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Uncrewed aircraft systems and advanced air mobility are associated with uncertain conditions, such as wind prediction errors, and they may deviate from dedicated airspaces referred to as corridors. However, further studies on these aspects are required. This study focuses on the covariance control for a stochastic discrete-time linear system under correlated uncertainties. A covariance control problem with chance constraints can be formulated as a convex-programming problem. Numerical simulations of uncrewed aircraft systems path planning can be used to compare two control laws: covariance control laws that consider correlated and noncorrelated noise. Numerical simulations were conducted to verify that the covariance control law considering correlated noise generates a trajectory that appropriately satisfies the constraints. Consequently, the effect of considering correlated noise in the covariance control law was clarified. In addition, covariance control has been demonstrated to generate appropriate trajectories for various state constraints. Moreover, numerical simulations indicated that covariance control facilitated the control of uncertainty, and the effectiveness of the covariance control was evaluated. The insights gained from the results of this study can inform enhanced uncertainty management for improving reliability and safety in real-world applications of uncrewed aircraft systems and advanced air mobility. [ABSTRACT FROM AUTHOR]

Discrete-time chaotic systems exhibit nonlinear and unpredictable dynamic behavior, making them very difficult to classify. They have dynamic properties such as the stability of equilibrium points, symmetric behaviors, and a transition to chaos. This study aims to classify the time series images of discrete-time chaotic systems by integrating deep learning methods and classification algorithms. The most important innovation of this study is the use of a unique dataset created using the time series of discrete-time chaotic systems. In this context, a large and unique dataset representing various dynamic behaviors was created for nine discrete-time chaotic systems using different initial conditions, control parameters, and iteration numbers. The dataset was based on existing chaotic system solutions in the literature, but the classification of the images representing the different dynamic structures of these systems was much more complex than ordinary image datasets due to their nonlinear and unpredictable nature. Although there are studies in the literature on the classification of continuous-time chaotic systems, no studies have been found on the classification of discrete-time chaotic systems. The obtained time series images were classified with deep learning models such as DenseNet121, VGG16, VGG19, InceptionV3, MobileNetV2, and Xception. In addition, these models were integrated with classification algorithms such as XGBOOST, k-NN, SVM, and RF, providing a methodological innovation. As the best result, a 95.76% accuracy rate was obtained with the DenseNet121 model and XGBOOST algorithm. This study takes the use of deep learning methods with the graphical representations of chaotic time series to an advanced level and provides a powerful tool for the classification of these systems. In this respect, classifying the dynamic structures of chaotic systems offers an important innovation in adapting deep learning models to complex datasets. The findings are thought to provide new perspectives for future research and further advance deep learning and chaotic system studies. [ABSTRACT FROM AUTHOR]

The dynamics of discrete-time two-species systems may not be simple even if they have no positive fixed points. To reveal the behaviour of such systems, we focus on a special class of discrete-time two-species systems whose degenerate cases have a line segment of positive fixed points. As a main result, we show that the line segment of positive fixed points persists as an invariant curve under a small perturbation of the degenerate case. The absence of a positive fixed point ensures that such an invariant curve consists of heteroclinic orbits connecting two axial fixed points. The general result is applied to a discrete-time competition model of Ricker type with reproductive delay. The application reveals the existence of heteroclinic orbits connecting two axial 2-cycles, not only heteroclinic orbits connecting two axial fixed points. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of transforming a single-input single-output discrete-time system into the extended observer form which comprises a linear observable component and a nonlinear injection term depending on the input, output and their forward shifts up to a finite order. The necessary and sufficient conditions for the existence of the extended observer form are provided in terms of vector fields. The algorithm is presented to find a parametrised state transformation necessary to transform the system into the extended observer form. The obtained results are applicable also in case of non-reversible systems. [ABSTRACT FROM AUTHOR]

In this paper, a class of linear discrete-time systems with input saturation is studied in a data-driven framework. Firstly, the input-state data are collected to represent the open-loop and closed-loop systems. While the open-loop data-based representation is a result that is parallel to system identification, the closed-loop representation bypasses the system identification and can be used for direct data-driven control law synthesis. Then, by a novel Lyapunov technique, sufficient conditions for system stability are derived, such conditions are independent of system matrices. Moreover, the attraction domain is estimated using two classes of shape reference sets. Finally, two examples are used to test the correctness of the data-driven control laws. [ABSTRACT FROM AUTHOR]

We study the structure at infinity of transfer matrices with time-varying coefficients. Such transfer matrices have their entries in a skew field F of rational fractions, i.e. of quotients of skew polynomials. Any skew rational fraction is the quotient of two proper ones, the latter forming a ring F p r (a subring of F) on which a "valuation at infinity" is defined. A transfer matrix G has both a "generalized degree" and a valuation at infinity, the sum of which is the opposite of the "defect" of G. The latter was first defined by Forney in the time-invariant case to be the difference between the total number of poles and the total number of zeros of G (poles and zeros at infinity included and multiplicities accounted for). In our framework, which covers both continuous- and discrete-time systems, the classic relation between the defect and Forney's left- and right-minimal indices is extended to the time-varying case. The exact model-matching problem is also completely solved. These results are illustrated through an example belonging to the area of power systems. [ABSTRACT FROM AUTHOR]

