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In this paper, we investigate the complex dynamics of a Darwinian Ricker system through a comprehensive qualitative and dynamical analysis. Our research shows that the system exhibits Neimark–Sacker bifurcation, period-doubling bifurcation, and codimension-two bifurcations associated with 1:2, 1:3, and 1:4 resonances. These findings are derived using bifurcation and center manifold theories. We numerically illustrate all bifurcation results and chaotic features, providing a thorough understanding of the system's behavior. This detailed examination of the Darwinian Ricker system, with a focus on the interplay between immigration and the strong Allee effect, enhances our understanding of the intricate mechanisms driving population dynamics. Furthermore, it highlights the significant implications for ecological modeling, particularly in predicting ecosystem responses to external perturbations such as climate change and species invasions. [ABSTRACT FROM AUTHOR]

The study proposes a dynamic analysis regarding interactions between the resources provided by the forest, the wildlife present inside or in the proximity of that environment and visitors revolving around the before mentioned socioecological framework. The mathematical model is described by a nonlinear system with three differential equations. The discrete time delay is introduced to illustrate the entire past impact of tourists on forest resources and wildlife. The basic assumption is that the wildlife species which inhabit the area are relying entirely on forest resources to meet their needs for food, shelter, and to attract tourists. Also, there is a positive correlation between ecotourism activities and the presence of forest resources and wildlife. The equilibrium states are determined, and they are subjected to a stability and bifurcation analysis. The study employs a Hopf bifurcation analysis in the neighborhood of the equilibrium states by choosing the time delay as the bifurcation parameter. The critical values of the time-delay that lead to oscillatory behavior are determined. Numerical simulations are carried out to show the system's qualitative behavior in the vicinity of the equilibria. [ABSTRACT FROM AUTHOR]

In this paper we determine the necessary and sufficient conditions for asymptotically stability of periodic cycles for periodic difference equations by using the Jury's conditions. Such conditions are obtained using the information of the Jacobian matrices of the individual maps, avoiding thus the computation of the Jacobian matrix of the composition operator, which in higher dimension can be an a very difficult task. We illustrate our ideas by using models in population dynamics and in economics game theory. • Coefficients of a characteristic polynomial. • Necessary and sufficient conditions for local stability of periodic maps. • Periodic Cournot Duopoly game model. • 3D periodic Ricker competition model. • Periodic delayed logistic model. [ABSTRACT FROM AUTHOR]

The fractional competitive neural networks (FCNNs) with multiple restrictions are considered in this article. Specially, the FCNNs with memristors and time-varying delays in complex field (FCMCNNs) are first introduced, as well as the asymptotic stability (AS) and quantitative synchronization (QTS) issues are investigated. Firstly, applying Filippov's conclusion theory, a model of FCMCNNs is reduced to a simpler one containing the time-switching memristive coefficients. Secondly, in virtue of the Banach fixed-point theorem, the AS is sufficiently discussed. Thirdly, in the light of the quantized controller (QTC), some concise inequality criteria are drawn to attain the QTS of the master–slave systems. Lastly, by providing two simulation examples, the results obtained manifest the availability and practicality. [ABSTRACT FROM AUTHOR]

The aim of this work is to study qualitative dynamical properties of a generalized hepatitis B epidemic model and its dynamically consistent discrete model. Positivity, boundedness, the basic reproduction number and asymptotic stability properties of the model are analyzed rigorously. By the Lyapunov stability theory and the Poincare–Bendixson theorem in combination with the Bendixson–Dulac criterion, we show that a disease-free equilibrium point is globally asymptotically stable if the basic reproduction number R 0 ≤ 1 and a disease-endemic equilibrium point is globally asymptotically stable whenever R 0 > 1. Next, we apply the Mickens' methodology to propose a dynamically consistent nonstandard finite difference (NSFD) scheme for the continuous model. By rigorous mathematical analysis, it is proved that the constructed NSFD scheme preserves essential mathematical features of the continuous model for all finite step sizes. Finally, numerical experiments are conducted to illustrate the theoretical findings and to demonstrate advantages of the NSFD scheme over standard ones. The obtained results in this work not only improve but also generalize some existing recognized works. • A generalized hepatitis B epidemic model is proposed and studied. • Qualitative dynamical properties of the proposed HBV model are analyzed rigorously. • A dynamically consistent NSFD scheme for the generalized HBV model is constructed. • A set of numerical examples is reported to support the theoretical findings. • The obtained results not only improve but also generalize some recognized works. [ABSTRACT FROM AUTHOR]

In this paper, based on sampled-data control method, we address the stabilization problem for a general class of linear continuous-time fractional systems whose solution contains the Mittag-Leffler function that does not obey the basic exponentiation identity. By considering the infinite memory and hereditary characteristics of fractional-order calculus, we propose a sampled-data controller that guarantees the resulting closed-loop system to be asymptotically stable. Simulation examples are presented to demonstrate the effectiveness of the proposed controller and verify the established results. [ABSTRACT FROM AUTHOR]

