-type. On the other hand, the full-state constraint and switched fault-tolerant problem is effectively solved even if the existence of actuator failures. Concomitantly, the novel switched tuning functions, the NN approximation technique and the integral barrier Lyapunov functions (IBLF) are combined to construct the backstepping controllers and adaptation laws. It can be proved that all the closed-loop states are restricted in the proper compact sets for any given initial values. Finally, A simulation is shown to demonstrate the validity and advantages of the presented control approach. [ABSTRACT FROM AUTHOR]

This paper investigates practical stabilization of multi-links highly nonlinear Takagi-Sugeno fuzzy complex networks with Lévy noise (MHFNLs) via aperiodically intermittent discrete-time observation control (AIDOC). It is worth pointing out that AIDOC is considered into MHFNLs for the first time. Due to the difficulty of satisfying linear conditions in real life, polynomial growth conditions are used instead of linear growth conditions. Meanwhile, a global Lyapunov function is constructed and sufficient conditions which can remain MHFNLs practically stable are gained. Finally, an application and its numerical simulations are presented to verify the effectiveness and availability of the theoretical results. • Polynomial growth conditions are used instead of linear growth conditions. • We consider Lévy noise and construct a global Lyapunov function. • Aperiodically intermittent discrete-time observation control is designed. • The theoretical result is applied to Van der Pol-Duffing oscillator. [ABSTRACT FROM AUTHOR]

This paper focuses on neutral stochastic quaternion-valued neural networks (NSQNNs). Employing some stochastic analysis and inequalities techniques, we establish several sufficient conditions for ensuring p th moment generalized exponential stability. Our results do not require the construction of any Lyapunov function or rely on the assumption of bounded variable coefficients. Furthermore, our results expand some existing works. At last, to illustrate the efficacy of our result, we present one simulation example. [ABSTRACT FROM AUTHOR]

This paper investigates the stability of semi-Markovian jump stochastic coupled nonlinear systems with mode-dependent sojourn time distributions. It is challenging to consider coupling in the semi-Markovian jump systems due to the different networked topologies. First, more realistic complex networks with coupling and semi-Markovian jump are established. Based on Lyapunov method and graph theory, a novel stochastic analysis method and linear comparable Lyapunov like functions are employed to ensure almost surely exponential stability (ASES). Then, without additional restrictions on the sojourn time, the sufficient criterion for ASES is developed. Compared with the most of existing works, which are restrictions on the independence and the distribution function of the sojourn time and the coupling are not considered, our results are meaningful and they can be directly applied to the coupled oscillator model. Finally, some numerical simulations are provided to demonstrate the validity of our results. [ABSTRACT FROM AUTHOR]

This paper is concerned with boundary stabilization of multi-dimensional hyperbolic systems of partial differential equations. By adapting the Lyapunov function previously proposed by the second author for linearized hyperbolic systems with relaxation structure, we derive certain control laws so that the corresponding solutions decay exponentially in time. The result is illustrated with an application to water flows in open channels. The effectiveness of the derived control laws is confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper studies the problem of safe stabilization of control-affine systems under uncertainty. Our starting point is the availability of worst-case or probabilistic error descriptions for the dynamics, a control barrier function (CBF) and a control Lyapunov function (CLF). These descriptions give rise to second-order cone constraints (SOCCs) whose simultaneous satisfaction guarantees safe stabilization. We study the feasibility of such SOCCs and the regularity properties of various controllers satisfying them. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the consensus tracking control for a class of heterogeneous multi-agent systems with multiple unknown time-varying control directions and unknown direction actuator faults. Different from existing work, the directions of the multiple time-varying control coefficients are subject to fault-induced sign-switching. To address this challenge, a series of high-order Lyapunov functions and differentiable functions are introduced to avoid non-integrable terms. Then, a novel contradiction statement and some Nussbaum functions are used to handle the summation of multiple unknown control coefficients with time-varying amplitudes and directions. Meanwhile, a novel distributed observer with quantized communication is introduced to track a reference trajectory with unknown dynamics. It is shown that all closed-loop signals are globally uniformly bounded and the tracking errors converge to residual sets that can be made arbitrarily small. Simulation results illustrate the effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