This paper deals with the issue of performanceguaranteed control for discrete-time systems under communication constraints. To alleviate communication burdens, an event-triggered mechanism and quantized data-based protocol is presented. The protocol integrates the advantages of the dualthreshold event-triggered mechanism and signal quantization, leading to a reduced channel occupancy rate compared to the normal weighted try-once-discard protocol and dual-threshold event-triggered protocol. Building upon this protocol, a state feedback controller relying on scheduling signals is proposed. A criterion on stability and energy-to-peak performance is established using the Lyapunov function method and some inequality approaches. Then, a numerically tractable method for determining the desired controller gain via solving linear matrix inequalities. Finally, a double-sided linear switched reluctance machine system is used as an example to illustrate the effectiveness of the designed protocol and the controller. [ABSTRACT FROM AUTHOR]

This paper addresses the control of a nonlinear system affected by deadzone effects, using a constrained actuator. The system itself incorporates a second-order oscillatory dynamic actuator, with an unknown nonlinear input-output relationship. The proposed algorithm not only accommodates the deadzone constraints on control inputs but also considers the actuator's saturation limits in control input calculations. It introduces a trajectory tracking mechanism that, instead of directly following the primary trajectory, adheres to an alternative trajectory capable of stable tracking, gradually converging to the main trajectory while accounting for operational constraints. In practical control systems, the actuator's input-output relationship is often nonlinear and unknown, requiring inversion for model-based control. This paper employs an offline-trained neural network trained on synthetic data to identify and approximate the actuator's behavior. To optimize the control system's performance and ensure stability during sudden error changes, the control input operates in two modes: position and velocity control. This dual-mode control allows for continuous switching between the two, facilitated by an innovative optimization technique based on the gradient descent method with a variable step size. Simulation results validate the effectiveness of the proposed algorithm in controlling systems constrained by hard limits and featuring nonlinear oscillatory actuators, providing a valuable contribution to the field of control systems. • Developing a dual mode non-predictive control algorithm based on discrete-time system equations. • Utilizing an offline-trained neural network for estimating the inverse of the nonlinear actuator relationship. • Stable desired trajectory mapping based on inherent and actuation constraints while maintaining asymptotic stability. • Substituting the trajectory within a fixed range outside of the constant deadzone and inside the variable saturation. • Optimized balancing position and velocity control modes through a weighted average of two control forces. [ABSTRACT FROM AUTHOR]

This paper is entirely devoted to analyzing robust control of sampled-data systems. For that, conditions for robust stability under static and dynamic norm-bounded uncertainty are presented and are all expressed through differential linear matrix inequality, a useful mathematical tool able to keep convex all problems to be dealt with. A suitable version of the celebrated small gain theorem (SGT) is then presented and proved in the context of sampled-data systems with inputs and outputs defined in both, continuous- and discrete-time domains. Some academic examples are solved to illustrate the theory and to put in evidence the computational burden needed to calculate their solutions. Since the SGT is only sufficient, the examples are used to discuss and evaluate its conservatism. [ABSTRACT FROM AUTHOR]

In the past few decades, there has been a significant focus on computational methods for periodic systems. In some of these works, various considerations were outlined to establish and categorize algorithms for designing periodic discrete‐time state‐space systems. In a recent work, a direct algorithm was proposed to obtain low‐dimensional realizations from a proper lifted system in state‐space form. This algorithm, which lies in a category often called "fast" algorithms, takes advantage on the structure of lifted representations being highly efficient. In a 1993 work by Ching‐An Lin and Chwan‐Wen King, another direct algorithm was proposed that appears to be quite similar to the algorithm outlined recently. These two algorithms generate state‐space periodic realizations that are both uniform, meaning that the dimension of the state remains constant at each time instant. The algorithms proposed in these two works require both a rank test applied to two different types of matrices, Kℓ$$ {K}_{\ell } $$ and ℓM$$ {}^{\ell }M $$, respectively (in chronologic order). Although the former algorithm establishes an upper bound for the state dimension à priori, by determining the maximum rank of the matrices Kℓ$$ {K}_{\ell } $$, the latter obtains an upper bound à posteriori, based on the rank of matrices ℓM$$ {}^{\ell }M $$. In this work, we proved that these matrices Kℓ$$ {K}_{\ell } $$ and ℓM$$ {}^{\ell }M $$ have the same rank for all ℓ$$ \ell $$, and we use this information to revise the latter algorithm and assess whether it represents an improvement. The algorithm presented as well its modified versions that were coded using the Python programming language. Surprisingly, the revised algorithm did not demonstrate any significant improvement in terms of computational efficiency. [ABSTRACT FROM AUTHOR]

This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model. [ABSTRACT FROM AUTHOR]

Variable structure control systems are known to provide a high level of robustness to external disturbances and modeling uncertainties with comparably low computational complexity. Thanks to these features, they have found applications in various fields, such as power engineering, electronics, robotics, and aviation. In recent decades, the field of sliding mode control has developed significantly. Therefore, this study aims to discuss the basic concepts and design methodology of such strategies. Although in the 20th century, continuous-time sliding mode control has been the center of the control engineering society's attention, it has certain major shortcomings. In particular, such control schemes result in undesirable high-frequency oscillations when applied digitally. Therefore, the more recent discrete-time approach to sliding mode control has gained recognition in the 21st century. Since the introduction of discrete-time sliding mode control strategies, the reaching law-based controller design method has been designed, within which two main paradigms may be named: the switching type and the nonswitching type quasi-sliding mode. This paper presents a broad review of the discrete-time sliding mode control strategies, starting from the definition of sliding mode through the controller design procedures and up to potential applications. The aim of this study is to provide an up-to-date state of the art and introduce readers to the newest trends and achievements in the field of sliding mode control. [ABSTRACT FROM AUTHOR]