Various efforts have been devoted to developing stabilizing distributed model predictive control (MPC) schemes for tracking piecewise constant references. In these schemes, terminal sets are usually computed offline and used in the MPC online phase to guarantee recursive feasibility and asymptotic stability. Maximal invariant terminal sets do not necessarily respect the distributed structure of the network, hindering the distributed implementation of the controller. On the other hand, ellipsoidal terminal sets respect the distributed structure, but may lead to conservative schemes. In this article, a novel distributed MPC scheme is proposed for reference tracking of networked dynamical systems, where the terminal ingredients are reconfigured online depending on the closed-loop states to alleviate the aforementioned issues. The resulting nonconvex infinite-dimensional problem is approximated using a quadratic program. The proposed scheme is tested in simulation, where the proposed MPC problem is solved using distributed optimization. [ABSTRACT FROM AUTHOR]

This article develops the sliding mode control (SMC) strategy for linear impulsive systems with matched disturbances. Such systems describe dynamical systems that evolve according to continuous process most of the time with matched disturbances, but instantaneously exhibit discontinuities, i.e., impulsive disturbances. A suitable sliding surface function is proposed and the resulting sliding mode dynamics are a class of linear impulsive systems. Some sufficient conditions coupled with impulse time sequences are proposed to guarantee the reachability of the predesigned sliding surface and the stability of the reduced-order impulsive systems under sliding motion, respectively. We show how restrictions on the structure of the systems and impulses should be imposed to ensure the feasibility of the proposed SMC strategy in comparison with general SMC in continuous space. To show the effectiveness of the proposed approach, two simulation examples are presented at the end. [ABSTRACT FROM AUTHOR]

This article aims to solve the problem of decentralized event-based finite-time control for a class of high-order interconnected nonlinear systems with an asymmetric output constraint. In order to achieve finite-time stability and reduce the update frequency of the controller, a novel controller and its event-trigger mechanism is proposed by adding a power integral technique and utilizing sign function. To fulfill the requirement of asymmetric output constraints, an asymmetric barrier Lyapunov function (BLF) is constructed, which is different from tan-type and log-type BLFs. Based on the contradictory idea and finite-time stability theory, it is proved that there is no Zeno phenomenon under this event-trigger mechanism and all state variables of the closed-loop system attenuate to the origin in the finite-time while the output signals never violate the constraint. Furthermore, the result in this article is expanded to fixed-time control. Finally, a simulation example is given to demonstrate the effectiveness of the presented strategy. [ABSTRACT FROM AUTHOR]

This article investigates a type of nonautonomous delayed differential equation (DDE) with discontinuity. Under the framework of the Filippov state solution, the finite-time stability (FNTS)/fixed-time stability (FXTS) problems of nonautonomous functional differential inclusion (FDI) are studied via the generalized Lyapunov functional method. The generalized Lyapunov functional used in this article is allowed to obtain an indefinite time derivative almost anywhere (a.a.) along the system’s state solutions. Nevertheless, the classic Lyapunov functional requires that its time derivative retains seminegative/negative definiteness anywhere. As a result, novel FNTS and FXTS criteria of the trivial state solution for FDI are established. Moreover, the settling time (ST) of FNTS/FXTS is provided. Then, the developed Lyapunov functional approach is applied to realize the finite-/fixed-time stabilization control of delayed neuron networks (DNNs) possessing discontinuous activation and ball motion models. The proposed method and results concerning FNTS/FXTS are of great significance in neural network (NN)/mechanical control engineering applications. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the global asymptotic stability and global exponential stability with respect to the Clifford-valued neutral-type neural network (NN) models with time delays. By considering the neutral term, a Clifford-valued NN model with time delays is formulated, which encompasses real-valued, complex-valued, and quaternion-valued NN models as special cases. In order to achieve our main results, the n -dimensional Clifford-valued NN model is decomposed into 2 m n -dimensional real-valued models. Moreover, a proper function is constructed to handle the neutral term and prove that the equilibrium point exists. Utilizing the homeomorphism theory, linear matrix inequality as well as Lyapunov functional methods, we derive the sufficient conditions corresponding to the existence, uniqueness, and global asymptotic stability with respect to the equilibrium point of the Clifford-valued neutral-type NN model. Numerical examples to demonstrate the effectiveness of the results are provided, and the simulations results are analyzed and discussed. [ABSTRACT FROM AUTHOR]

In this paper, global event-triggered adaptive prescribed tracking output feedback control is investigated for a class of nonlinear uncertain systems with unknown control direction. Different from the existing works, the design of the tracking error-dependent normalized function and prescribed boundary is based on our uniformly defined blow-up function rather than a specific function, and the asymmetric constraint requirements on tracking error can be achieved by appropriately selecting the blow-up function. By utilizing the Kalman filter ($K$ -filter) and dynamic gain technique, a new reduce-order observer is proposed, which can make the estimated error exponentially converge to zero. In addition, by introducing a dynamic signal into the trigger condition, a novel event-triggered mechanism is proposed, which can extend the trigger time interval and completely counteract the event-triggered errors in terms of asymptotic stability by sacrificing part of the system transient performance. Furthermore, an adaptive controller is designed based on the backstepping method, which ensures the boundedness of the state of the closed-loop system, while regulating the tracking error meets the global prescribed performance requirements and approaches to zero asymptotically. Two examples are given to illustrate the effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