This paper proposes a convex embedding-based homogeneous finite-time controller design method for a class of nonlinear systems. The controlled system is first converted into a convex combination of linear systems. By utilizing a parallel distributed compensation approach, we derive a homogeneous stabilization condition for the control systems. The condition is expressed in the form of a set of linear matrix inequalities (LMIs). Finite-time stability is guaranteed by using a canonical homogeneous norm as a Lyapunov function. The homogeneous finite-time controller is obtained by solving the LMIs. The hybrid Van der Pol–Rayleigh system with an unstable limit cycle is used as an example to demonstrate how effectively the controller design performs. [ABSTRACT FROM AUTHOR]

This paper considers a one-dimensional wave equation on [ 0 , 1 ] , with dynamic boundary conditions of second order at x = 0 and x = 1 , also referred to as Wentzell/Ventzel boundary conditions in the literature. In additions the wave is subjected to constant disturbance in the domain and at the boundary. This model is inspired by a real experiment. By the means of a proportional integral control, the regulation with exponential converge rate is obtained when the damping coefficient is a nowhere-vanishing function of space. The analysis is based on the determination of appropriate Lyapunov functions and some further analysis on an associated error system. The latter is proven to be exponentially stable towards an attractor. Numerical simulations on the output regulation problem and additional results on related wave equations are also provided. [ABSTRACT FROM AUTHOR]

This paper investigates the decentralized linear quadratic optimization and stabilization problem for Itô systems, where the system's controller has two parts: the deterministic and random parts. Unlike previous works, with positive semi-definite weighting matrices, finite-horizon optimization and infinite-horizon stabilization problems are considered. The chief challenge lies in solving the forward and backward stochastic differential equations and selecting the Lyapunov function. The relationship between the forward and backward processes is established using a modified version of the four-step scheme combined with the information pattern of the problem. The equivalent condition for the optimization problem is obtained based on the Riccati differential equation. Besides, the necessary and sufficient conditions for the stabilization problem are presented using the Lyapunov function defined by the optimal cost function. Finally, numerical examples illustrate the validity of the presented strategies. [ABSTRACT FROM AUTHOR]

This paper studies the prescribed-time output-constrained tracking control problems for Mars entry vehicle systems. By using the properties of the time-varying high-gain function and output-constrained conditions, time-varying barrier Lyapunov functions are constructed. Based on such Lyapunov functions, time-varying adaptive controllers are designed to solve the considered problem. It is proved that the proposed controllers can drive the errors converge to zero in a prescribed time under unknown disturbances, and the control signals are bounded. Both the symmetric and asymmetric cases are considered. Finally, the effectiveness of the proposed methods is illustrated by several numerical simulations. • A class of novel time-varying barrier Lyapunov functions are constructed. • Based on these functions, two time-varying adaptive controllers are desgined. • The Mars entry vehicle can arrive at the target location under output constraints in a prescribed time by the proposed methods. [ABSTRACT FROM AUTHOR]

This paper uses reinforcement learning techniques to introduce a novel approach to the controller design for a wide range of serial chain robots and cable-driven serial chain robots. The method addresses the regulation problem by designing a regulator and steady-state torques without requiring knowledge of the Coriolis vector, a complex part of the robot's dynamic model. The approach relies on Denavit–Hartenberg parameters to determine regulator and desired steady-state torques, using an actor–critic neural network for adaptation and a multi-layer perceptron neural network for desired steady-state torque. Stability is ensured through Lyapunov functions, with only the mass matrix and gravity vector required. The proposed control scheme offers adaptability, robustness, scalability, and optimization features compared to traditional controllers. Simulations on a 4-degrees-of-freedom cable-driven serial chain robot validate the proposed control method's effectiveness. A comparative benchmark is performed, demonstrating that the reinforcement learning controller outperforms other controllers in terms of regulation error, reducing it by at least 17.14% compared to deep deterministic policy gradient and robust integral of the sign of the error methods. • Regulation control system for Serial Chain Robots (SCRs). • Exploring RL as a computationally intensive alternative to traditional optimal control. • Reduced reliance on robot dynamics knowledge. • Limiting computational torque. • Neural Network-based adaptation laws and stability guaranteeing. [ABSTRACT FROM AUTHOR]