We consider a general impulsive reaction-diffusion equation with shifting environment and birth pulse, both induced by climate changes, to capture essential features of the dynamics of species exhibiting distinct stages of reproduction and dispersal. We convert this model into a discrete-time semiflow, and hence to a discrete-time recursion system. We establish the existence of forced waves and asymptotic spreading properties of solutions, and obtain sufficient conditions for the global asymptotic stability of the forced waves. [ABSTRACT FROM AUTHOR]

Port-Hamiltonian (pH) systems have been studied extensively for linear continuous-time dynamical systems. This manuscript presents a discrete-time pH descriptor formulation for linear, completely causal, scattering passive dynamical systems based on the system coefficients. The relation of this formulation to positive and bounded real systems and the characterization via positive semidefinite solutions of Kalman–Yakubovich–Popov inequalities is also studied. [ABSTRACT FROM AUTHOR]

Parameter estimation is important in data-driven fractional chaotic systems. Less work has been reported due to challenges in discretization of fractional calculus operators. In this paper, several numerical schemes are newly derived for delay fractional difference equations of Caputo and Riemann–Liouville types. Then, loss functions are constructed and unknown parameters of the discrete fractional chaotic system are estimated by a neural network method. Parameter estimation results demonstrate high accuracy compared with real values. Robust analysis is provided under different noise levels. It can be concluded that this paper provides an efficient deep learning method based on fractional discrete-time systems. [ABSTRACT FROM AUTHOR]

Incorporating a weak Allee effect in a two-dimensional biological model in ℜ 2 , the study delves into the application of bifurcation theory, including center manifold and Ljapunov–Schmidt reduction, normal form theory, and universal unfolding, to analyze nonlinear stability issues across various engineering domains. The focus lies on the qualitative dynamics of a discrete-time system describing the interaction between prey and predator. Unlike its continuous counterpart, the discrete-time model exhibits heightened chaotic behavior. By exploring a biological Mmdel with linear functional prey response, the research elucidates the local asymptotic properties of equilibria. Additionally, employing bifurcation theory and the center manifold theorem, the analysis reveals that, for all α 1 (i.e., intrinsic growth rate of prey), ð 1 ˙ (i.e., parameter that scales the terms y n), and m (i.e., Allee effect constant), the model exhibits boundary fixed points A 1 and A 2 , along with the unique positive fixed point A ∗ , given that the all parameters are positive. Additionally, stability theory is employed to explore the local dynamic characteristics, along with topological classifications, for the fixed points A 1 , A 2 , and A ∗ , considering the impact of the weak Allee effect on prey dynamics. A flip bifurcation is identified for the boundary fixed point A 2 , and a Neimark–Sacker bifurcation is observed in a small parameter neighborhood around the unique positive fixed point A ∗ = (m ð 1 ˙ − 1 , α 1 − 1 − α 1 m ð 1 ˙ − 1). Furthermore, it implements two chaos control strategies, namely, state feedback and a hybrid approach. The effectiveness of these methods is demonstrated through numerical simulations, providing concrete illustrations of the theoretical findings. The model incorporates essential elements of population dynamics, considering interactions such as predation, competition, and environmental factors, along with a weak Allee effect influencing the prey population. [ABSTRACT FROM AUTHOR]

Why do we remember the past, and plan the future? We introduce a toy model in which to investigate emergent time asymmetries: the causal multibaker maps. These are reversible discrete-time dynamical systems with configurable causal interactions. Imposing a suitable initial condition or "Past Hypothesis", and then coarse-graining, yields a Pearlean locally causal structure. While it is more common to speculate that the other arrows of time arise from the thermodynamic arrow, our model instead takes the causal arrow as fundamental. From it, we obtain the thermodynamic and epistemic arrows of time. The epistemic arrow concerns records, which we define to be systems that encode the state of another system at another time, regardless of the latter system's dynamics. Such records exist of the past, but not of the future. We close with informal discussions of the evolutionary and agential arrows of time, and their relevance to decision theory. [ABSTRACT FROM AUTHOR]

In this paper, we present conditions for the existence and uniqueness of chain control sets of discrete-time linear systems on the affine two-dimensional Lie group. More specifically, we prove that these chain control sets are given by the union of an infinite number of control sets with empty interiors. [ABSTRACT FROM AUTHOR]