This article considers a codesign problem for industrial networked control systems to ensure both stability and efficiency properties of such systems. This problem is particularly challenging due to the fact that wireless communications in industrial environments are not only subject to shadow fading, but also stochastically correlated with their surrounding environments. This article first introduces a novel state-dependent Markov channel (SD-MC) model that explicitly captures the state-dependent features of industrial wireless communication systems by defining the proposed model’s transition probabilities as a function of both environments’ states and transmission power. Under the SD-MC model, sufficient conditions on Maximum Allowable Transmission Interval are presented to ensure both asymptotic stability in expectation and almost sure asymptotic stability properties of a nonlinear control system with state-dependent fading channels. Based on these stability conditions, the codesign problem is then formulated as a constrained polynomial optimization problem (CPOP), which can be efficiently solved using semidefinite programming methods for the case of a two-state SD-MC model. The solutions to such a CPOP represent optimal control and power strategies that optimize the average expected joint costs in an infinite time horizon while respecting the stability constraints. For a general SD-MC model, this article further shows that suboptimal solutions can be obtained from linear programming formulations of the considered CPOP. Simulation results are given to illustrate the efficacy of the proposed codesign scheme. [ABSTRACT FROM AUTHOR]

In this article, we report several new geometric and Lyapunov characterizations of incrementally stable systems on Finsler and Riemannian manifolds. A new and intrinsic proof of an important theorem in contraction analysis is given via the complete lift of the system. Based on this, two Lyapunov characterizations of incrementally stable systems are derived, namely, converse contraction theorems, and revelation of the connection between incremental stability and stability of an equilibrium point, in which the second result recovers and extends the classical Krasovskii’s method. [ABSTRACT FROM AUTHOR]

In this article, we show that linear dynamic controllers with integer coefficients are usually unstable. In fact, asymptotic stability can only be achieved if all controller eigenvalues are equal to zero. Moreover, for a fixed controller order, there exist only finitely many characteristic polynomials with integer coefficients that lead to marginally stable eigenvalues on the unit circle and we characterize these setups. The obtained results are, in particular, relevant to encrypted control, where (nontrivial) stable controllers with integer coefficients were on the “wish list.” [ABSTRACT FROM AUTHOR]

This article is devoted to the global continuous control for stochastic low-order cascade nonlinear systems with time-varying delay and stochastic inverse dynamics. Compared with existing results, the nature of only continuous, but nonsmooth, is unfolded since the power of the stochastic cascade system is of low order; and all the traditional growth conditions on unknown drift and diffusion nonlinearities and local Lipschitz condition are quitted, which largely extends the scope of application. Combining with stochastic input-to-state stability, two new lemmas are developed with rigorous proofs to deal with uncertain nonlinear terms and unmeasurable stochastic inverse dynamics. A continuous control scheme consisting of a delay-independent partial state feedback controller and a serial of dynamic update laws is proposed to guarantee the globally asymptotical stability of the closed-loop system. [ABSTRACT FROM AUTHOR]

This article proposes a method for enlarging the region of attraction of linear model predictive controllers (MPC) when tracking piecewise-constant references in the presence of pointwise-in-time constraints. It consists of an add-on unit, the feasibility governor (FG), that manipulates the reference command so as to ensure that the optimal control problem that underlies the MPC-feedback law remains feasible. Offline polyhedral projection algorithms based on multiobjective linear programming are employed to compute the set of feasible states and reference commands. Online, the action of the FG is computed by solving a convex quadratic program. The closed-loop system is shown to satisfy constraints, be asymptotically stable, exhibit zero-offset tracking, and display finite-time convergence of the reference. [ABSTRACT FROM AUTHOR]

In this article, the finite-time stabilization problem is solved for a linear time-varying system with unknown control direction by exploiting a modified version of the classical extremum-seeking algorithm. We propose to use a suitable oscillatory input to modify the system dynamics, at least in an average sense, so as to satisfy a differential linear matrix inequality condition, which in turn guarantees that the system’s state remains inside a prescribed time-varying hyperellipsoid in the state space. The finite-time stability (FTS) of the averaged dynamics implies the FTS of the original system, as the distance between the original and the averaged dynamics can be made arbitrarily small by choosing a sufficiently high value of the dithering frequency used by the extremum-seeking algorithm. The main advantage of the proposed approach resides in its capability of dealing with systems with unknown control direction, and/or with a control direction that changes over time. Being FTS a quantitative approach, this article also gives an estimate of the necessary minimum dithering/mixing frequency provided, and the effectiveness of the proposed finite-time stabilization approach is analyzed by means of numerical examples. [ABSTRACT FROM AUTHOR]