In this paper, an event-triggered tracking optimization control method is proposed for nonlinear uncertain systems with H ∞ discounted cost. First, the linearization method using the infinite series expansion theorem is given. And the tracking control design problem is solved by appropriate state augment. Secondly, the zero sum differential game strategy is introduced to address the control design problem of uncertain systems with event-triggered inputs. The actor-critic-disturbance networks framework is used to approximate the optimization of event- triggered controller strategy, optimization costs, and the disturbance strategy, respectively. Due to the consideration of discrete time and continuous time dynamics, we put the impulsive system method to use and choose appropriate Lyapunov functions to prove stability and boundedness, at the same time, there will be no infinite triggering situation. Finally, the effectiveness of the proposed scheme is demonstrated by an example of a practical tractor system with n trailers through simulation compared with another typical design method. [ABSTRACT FROM AUTHOR]

• The lagrange dynamics model of wind turbines is developed and validated. • A novel fractional-order active disturbance rejection controller is designed. • The novel controller achieves high disturbance estimation performance. • The controller effectively reduces the power oscillation and tower vibration. Alleviating active power oscillations is important for horizontal-axis wind turbines (HAWTs), which directly determines the safe operation of the power grid. In this paper, an optimization framework is proposed to achieve active power regulation, which combines a wind turbine Lagrange dynamics model (LDM-WT) and a variable pitch fractional-order model-assisted active disturbance rejection controller (FOMA-ADRC). The LDM-WT is constructed as the database source to obtain a fractional-order servo speed model, which provides a great deal of information for creating a fractional-order extended state observer (FO-ESO). Then the stability of FOMA-ADRC with model uncertainty is proved by the Lyapunov function. The proposed framework is validated on a 5 MW NREL wind turbine under step and IEC turbulence wind speed conditions. Compared with the traditional control strategies, FOMA-ADRC reduces active power and tower acceleration variance by nearly a factor of five while maintaining robustness to disturbances. The outcomes systematically validate the efficacy of FOMA-ADRC in achieving active power regulation with excellent regulation rapidity and power stability. [ABSTRACT FROM AUTHOR]

This paper is centered on the local stabilization of discrete-time positive systems subject to input saturation using a static linear feedback. To estimate the domain of attraction for systems with open-loop positivity, some sufficient criteria are proposed to construct two types of sets maintaining contractive invariance for the closed-loop system, namely hyperpyramids and hyperrectangles, which are the level sets corresponding to sum-separable and max-separable Lyapunov functions, respectively. Furthermore, these criteria are nonconservative for the single-input case. In the absence of open-loop positivity, some sufficient criteria are provided to guarantee that a hyperrectangle still maintains contractive invariance for the system. Finally, two numerical experiments are presented to demonstrate the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

Most research on control of nonlinear systems using backstepping concentrates on construction of feedback controllers to achieve stability and/or steady-state tracking performance. Little research considers systematic methods for tuning nonlinear feedback controllers to guarantee the transient performance. This paper investigates how parameters of a backstepping controller can be determined to achieve the predefined settling time and overshoot, which are basic criteria for the transient performance. First, some modifications are made for the backstepping design method by introducing more parameters so that there are more degrees of freedom for parameter tuning. Second, the pole-placement method is used for the linear part of the closed-loop system corresponding to a backstepping controller. Third, an objective function is defined by summing the square of errors between the corresponding coefficients of the desired and real characteristic polynomials. Fourth, constraints are introduced to guarantee the negative semi-definiteness of the time derivative of the Lyapunov function. Fifth, the controller parameters can be found by minimizing the objective function. Finally, simulation and experimental results show that, compared with the existing method, the proposed method is more effective and efficient for fine tuning backstepping controllers. [ABSTRACT FROM AUTHOR]