The ongoing transmission of mpox in specific countries and regions necessitates urgent action. It is essential to implement targeted containment strategies that concentrate on high-risk populations and critical locations, such as college campuses, to effectively curb the spread of mpox. This study is dedicated to evaluating the performance of various vaccination and quarantine strategies in curbing the spread of mpox and estimating the outbreak risk. To accomplish this, we constructed a stochastic, agent-based, discrete-time susceptible-latent-infectious-recovered (SLIR) model, to examine mpox transmission on a simulated college campus. Our findings reveal that relying solely on PEP is insufficient in containing mpox effectively. To bolster the population immunity and protect the vulnerable, pre-exposure vaccination among high-risk populations prior to an outbreak is imperative. Our study demonstrates that a pre-exposure vaccination rate of 50% in highrisk populations can led to a remarkable 74.2% reduction of infections. This translated to a mere 1.0% cumulative infection incidence in the overall population. In cases where the desired vaccination coverage is not attainable, enhancing case detection and isolation measures can serve as an effective emergency response to contain mpox outbreaks. For pre-exposure vaccination coverage of 20% or lower, a 40% isolation ratio is necessary to keep the cumulative number of infections in check. However, when the coverage exceeds 30%, a reduced isolation ratio of 20% becomes sufficient to manage the outbreak effectively. These insights underscore the importance of strategic pre-exposure vaccination in conjunction with robust surveillance and isolation protocols to safeguard public health and prevent the escalation of mpox outbreaks. [ABSTRACT FROM AUTHOR]

This paper examines the event-triggered filtering problem related to discrete-time nonlinear systems that are described by interval type-2 (IT2) fuzzy models. The filter being studied is prone to a non-stationary Markovian process when both quantization output and deception attack are taken into account simultaneously. It is proposed to implement an asynchronous IT2 fuzzy filter characterized by two different piecewise-stationary Markov chains specifying the deception attacks and the modes of the system. A new event-triggering protocol (ETP) is investigated as a means of reducing unnecessary signal transmissions on the communication channel. Based on the linear matrix inequality analysis and using the information on upper and lower membership functions, it is demonstrated that stochastic sufficient conditions exist for the desired filter such that it exhibits mean square stability and achieves the prescribed mixed H ∞ and passivity performance index. Moreover, an optimization-based problem for computing filter gains is proposed. An experimental numerical illustration based on a truck-trailer system is used to validate the developed scheme. [ABSTRACT FROM AUTHOR]

In this paper, the problem of direct data-driven control is studied for a class of discrete-time switched systems with input saturation. For unknown switched systems, a data-driven approach is adopted to parameterize the controller directly from the input-state data of the system, which does not depend on the exact mathematical model. In addition, the input saturation problem is addressed by using the polyhedral convex hull method, and the data representation is given for the closed-loop system. By using Lyapunov theory and dwell time method, the exponential stability conditions of linear matrix inequalities (LMIs) form are obtained, and the desired attractive domain is estimated. Moreover, considering the data polluted by process noise, a robust data-driven state feedback controller is designed and the performance of $ \mathcal{L}_{2} $ gain is guaranteed. Finally, the advantage of the proposed data-driven based control method is verified by two numerical examples. [ABSTRACT FROM AUTHOR]

In this manuscript, it is investigated that the stability property of a discrete-time switched system consisting of all unstable subsystems. Under a switching signal with certain conditions, the sufficient constraints for asymptotic stability of a discrete-time switched system composed of all unstable subsystems are obtained via Lyapunov functions and the defined divergence time. Furthermore, based on this result, linear matrix inequalities are obtained for asymptotic stability of a linear discrete-time switched system composed of all unstable subsystems. The efficiency of the acquired theorems is exhibited by three numerical examples. [ABSTRACT FROM AUTHOR]

This paper focuses on the containment control problem for a class of nonlinear multi-agent systems (MASs) with sampled-data. To enhance the efficiency of utilizing communication resources, a new distributed sampled-data-based event-triggered transmission strategy is proposed. This event-driven strategy requires that event detector works only at periodic sampling instants. By employing the techniques such as input delay method, inequality technique and the Lyapunov stability theory, sufficient criteria are derived to ensure that each follower converges to the convex hull spanned by the leaders. A convex optimization method is employed to search for the desired controller gain by maximizing the maximum-allowable bound of sampling intervals. Additionally, for some special scenarios, to reduce computational complexity, the matrix decoupling technique is utilized to reduce the dimension of matrix inequalities, thereby facilitating application to large-scale MASs. Finally, the effectiveness of the proposed theory is verified by a simulation example. [ABSTRACT FROM AUTHOR]

This paper is concerned with the bumpless transfer sliding mode control problem for discrete-time switched systems under average dwell-time (ADT) switching signals. In order to deal with the external disturbances and suppress the control input bumps, a sliding mode controller is synthesized with the combination of the bumpless transfer technique. Particularly, by introducing a reference input signal, a novel bumpless transfer constraint is imposed for the switched systems driven by the sliding mode control, and sufficient conditions are presented to ensure the stability as well as the bumpless transfer performance of the resultant sliding mode dynamics with the help of the ADT method and the Lyapunov function technique. Finally, the feasibility and effectiveness of the proposed results are demonstrated by two examples, including an application of an aero-engine control system. [ABSTRACT FROM AUTHOR]

This article proposes a novel robust invariance condition for uncertain linear discrete-time systems with state and control constraints, utilizing a method of semidefinite programming duality. The approach involves approximating the robust invariant set for these systems by tackling the dual problem associated with semidefinite programming. Central to this method is the formulation of a dual programming through the application of adjoint mapping. From the standpoint of semidefinite programming dual optimization, the paper presents a novel linear matrix inequality (LMI) conditions pertinent to robust positive invariance. Illustrative examples are incorporated to elucidate the findings. [ABSTRACT FROM AUTHOR]