In this article, the finite-time and fixed-time attractiveness problems are investigated for nonlinear impulsive systems. The aim of the proposed problems is to establish some general Lyapunov theorems and settling-time estimates for finite-time and fixed-time attractiveness of nonlinear impulsive systems by analysis technics. Moreover, some comparisons with the existing results are also given. The classical finite-time and fixed-time convergence theorems for nonlinear impulse-free systems are well extended to nonlinear impulsive systems by our results. Furthermore, the existing results of finite-time and fixed-time attractiveness for nonlinear impulsive systems are well improved. Finally, some simulations are utilized to illustrate the usefulness of the theoretical analysis. [ABSTRACT FROM AUTHOR]

We introduce a new class of large, infrequent disturbances to complement the small, persistent disturbances typically considered in robustness analysis. This new class of disturbances includes discrete disturbances that become pertinent when considering discrete actuators and production scheduling in control problems. To properly account for the infrequent nature of these disturbances, we define a stochastic form of robustness. Under suitable assumptions, we prove that certain closed-loop systems subject to large, infrequent disturbances admit an SISS-Lyapunov function and are robust in this stochastic context. We apply these results to economic model predictive control (MPC) with a strictly dissipative nominal system and stage cost, which includes tracking MPC as a special case, and prove that economic MPC is robust to large, infrequent disturbances. Without dissipativity assumptions, we define and establish robust asymptotic performance for economic MPC. We present a simple tracking problem to illustrate the results of this work, and a production scheduling (economic MPC) problem, to demonstrate the relevance of this analysis to practical applications. [ABSTRACT FROM AUTHOR]

This article studies the positivity and stability of homogeneous coupled differential-difference equations with time-varying delays. First, a sufficient positivity condition is proposed for the nonlinear coupled differential-difference equations with delays. Then, based on this positivity condition, we present necessary and sufficient conditions ensuring the exponential stability and bounding the decay rate for time-delay homogeneous coupled differential-difference equations with homogeneity of degree one. Furthermore, the necessary and sufficient condition is extended to the global polynomial stability analysis of homogeneous coupled differential-difference equations when the degree of homogeneity is greater than one, and the decay rate is also investigated. Two numerical examples are employed to show the effectiveness of the obtained results. [ABSTRACT FROM AUTHOR]

We investigate the implementation of a sparsitypromoting hands-off control scheme using the alternating direction method of multiplies (ADMM). In order to minimize the numerical control effort along with the actuation one, only a single ADMM iteration per time step is considered. We analyze the resulting closed-loop dynamics for linear systems with additive disturbances and show that the proposed scheme provides sparse controls as desired and, in addition, ensures input-to-state practical stability. We further point out a close relation between the proposed real-time scheme and (nonminimum time) dead-beat control. Finally, characteristics and effectiveness of the novel hands-off controller(s) are illustrated with numerical examples. [ABSTRACT FROM AUTHOR]

This article presents some new criteria for the partial exponential stability of a slow–fast nonlinear system with a fast scalar variable using periodic averaging methods. Unlike classical averaging techniques, we construct an averaged system by averaging over this fast scalar variable instead of the time variable. We show that the partial exponential stability of the averaged system implies that of the original one. We then apply the obtained criteria to the study of remote synchronization of Kuramoto–Sakaguchi oscillators coupled by a star network with two peripheral nodes. We show that detuning the natural frequency of the central mediating oscillator increases the robustness of the remote synchronization against phase shifts. This article appears to be the first-known attempt to analytically study the phase-unlocked remote synchronization. [ABSTRACT FROM AUTHOR]

This article investigates the event-triggered control problem for switched affine systems (SASs). The presence of affine terms brings many difficulties on the exclusion of triggering Zeno behavior when ensuring asymptotic stability. We propose an event-triggered control strategy dynamically updated with triggering to solve this problem, in which the triggering condition is associated with the affine terms and given with a time-varying term that is updated at triggering instants. Based on the triggering strategy, the controllers for subsystems and a switching rule are designed to achieve asymptotic stability of the resulting closed-loop system. Moreover, due to the special feature of event-triggered SASs, a new method for proving the exclusion of Zeno behavior is given. Finally, the developed results are illustrated by an electric circuit example. [ABSTRACT FROM AUTHOR]

In this article, we study positive invariance and attractivity properties for nonlinear control systems, which are monotone with respect to proper cones. Monotonicity simplifies such analysis for specific sets defined by the proper cones. Instead of Lyapunov functions, a pair of so-called paths in the state space and input space play important roles. As applications, our results are utilized for analysis of asymptotic stability and also input-to-state stability on proper cones. The results are illustrated by means of examples. [ABSTRACT FROM AUTHOR]