This paper tackles the constrained control problem of unmanned aerial vehicles with planar multirotors. The proposed solution splits the constrained control problem into two separate tasks, i.e. stabilization and constraint enforcement. It is shown that the problems addressed by each individual layer is much simpler than the original combined problem. For the unconstrained control of UAVs we consider a control scheme based on a cascade structure. The Lyapunov function for the stabilized cascaded system is then derived. Using this Lyapunov function, we develop an Explicit Reference Governor for constraint enforcement. Numerical simulation shows the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

In contrast with most existing results concerning quadrotor unmanned aerial vehicle (UAV) wherein time-triggered controllers or only symmetric state constraints are considered, this paper deals with the event-triggered finite-time trajectory tracking control problem for quadrotor UAV with asymmetric time-varying state constraints and unknown external disturbances. Firstly, the fuzzy logic system is used to approximate the nonlinear relationship of the quadrotor UAV system, and a disturbance observer is designed to compensate for composite disturbances. Secondly, the command filter and the event-triggered mechanism are introduced into the controller design, while asymmetric time-varying Lyapunov functions are constructed. Thus, the computational complexity and communication burden are reduced, and the event-triggered finite-time adaptive fuzzy controller is guaranteed to stabilize the quadrotor UAV in finite-time without violating all asymmetric time-varying state constraints. Finally, the simulation results demonstrate the validity of the proposed control strategy. • A asymmetric time-varying constraint finite-time control scheme for quadrotor UAV systems is developed. • A disturbance observer is designed to compensate for composite disturbances of quadrotor UAV. • The asymmetric time-varying Lyapunov functions are employed to satisfy the condition of the state constraints. • The event-triggered mechanism is introduced to reduce the computational complexity and communication burden. [ABSTRACT FROM AUTHOR]

In this research endeavor, a novel synthesis variable-gain robust model predictive control (SVGRPC) method using the min-max technique with parameter dependent Lyapunov functions is introduced to achieve the desired trajectory tracking of oxygen excess ratio (OER) and cathode pressure in the polymer electrolyte membrane fuel cells (PEMFCs) system. Initially, a simplified control-oriented model of the air supply system is developed and then transformed into a polytopic form to accommodate the inherent uncertainties in the PEMFC. Subsequently, the polytopic model is integrated with the reference trajectory to construct an augmented state-space model for deriving an error state representation. In the framework of robust model predictive control (RPC) utilizing a parameter-dependent Lyapunov function, a series of variable feedback gains are employed to mitigate conservatism. Additionally, the online solution process imposes a significant computational burden, presenting challenges for the real-time implementation of RPC-based control strategy. Therefore, the offline computing is introduced to significantly reduce the computational burden, resulting in the development of the SVGRPC strategy proposed in this paper. Subsequently, the SVGRPC strategy computes explicit linear state-feedback control laws by solving linear matrix inequalities (LMIs) using an offline control algorithm. The effectiveness of the proposed controller is then validated through assessments conducted under three distinct operating conditions of the PEMFC system. The outcomes of this study affirm that the proposed controller improves the requirements of control performance when compared to the online RPC with a quadratic Lyapunov function while significantly alleviating the computational workload. • A polytopic air supply subsystem model to capture the uncertainties inherent in the PEMFC. • A robust model predictive control framework with variable feedback gains is employed to mitigate conservatism. • The offline computation method is used to reduce the computational burden. • Comparison with other methods shows the advantages of the proposed method. [ABSTRACT FROM AUTHOR]