In this paper, we study the balance control for the rotary inverted pendulum system with two joints both subject to uncertainty. To facilitate the experiment, we apply a classical energy-based swing-up control, eschewing compensation for the uncertainty. In balance control, we employ a novel approach in the form of a modified signal compensation-based balance control, which models the uncertainty as its previously sampled term and its variation. The signal compensation-based balance control involves three steps. First, for the linearized discrete-time state-space model around the upright equilibrium point, we design the main control signal by using the pole-placement technique. Second, we estimate the discrete-time model of the system by using the least squares identification method, thereby unveiling key points in the identification procedure. The discrete-time model presents the uncertainty as a previously sampled term and its variation. Third, we design two discrete-time compensation signals for the previously sampled term and the variation. By combining the main control signal and the two compensation signals, we formulate the balance control law. We further optimize the signal compensation-based balance control by adding an extra parameter, successfully circumventing the critical stability problem, and analyze the performance of the closed-loop system. Numerical simulation and comparative experiments demonstrate its effectiveness and strong robustness against the uncertainty in frictions and modeling errors of the system. [ABSTRACT FROM AUTHOR]

This paper investigates the sliding mode control (SMC) problem of discrete-time singular Markovian jump systems with time-varying delay under an event-triggered strategy (ETS). In the system we study, there are uncertainties in the system matrix, especially in the difference matrix. A state augmentation strategy is proposed due to uncertainties in the difference matrix. A suitable sliding mode surface (SMS) function is built, and the corresponding sliding mode dynamics (SMD) is derived based on ETS. Some sufficient conditions are presented to guarantee that SMD is H ∞ -admissible for all uncertainties. Furthermore, an SMC law under ETS is derived so that the system trajectories can be driven onto the prescribed SMS in finite time. Finally, the effectiveness of the approach in the paper is demonstrated by two simulated examples. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new passivity‐based controller design technique for discrete‐time fully actuated systems. The controller establishes finite‐time and fixed‐time convergence of dynamical system trajectories to an equilibrium state. A new form of a dissipation function, selected a priori, is introduced to design a feedback control rule to achieve such convergence properties. An energy shaping and damping injection methodology is extended to achieve non‐asymptotic stabilization. A numerical example to validate the proposed methods is provided. [ABSTRACT FROM AUTHOR]

This article presents two novel mixed‐uncertainty state estimators for discrete‐time descriptor linear systems, namely linear time‐varying mixed‐uncertainty filter (LTVMF) and linear time‐invariant mixed‐uncertainty filter (LTIMF). The former is based on the minimum‐variance approach, from which quadratic and explicit (special case of quadratic) formulations are derived and addressed to LTV systems. Both formulations incorporate the knowledge of state linear constraints, such as equality (in the descriptor form) and inequality, to mitigate precision and accuracy issues related to initialization and evolution of the state estimates. The LTIMF algorithm is based on the mixed H2/H∞$$ {H}_2/{H}_{\infty } $$ criterion and addressed to LTI systems, with the low‐cost computation being its motivation. Both LTVMF and LTIMF algorithms solve state‐estimation problems in which the uncertainties are combined to yield the so‐called mixed‐uncertainty vector, which is composed by set‐bounded uncertainties, characterized by constrained zonotopes, and stochastic uncertainties, characterized by Gaussian random vectors. As mixed‐uncertainty vectors imply biobjective optimization problems, we innovatively present multiobjective arguments to justify the choice of the solution on the Pareto‐optimal front. In order to discuss the advantages and drawbacks, the state estimators are tested in two numerical examples. [ABSTRACT FROM AUTHOR]

This article deals with the stability and H∞$$ {H}_{\infty } $$ control synthesis for a class of linear sampled‐data systems. First, a novel integral inequality with the cubic term of integral interval length instead of reciprocal one of integral interval length is constructed by non‐orthogonal polynomials. This can make full use of slack matrix variables and additional information about sawtooth structural sampling pattern. Then, on the basis of the constructed integral inequality, a cubic‐term‐dependent discontinuous exponent Lyapunov–Krasovskii Functional (LKF) is developed containing additional information about system states to design an H∞$$ {H}_{\infty } $$ sampled‐data state feedback controller. To better estimate the upper bound of the derivative of LKF, a kind of multiple convex function approximation approach is developed, which can be used to deal with the two‐variable polynomial negative definite issue by dividing the variable interval into multiple subintervals. By the constructed integral inequality and multiple convex function approximation approach, sufficient conditions with less conservatism are deduced for the feasibility of H∞$$ {H}_{\infty } $$ sampled‐data state feedback controller. Moreover, by the inner convex approximation solution technique and proposed iterative algorithm, the bilinear matrix inequalities can be transformed into linear matrix ones, which can be easily tackled, to obtain the desired sampled‐data controller gain. Finally, by comparing with existing results, the advantages and superiority of our proposed approaches can be confirmed via two numerical examples. [ABSTRACT FROM AUTHOR]

Summary: This article addresses the challenge of estimating the state of a discrete‐time stochastic multiplicative system with zonotopic set‐membership and stochastic uncertainties. The stochastic system model incorporates additive and multiplicative Gaussian and zonotopic set‐membership uncertainties, posing challenges in accurately managing these sources of uncertainty. In practical scenarios with limited communication resources, it is crucial to reduce communication overhead, save resources, and prevent unnecessary information transmission. To achieve these objectives, this article proposes an event‐triggered mechanism and a corresponding state estimator. The optimal gain matrix of the state estimator is derived to minimize the estimation uncertainty represented by the size of zonotope and Gaussian confidence ellipsoid regions. Conditions are established to guarantee the mean square stability of the estimation error, ensuring reliable estimation performance. The configuration of the triggering condition parameters, which play a vital role in determining the event‐triggered updates, is presented. is presented. The effectiveness of the proposed event‐triggered mechanism and the corresponding estimator is demonstrated through simulation results and analyses, using specific metrics and evaluation criteria. [ABSTRACT FROM AUTHOR]