This article contributes to extending the validity of Lyapunov function partial differential equations (PDEs) whose solution is conjectured to be able to behave as a Lyapunov function in stability analysis to more mass-action chemical reaction networks. First, we have proved that the Lyapunov function PDEs method is valid in capturing the asymptotic stability of the networks compounded of a complex balanced network and any species-dependent two-species autocatalytic network if some moderate conditions are included. Then, by defining a new class of networks, called complex balanced produced networks, we also show the asymptotic stability of this class of networks, and also to their compound with any species-independent one-dimensional network and with any species-dependent two-species autocatalytic network under some conditions by using the same method. A notable point is that these classes of networks are nonweakly reversible, of any dimension, and of any deficiency. Finally, we apply our results to some practical biochemical reaction networks, including birth-death processes, motifs related networks, etc., to illustrate validity. [ABSTRACT FROM AUTHOR]

This article investigates the stability and synchronization of nonautonomous reaction–diffusion neural networks with general time-varying delays. Compared with the existing works concerning reaction–diffusion neural networks, the main innovation of this article is that the network coefficients are time-varying, and the delays are general (which means that fewer constraints are posed on delays; for example, the commonly used conditions of differentiability and boundedness are no longer needed). By Green’s formula and some analytical techniques, some easily checkable criteria on stability and synchronization for the underlying neural networks are established. These obtained results not only improve some existing ones but also contain some novel results that have not yet been reported. The effectiveness and superiorities of the established criteria are verified by three numerical examples. [ABSTRACT FROM AUTHOR]

This paper studies the prescribed-time input-to-state stabilization problem of normal nonlinear systems. With the help of some key properties of a class of parametric Lyapunov equations, the prescribed-time input-to-state stabilization problem of normal nonlinear systems under matched uncertainties is studied. Some bounded time-varying controllers are proposed. It is shown that the closed-loop systems are prescribed-time input-to-state stable. Finally, the effectiveness of the established methods is illustrated by two physical systems. [ABSTRACT FROM AUTHOR]

This article presents a time-invariant extremum seeking controller (ESC) for nonlinear autonomous systems with limit cycles. For this time-invariant ESC, we propose a method to prove the closed-loop system has an asymptotically stable limit cycle. The method is based on a perturbation theorem for maps, and, unlike existing techniques that use averaging and singular perturbation tools, it is not limited to weakly nonlinear systems. We use a typical example system to show that our method does indeed establish asymptotic stability of the limit cycle with minimal amplitude. Utilizing the example, we provide a general guide for analytic computations that are required to apply our method. The corresponding Mathematica code is available as supplementary material. [ABSTRACT FROM AUTHOR]

This article is devoted to reveal some essential features of stochastic control systems with sampled data (SCSwSD). First, it is shown by a proposition that the moment asymptotic stability of the underlying system is equivalent to that of any regular accurate numerical scheme under simple conditions, which is convenient to be structured specially for SCSwSD. This kind of principle provides a way for inferring moment asymptotic stability of SCSwSD by numerical simulations logically. As the first application of the proposition, the accurate scheme construction procedure is introduced in a general framework and illustrated for the quasi-linear models, the mean square asymptotic stability of linear SCSwSD is investigated. The restriction to the upper bound of the sampling period is confirmed by the way. As the second application of the proposition, the almost sure stability of a kind of controlled system with sampled noise is analyzed via the discrete scheme approach. The concepts of accurate numerical computation and simulation (ANCS) are proposed. A distinctive character, sampled data based control (SDBC) only, for SDBC is reported and studied preliminarily based on ANCS and the equivalence proposition. Some important remarks are given as further analyses on related issues. Finally, numerical examples are given to illustrate the applications of the theoretical results. [ABSTRACT FROM AUTHOR]

A novel method is proposed to ensure stability and constraint satisfaction, i.e., “compatibility,” for nonlinear affine systems. We require an asymptotically stabilizing control law and a zeroing control barrier function, and define a region of attraction for which the proposed control safely stabilizes the system. Our methodology requires checking conditions of the system dynamics over the state space, which may be computationally expensive. To facilitate the search for compatibility, we extend the results to a class of nonlinear systems, including mechanical systems, for which a novel controller is designed to guarantee passivity, safety, and stability. The proposed technique is demonstrated using numerical examples. [ABSTRACT FROM AUTHOR]

This article addresses analysis and control of the SIR model of infectious diseases in the framework of input-to-state stability (ISS) with respect to the net flow of susceptible individuals into a region in both disease-free and epidemic situations. The key development is the construction of a continuously differentiable strict Lyapunov function. First, this article clarifies that a continuously differentiable Lyapunov function whose derivative is nonpositive can deduce asymptotic stability on the whole state space. Second, it is demonstrated that a new idea of rendering the derivative strictly negative allows one to detect a margin proving ISS of the SIR model. The accomplishment is based on the pursuit of a Lyapunov function that is not entirely separable into components. It contrasts with previously studied and popular Lyapunov functions that are proven to be incapable of assessing robustness properties such as ISS. Third, two types of feedback control laws are proposed for mass vaccination of immigrants and inhabitants by making use of the strict Lyapunov functions. One type modifies the other type by focusing on the reduction of peaks of the infected population within the ISS guarantees. [ABSTRACT FROM AUTHOR]