This article focuses on the finite‐time mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passive filtering problem for discrete‐time singular systems with randomly occurring nonlinear perturbations. The main purpose is to design a filter, which ensures the singular error system is stochastically finite‐time bounded and satisfies mixed ℋ∞$$ {\mathscr{H}}_{\infty } $$ and passive performance. By constructing an augmented matrix, the properties of matrix determinant and rank are used to prove that the singular system is regular and causal, Finsler's lemma and Projection lemma are used in the design process to acquire additional slack variable matrices, thereby enhancing the solution space with extra degrees of freedom. Then, the unknown parameters of the filter are obtained by solving the less conservative linear matrix inequalities. Finally, the feasibility of the proposed method is verified through a common numerical example and by controlling a DC motor for an inverted pendulum. [ABSTRACT FROM AUTHOR]

The looped-functional approach has been extensively used for stability analysis of sampled-data systems. For this approach, this paper introduces two new functionals to minimise the conservatism of stability conditions. The first one is called a non-negative integral functional (NIF) that is added to the derivative of a common Lyapunov functional. The second one is a general looped-functional (GLF), whose values at sampling instants are traditionally not well-defined, and are defined here in terms of their limits. Leveraging further affine canonical Bessel-Legendre inequalities expressed by simplified polynomials, a polynomial-based NIF, a polynomial-based GLF, and a polynomial-based zero equality are tailored for obtaining hierarchical types of stability conditions in the form of linear matrix inequalities. Finally, numerical examples show that: (i) the proposed functionals lead to less conservatism when compared with several state-of-the-art methods; and, (ii) the resulting stability conditions exhibit a hierarchical characteristic in the sense that the higher level of hierarchy, the less conservatism of the criteria. [ABSTRACT FROM AUTHOR]

This paper presents a new method for regional stabilization of discrete-time nonlinear systems by static output feedback based on polynomial Lyapunov functions. The considered class of nonlinear systems subject to time-varying parameters can be described by difference-algebraic representation and an equivalent polytopic model is obtained, making it possible to apply Lyapunov theory and linear matrix inequality-based tool. In this sense, a convex optimization problem in terms of LMI is provided to guarantee the closed-loop system's robust stabilization and to enlarge the estimated domain of attraction (DoA). The proposed control design is a one-step approach that can be applied to systems with nonlinear output matrices. It requires no iterative algorithms or congruence transformation, and auxiliary decision variables are introduced only aiming at less conservative results. Besides that, the use of polynomial Lyapunov functions allows us to obtain asymmetric and non-convex estimated DoA, reducing the conservativeness. Numerical examples are provided to illustrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper investigates the consensus problem for discrete-time leader-following multi-agent systems subject to large time delays. Building upon two assumptions, a novel fully distributed protocol is devised by utilizing a normalized weighting matrix, depending solely on the relative output measurement. It is shown that, for arbitrarily large yet bounded input and communication delays that are constant and exactly known, the consensus problem can be effectively addressed by both the proposed protocol and its truncated version. Assuming further that followers incorporate solely input delays, then the permitted delays can be time-varying and different. The proposed protocols do not rely on global information of the directed communication topology, thus ensuring robustness against alterations in the communication topology. A numerical example is employed to validate the effectiveness of the suggested approach. • A new fully distributed protocol suitable for discrete-time setting is designed. • The MASs are influenced by large time-varying input and communication delays. • The proposed consensus protocol employs relative output measurements. • The protocol is robust to changes in communication structure. [ABSTRACT FROM AUTHOR]

The dynamics of plant-herbivore interactions are essential for understanding ecosystem stability and resilience. This article investigated the effects of incorporating a harvesting effect on the dynamics of a discrete-time plant-herbivore system. An analysis was performed to determine the existence and stability of fixed points. In addition, studies have shown that the system experienced transcritical, period-doubling, and Neimark-Sacker bifurcations. Moreover, we provided numerical simulations to substantiate our theoretical results. Our research indicated that harvesting in excessive amounts may have negative effects on the populations of both plants and herbivores. However, when harvesting was done at moderate levels, it promoted the coexistence and stability of both populations. The findings of our analysis provided a deep understanding of the intricate dynamics of ecological systems and underscored the need to use sustainable harvesting methods for the management and preservation of ecosystems. [ABSTRACT FROM AUTHOR]

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The article examines the topic of extended dissipative filtering design for a class of discrete-time interval type 2 fuzzy switching systems (IT2FSS). The asymptotic stability problem of IT2FSS is handled by employing an average dwell time (ADT) technique that dwells between the subsystems. The IT2FSS under discussion is represented with a time-varying delay, which enables a more precise depiction of nonlinear dynamical systems than conventional state space representation. In comparison to earlier findings, a set of piecewise Lyapunov-Krasovskii functional (LKF) candidates are provided, which are fuzzy and delay-dependent functional. The Lyapunov stability theory-based suitable criterion is derived by the LKF candidates for the stability and performance evaluations of the filtering error system. Extended dissipative filtering is a technique which employs an extended performance index to analyse H ∞ , L 2 - L ∞ , passive, and (Q , S , R) - γ dissipative filtering in a single structure. As a special case, the criteria for constant delay are also discussed. Two real-world numerical examples for both time-varying delay and constant delay demonstrate the applicability and reliability of the known theoretical findings. [ABSTRACT FROM AUTHOR]