This article studies the prescribed performance fault-tolerant control problem for a class of uncertain nonlinear multi-input and multioutput systems. A learning-based fault-tolerant controller is proposed to achieve the asymptotic stability, without requiring a priori knowledge of the system dynamics. To deal with the prescribed performance, a new error transformation function is introduced to convert the constrained error dynamics into an equivalent unconstrained one. Under the actor–critic learning structure, a continuous-time long-term performance index is presented to evaluate the current control behavior. Then, a critic network is used to approximate the designed performance index and provide a reinforcement signal to the action network. Based on the robust integral of the sign of error feedback control method, an action network-based controller is developed. It is shown by the Lyapunov approach that the tracking error can converge to zero asymptotically with the prescribed performance guaranteed. Simulation results are provided to validate the feasibility and effectiveness of the proposed control scheme. [ABSTRACT FROM AUTHOR]

In this article, we investigate the interval consensus for a network of agents with flocking dynamics, i.e., second-order multiagent systems, where each agent imposes an interval constraint on its preferred consensus values, with the aim of driving the agent into a favorable interval. Specifically, we work on two different frameworks of interval constraints, viz., the first one that the node states are constrained in their own constraint intervals and the second one that the node states are constrained in their neighbors’ constraint intervals. For both of the frameworks, we provide a complete solution to the equilibrium seeking problem by resolving a system of nonlinear equations. It is proved that if the underlying graph is strongly connected and the intersection of constraint intervals is empty, then there exists a unique equilibrium point; and if the intersection is nonempty, then there exist multiple equilibrium points, all of which lead to state consensus. We also establish several conditions for the local stability of the unique equilibrium point (corresponding to the case with empty intersection of constraint intervals) or local constraint consensus (corresponding to the case with nonempty intersection of constraint intervals) by invoking Lyapunov’s indirect method. Characterization of the global behavior of such a second-order multiagent system is technically rather challenging at this stage. As a first step toward this end, we show in two special cases that global convergence to the unique equilibrium point or state consensus can be guaranteed by employing Lyapunov stability theory and robust analysis techniques. Finally, some numerical examples are provided to illustrate the theoretical findings. [ABSTRACT FROM AUTHOR]

This article concerns robustness analysis for interconnections of two dynamical systems (described by upper semicontinuous differential inclusions) using a generalized notion of derivatives associated with locally Lipschitz Lyapunov functions obtained from a finite family of differentiable functions. We first provide sufficient conditions for input-to-state stability for differential inclusions, using a class of nonsmooth (but locally Lipschitz) candidate Lyapunov functions and the concept of Lie generalized derivative. In general our conditions are less conservative than the more common Clarke derivative-based conditions. We apply our result to state-dependent switched systems, and to the interconnection of two differential inclusions. As an example, we propose an observer-based controller for certain nonlinear two-mode state-dependent switched systems. [ABSTRACT FROM AUTHOR]

This article focuses on the stability analysis of a formation shape displayed by a team of mobile robots that uses a heterogeneous sensing mechanism. For the setups consisting of three robots, we show that the use of heterogeneous gradient-based control laws can give rise to undesired invariant sets where a distorted formation shape is possibly moving at a constant velocity. We guarantee local asymptotic stability for the correct and desired formation shape. For the setup with one distance and two bearing robots, we identify the conditions such that an incorrect moving formation is locally attractive. [ABSTRACT FROM AUTHOR]

A linear dynamical system is called $k$ -positive if its dynamics maps the set of vectors with up to $k-1$ sign variations to itself. For $k=1$ , this reduces to the important class of positive linear systems. Since stable positive linear time-invariant systems always admit a diagonal quadratic Lyapunov function, i.e., they are diagonally stable, we may expect that this holds also for stable $k$ -positive systems. We show that, in general, this is not the case both in the continuous-time and discrete-time (DT) case. We then focus on DT $k$ -positive linear systems and introduce the new notion of the DT $k$ -diagonal stability. It is shown that this is a necessary condition for the standard DT diagonal stability. We demonstrate an application of this new notion to the analysis of a class of DT nonlinear systems. [ABSTRACT FROM AUTHOR]

The problem of finite-time adaptive tracking control against event-trigger error is investigated in this article for a type of uncertain nonlinear systems. By fusing the techniques of command filter backstepping technical and event-triggered control (ETC), an adaptive event-triggered design method is proposed to construct the controller, under which the effect of event-triggered error can be compensated completely. Moreover, the proposed controller can increase robustness against uncertainties and event error in the backstepping design framework. In particular, we establish the finite-time convergence condition under which the tracking error asymptotically converges to zero in finite time with the aid of a scaling function. Detailed and rigorous stability proofs are given by making use of the improved finite time stability criterion. Two simulation examples are provided to exhibit the validity of the designed adaptive ETC approach. [ABSTRACT FROM AUTHOR]

In this article, we consider the remote state estimation for nonlinear dynamic systems with known linear dynamics and unknown nonlinear perturbations. The nonlinear dynamic plant is monitored by multiple distributed sensors over a random access wireless network with shared common radio channel. We focus on the communication strategy and remote state estimation algorithm design so as to achieve a remote state estimation stability subject to unknown nonlinearities in plant and various wireless impairments, such as multisensor interference, wireless fading, and additive channel noise. By exploiting the additive properties of the physical wireless channels, we propose a novel information fusion over-the-air mechanism to address the signal collision and interference among the sensors. Utilizing the partial knowledge on the linear dynamics of the plant, we also propose a novel recurrent neural network (RNN)-based remote state estimator aided by a virtual state estimation mean-square-error (MSE) process. We further propose a novel online training algorithm such that the RNN at the remote estimator can effectively learn the unknown plant nonlinearities. Using the Lyapunov drift analysis approach, we establish closed-form sufficient requirements on the communication resources needed to achieve almost sure stability of both state estimation and RNN online training in high signal-to-noise ratio (SNR) regime. As a result, our proposed scheme is asymptomatic optimal for large SNR in the sense that both the plant state and the unknown plant nonlinearities can be perfectly recovered at the remote estimator. The proposed scheme is also compared with various baselines and we show that significant performance gains can be achieved. [ABSTRACT FROM AUTHOR]

This article studies the group coordinated control problem for distributed nonlinear multiagent systems (MASs) with unknown dynamics. Cloud computing systems are employed to divide agents into groups and establish networked distributed multigroup-agent systems (ND-MGASs). To achieve the coordination of all agents and actively compensate for communication network delays, a novel networked model-free adaptive predictive control (NMFAPC) strategy combining networked predictive control theory with model-free adaptive control method is proposed. In the NMFAPC strategy, each nonlinear agent is described as a time-varying data model, which only relies on the system measurement data for adaptive learning. To analyze the system performance, a simultaneous analysis method for stability and consensus of ND-MGASs is presented. Finally, the effectiveness and practicability of the proposed NMFAPC strategy are verified by numerical simulations and experimental examples. The achievement also provides a solution for the coordination of large-scale nonlinear MASs. [ABSTRACT FROM AUTHOR]

This study considers the boundary stabilization for stochastic delayed Cohen–Grossberg neural networks (SDCGNNs) with diffusion terms by the Lyapunov functional method. In the realization of NNs, sometimes time delays and diffusion phenomenon cannot be ignored, so Cohen–Grossberg NNs with time delays and diffusion terms are studied in this article. Moreover, different from the previously distributed control, the boundary control is used to stabilize the system, which can reduce the spatial cost of the controller and is easy to implement. Boundary controllers are presented for system with Neumann boundary and mixed boundary conditions, and criteria are derived such that the controlled system achieves mean-square exponential stabilization. Based on the criterion, the effects of diffusion matrix, coupling strength, coupling matrix, and time delays on exponentially stability are analyzed. In the process of analysis, two difficulties need to be addressed: 1) how to introduce boundary control into system analysis? and 2) how to analyze the influence of system parameters on stability? We deal with these problems by using Poincaré’s inequality and Schur’s complement lemma. Moreover, mean-square exponential synchronization of stochastic delayed Hopfield NNs with diffusion terms, as an application of the theoretical result, is considered under the boundary control. Examples are given to illustrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This paper considers weakly and strongly input-to-state stability (ISS) of a discrete-time time-varying delayed system with synchronous impulses and switches. By employing the uniformly asymptotically stable function and mode-dependent dwell time conditions, ISS criteria are derived using the Krasovskii and Razumikhin techniques. The time differences of the Krasovskii functionals or the Razumikhin functions can be mode-dependent and time-varying, which release constraints of some existing results. As subsequent results, we apply the derived ISS criteria to the multi-agent systems (MASs). Finally, two examples considering the quasi-consensus of MASs are given to verify the established results. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel class of piecewise smooth Lyapunov functions leading to linear-matrix-inequality-based stability/performance analysis and control design for linear systems with saturating inputs. We provide conditions for global properties, and also conditions for local properties and guaranteed estimates of the basin of attraction. The backbone of our result consists in using quadratic forms with constant matrices that are not necessarily sign definite, thereby providing additional degrees of freedom. Using generalized sector conditions involving the dead-zone nonlinearity and its derivative, we formulate convex optimization conditions to verify their positivity in the region of interest. Several numerical examples with connections to existing results illustrate the potential behind our novel construction. [ABSTRACT FROM AUTHOR]

During the analysis and design of a network system, a frequently encountered situation is when the network structure is known but the node dynamics is practically unknown. Thus, structural analysis in which the prior knowledge is mostly about the network structure has received attention in recent years. Motivated by this line of research, this article focuses on a structural design problem called the structural equilibrium control problem, which is used to find a sign pattern in the control input such that any constant input with the sign pattern drives the system to a desirable steady state in a qualitative sense. A solution is presented by reducing it to a design problem of the so-called sign-solvable equation, which is a linear equation whose qualitative solution can be determined from the prior knowledge of the sign pattern of the coefficients. [ABSTRACT FROM AUTHOR]