The paper discusses the inventory management problem with a single product stored in two warehouses, where each has its unique suppliers with certain lead times. Moreover, one of the warehouses may act as a backup supplier for the other. In other words, product exchange between two different warehouses within one company is allowed. The first warehouse operates under an a priori known time-variant contractual demand and a bounded random one. Its secondary goal is to accumulate emergency stock that can be delivered to the second warehouse within one time period. For this warehouse we use a desired trajectory generator to shape the required stock level and then utilize a trajectory following control law. The demand in the second warehouse is unknown but bounded, and its suppliers have limited delivery capacity. The challenge is to fulfill the customers’ needs, although they might exceed the order limit. Therefore, occasional backup supplies from the first warehouse are necessary. For the control of the second warehouse, a simple sliding mode (SM) scheme is applied. The paper proves that, with appropriate compensation of the emergency deliveries in the first warehouse, our proposed control scheme ensures full demand satisfaction in both warehouses despite the second one’s control limit.

Bounding the price of anarchy, which quantifies the damage to social welfare due to selfish behavior of the participants, has been an important area of research in algorithmic game theory. Classical work on such bounds in repeated games makes the strong assumption that the subsequent rounds of the repeated games are independent beyond any influence on play from past history. This work studies such bounds in environments that themselves change due to the actions of the agents. Concretely, we consider this problem in discrete-time queuing systems, where competitive queues try to get their packets served. In this model, a queue gets to send a packet at each step to one of the servers, which will attempt to serve the oldest arriving packet, and unprocessed packets are returned to each queue. We model this as a repeated game where queues compete for the capacity of the servers, but where the state of the game evolves as the length of each queue varies. We analyze this queuing system from multiple perspectives. As a baseline measure, we first establish precise conditions on the queuing arrival rates and service capacities that ensure all packets clear efficiently under centralized coordination. We then show that if queues strategically choose servers according to independent and stationary distributions, the system remains stable provided it would be stable under coordination with arrival rates scaled up by a factor of just e/ e−1. Finally, we extend these results to no-regret learning dynamics: if queues use learning algorithms satisfying the no-regret property to choose servers, then the requisite factor increases to 2, and both of these bounds are tight. Both of these results require new probabilistic techniques compared to the classical price of anarchy literature and show that in such settings, no-regret learning can exhibit efficiency loss due to myopia. [ABSTRACT FROM AUTHOR]

This paper deals with the discrete-time antiwindup compensator (AWC) synthesis for nonlinear discrete-time systems under input saturation. The proposed method considers the objective of an optimal AWC design for fast convergence and for improved performance against the saturation nonlinearity. A discrete-time full-order AWC architecture is presented for nonlinear discrete-time systems to achieve an improved performance against the saturation nonlinearity. Additionally, an equivalent decoupled AWC architecture for nonlinear discrete-time system is derived through algebraic analysis and transformation of saturation to dead-zone function. To achieve fast convergence, a more generic Lyapunov function has been applied for the AWC design by incorporating an exponential term in the Lyapunov function. Then, new conditions for the AWC synthesis are revealed by application of the resultant decoupled discrete-time architecture, nonlinearity condition, a modified quadratic-exponential Lyapunov function, optimally exponential L 2 approach, and input saturation properties. The design conditions are provided for both global and local design scenarios, which can be applied to both stable and unstable plants. Compared with the conventional methods, the proposed approach deals with nonlinear systems, can be more practical due to discrete-time scenario, provides an optimal design for both fast convergence and performance, and applicable to both stable and unstable plants. A simulation example has been provided to demonstrate the efficacy of the proposed nonlinear AWC design. [ABSTRACT FROM AUTHOR]

We describe a procedure for the generation of functional digraphs up to isomorphism; these are digraphs with uniform outdegree 1, also called mapping patterns, finite endofunctions, or finite discrete-time dynamical systems. This procedure is based on a reverse search algorithm for the generation of connected functional digraphs, which is then applied as a subroutine for the generation of arbitrary ones. Both algorithms output solutions with O (n 2) delay and require linear space with respect to the number n of vertices. [ABSTRACT FROM AUTHOR]

In this paper, the problem of data-driven quadratic optimal control is investigated for discrete-time linear systems without the exact knowledge of system dynamics. A value iteration-based algorithm is proposed to obtain the optimal feedback gain. The main idea of the proposed approach is to obtain two sequences for the approximation of the unique positive definite solution of the corresponding algebraic Riccati matrix equation and the optimal feedback gain by using the collected data of the system states and control inputs. The proposed algorithm could be activated by an arbitrary bounded control input and a simple initial value of the Lyapunov matrix. An important feature of this algorithm is that an original stabilising feedback gain is not required. Finally, the effectiveness of the proposed approach is verified by two examples. [ABSTRACT FROM AUTHOR]

In this paper, the energy-to-peak filtering problem for the uncertain discrete-time singular bilinear systems is studied. This paper considers the uncertainties that consist of real systems and the possible data packet dropouts when performance output signals and measurement output signals are transmitted over digital channels. In the course of the study, the phenomenon is elucidated utilising the Bernoulli random binomial distribution. The goal is to design the desired filter, so that the filtering error system is admissible, and meets the specified energy-to-peak performance index. The design conditions of energy-to-peak filters for uncertain discrete-time singular bilinear systems are given by introducing the Lyapunov function and using linear matrix inequalities (LMIs). The impact of uncertainty on singular bilinear systems is addressed using a two-step approach. At last, a numerical illustration is provided to demonstrate the validity of the design. [ABSTRACT FROM AUTHOR]

Since decades mathematicians have been designing the transfer function for the available physical models followed by the involvement of control engineers to work on it. Through the study of the offered representations, many systems were found to be of higher order which are nevertheless not easy to study and analyze in their core form. Furthermore, again uncertainties within the system was found that cannot be ignored. All these increases the complexities for analysis of the physical systems. This demands a technique for order reduction to derive an approximate lower order representation of the higher order systems. In continuation, this paper is an attempt to propose a computationally efficient approach for obtaining the reduced interval model based on Routh Approximation technique. The proposed approach is a novel method for discrete-time interval system and is discussed in detail in the article content ahead. The provided examples offer the desired explanation for the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

This paper proposes a saturation-optimized, quasi-sliding-mode model-free adaptive control (SM-MFAC) method to control the postcollision calming motion of an unstable free-flying space robot with saturated output torque. Initially, the dynamics model of the unstable free-flying space robot is transformed into a class of multiple-input, multiple-output (MIMO) discrete-time nonlinear systems. Here, the system characteristics can be estimated based on measured base attitude and joint angle data. The discrete sliding-mode control helps calculate the desired angular velocity at the current moment. Next, Hildreth's method is used to introduce constraints to the control input criterion function for real-time tracking of the desired angular velocity, which enables the completion of the calming motion control of the free-flying space robot. The proposed algorithm simplifies the traditional calming motion control process by avoiding complex and redundant modeling requirements, ensuring that the control torque remains within predefined limits to optimize possible saturation. It also proves the convergence of the system output theoretically, and good stability and dynamic characteristics of the control scheme are verified through numerical simulations. [ABSTRACT FROM AUTHOR]

This study reports the finite/fixed-time synchronized stability of autonomous discrete-time dynamical systems. The specific objective is to ensure simultaneous convergence of all system states to the equilibrium point and remain there thereafter. The novel Lyapunov and converse Lyapunov theorems are introduced to analyze the finite/fixed-time stability of three distinct discrete-time systems. Additionally, we propose the use of generalized p-norm on finite-dimensional vector spaces, which is based on the function of scaled p-norm that we previously proposed. This can be utilized in dynamical systems to accelerate the convergence rate of the system. Finally, numerical simulations show the effectiveness of finite/fixed-time synchronized stability, and the advantages of utilizing the scaled p-norm in fast convergence. [ABSTRACT FROM AUTHOR]

This paper proposes a distributed model predictive control (DMPC) algorithm for dynamic decoupled discrete‐time nonlinear systems subject to nonlinear (maybe non‐convex) coupled constraints and costs. Solving the resulting nonlinear optimal control problem (OCP) using a DMPC algorithm that is fully distributed, termination‐flexible, and recursively feasible for nonlinear systems with coupled constraints and costs remains an open problem. To address this, we propose a fully distributed and globally convergence‐guaranteed framework called inexact distributed sequential quadratic programming (IDSQP) for solving the OCP at each time step. Specifically, the proposed IDSQP framework has the following advantages: (i) it uses a distributed dual fast gradient approach for solving inner quadratic programming problems, enabling fully distributed execution; (ii) it can handle the adverse effects of inexact (insufficient) calculation of each internal quadratic programming problem caused by early termination of iterations, thereby saving computational time; and (iii) it employs distributed globalization techniques to eliminate the need for an initial guess of the solution. Under reasonable assumptions, the proposed DMPC algorithm ensures the recursive feasibility and stability of the entire closed‐loop system. We conduct simulation experiments on multi‐agent formation control with non‐convex collision avoidance constraints and compare the results against several benchmarks to verify the performance of the proposed DMPC method. [ABSTRACT FROM AUTHOR]

This article is concerned with the optimal sequential fusion filter design issue for a class of sampled‐data systems subject to random transmission delays and multiplicative noise. The considered delay is modeled as a multistate Markov chain, while the multiplicative noise corrupting the observation measurements is assumed be a white noise sequence with known statistical properties. First, by reorganizing the original measurements, the solvability of the addressed problem is cast into the feasibility of an optimal estimation issue for the hybrid Markovian jump system without delays. Then, an optimal sequential fusion filter is constructed by utilizing a dynamic model with finite jumps on basis of the arrival order of measurements from different sensors, guaranteeing estimation performances both at sampling instants and within the sampling intervals. Moreover, the desired estimator gains can be computed via solving a series of coupled differential Riccati equations with jumps and coupled differential Lyapunov equations. Further, a stationary sequential fusion filter is achieved with the guarantee of the exponentially mean‐square stability. Finally, two simulation examples are provided to verify the validity of the proposed algorithms. [ABSTRACT FROM AUTHOR]