In this article, we propose a novel technique for the stability analysis of discrete-time switched systems under constrained switching based on the semitensor product (STP) of matrices and vector-representation of logic. We assume that the admissible switching signals are generated by a logic dynamical system, referred to as the logic dynamical generator (LDG) of the admissible switching. We demonstrate that switching with minimum dwell-time and restricted successors represent two special cases of this type, by constructing their respective LDGs. First, we transfer the LDG into algebraic form, based on the vector-representation of logic. Next, we merge the logic state of the LDG and the continuous state of the original switched system using the STP and derive the dynamics of the merged state; a switched system without constraints on switching. The stability of the switched system under constrained switching is equivalent to the stability of the merged system under arbitrary switching. Based on this, sufficient conditions for the asymptotical stability of nonlinear switched systems with analytic subsystems under constrained switching are obtained. Specifically, in the case of all subsystems being linear, necessary and sufficient conditions for asymptotical stability under constrained switching are proposed. [ABSTRACT FROM AUTHOR]

Semilinear discrete-time control systems with periodic coefficients are considered. The problem of uniform global asymptotic stabilization of the zero equilibrium of the closed-loop system by state feedback is studied. It is assumed that the free dynamic system has a Lyapunov stable zero equilibrium. The method for constructing a damping control is extended from time-invariant systems to time varying periodic semilinear discrete-time systems. By using this approach, sufficient conditions for uniform global asymptotic stabilization for those systems are obtained. Moreover, the converse Lyapunov theorem on Lyapunov (nonasymptotic) stability is proved for complex and real linear periodic discrete-time systems. Finally, examples of using the obtained results are presented. [ABSTRACT FROM AUTHOR]

LaSalle’s invariance principle is a commonly used extension of Lyapunov’s second method to study asymptotic stability of nonlinear systems. If the system can be written in polynomial form, the examination can be automated using algebraic geometry and quantifier elimination. This article addresses this automated examination using a method relying on polynomial ideals and applies it on some example systems. In addition, some properties of these special ideals are derived that allow to reduce the computational effort significantly. [ABSTRACT FROM AUTHOR]

In this article, we provide several characterizations of integral input-to-state stability (iISS) of time-delay systems. These characterizations differ in the way the considered Lyapunov–Krasovskii functionals (LKFs) dissipate along the solutions of the system. This dissipation can involve the LKF itself, as in existing iISS characterizations, but can alternatively involve the instantaneous value of the solution’s norm (pointwise dissipation), the supremum norm of the state history (historywise dissipation), or a mix of the two (${\mathcal K}{\mathcal L}$ dissipation). We show that all of them guarantee iISS. By relying on a recent converse result by Y. Lin and Y. Wang, we show that most of them are also necessary for iISS. These relaxed dissipation rates simplify the iISS analysis of time-delay systems and contribute to uniforming iISS theory with that of input-free systems. Proofs rely on several results for time-delay systems that may be of interest on their own, including a novel characterization of global asymptotic stability and the fact that iISS is equivalent to global asymptotic stability of the input-free system plus a uniform bounded energy-bounded state property. [ABSTRACT FROM AUTHOR]

This article aims to reveal an interesting phenomenon about the time delays (TDs) in control systems: stability preservation with over large intermittently or unbounded variable TDs. That is, given a system asymptotically stable for bounded TDs, it could remain to be stable when the TDs are enhanced to have peak values over large intermittently or unbounded. The investigation is carried out by theoretical analysis plus case studies with the stochastic system models. The stability of systems is the core issue; the explicit involvement of the TDs in the stability criteria is the premise for them being concerned. To these ends, a series of lemmas are established preliminarily, a new type stability theorem with its practical version is established in succession, and a stability criterion with the TDs as explicit parameters is induced. The Lyapunov function method is applied for less restriction and conservativeness. The mechanism and the approach for the emergence of the phenomenon under probe are analyzed. Implementation is considered for the linear system model. Typical variable TDs are constructed for illustrations theoretically. Finally, the obtained results are verified with numerical experiments. [ABSTRACT FROM AUTHOR]

This article is concerned with an issue of fixed time adaptive neural control for a class of uncertain nonlinear systems subject to hysteresis input and immeasurable states. The state observer and neural networks (NNs) are used to estimate the immeasurable states and approximate the unknown nonlinearities, respectively. On this foundation, an adaptive fixed time neural control strategy is developed. Technically, this control strategy is based on a novel fixed-time stability criterion. Different from the research on fixed-time control in the conventional literature, this article designs a new controller with two fractional exponential powers. In the light of the established stability criterion, the fixed-time stability of the systems is guaranteed under the proposed control scheme. Finally, a simulation study is carried out to test the performance of the developed control strategy. [ABSTRACT FROM AUTHOR]