Set Of Sufficient Conditions Research Articles

Auslander–Reiten theory in extriangulated categories

The notion of an extriangulated category gives a unification of existing theories in exact or abelian categories and in triangulated categories. In this article, we develop Auslander–Reiten theory for extriangulated categories. This unifies Auslander–Reiten theories developed in exact categories and triangulated categories independently. We give two different sets of sufficient conditions on the extriangulated category so that existence of almost split extensions becomes equivalent to that of an Auslander–Reiten–Serre duality. We also show that existence of almost split extensions is preserved under taking relative extriangulated categories, ideal quotients, and extension-closed subcategories. Moreover, we prove that the stable category C _ \underline {\mathscr {C}} of an extriangulated category C \mathscr {C} is a τ \tau -category (see O. Iyama [Algebr. Represent. Theory 8 (2005), pp. 297–321]) if C \mathscr {C} has enough projectives, almost split extensions and source morphisms. This gives various consequences on C _ \underline {\mathscr {C}} , including Igusa–Todorov’s Radical Layers Theorem (see K. Igusa and G. Todorov [J. Algebra 89 (1984), pp. 105–147]), Auslander–Reiten Combinatorics on dimensions of Hom-spaces, and Reconstruction Theorem of the associated completely graded category of C _ \underline {\mathscr {C}} via the complete mesh category of the Auslander–Reiten species of C _ \underline {\mathscr {C}} . Finally we prove that any locally finite symmetrizable τ \tau -quiver (=valued translation quiver) is an Auslander–Reiten quiver of some extriangulated category with sink morphisms and source morphisms.

A study of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1

This paper considers a class of nonlocal fractional neutral stochastic integrodifferential inclusions of order 1 < α < 2 with impulses in a Hilbert space. We study the existence of the mild solution for the cases when the multi-valued map has convex and non-convex values. The results are obtained by combining fixed-point theorems with the fractional order cosine family, semigroup theory, and stochastic techniques. A new set of sufficient conditions is developed to demonstrate the approximate controllability of the system. Finally, an example is given to illustrate the obtained results.

A class of time-optimal feedback control for fractional neutral evolution hemivariational inequalities with fixed delay

ABSTRACT In this paper, we study a class of optimal feedback control for a neutral fractional system with hemivariational inequalities. Initially, we derive some existence results of mild solutions for the system by applying the Marteli's fixed point theorem of multivalued maps, properties of generalized Clarke's subdifferential and semigroup operators. Then, by using the Filippov theorem and the Cesari property, a new set of sufficient conditions are formulated to ensure the existence results of a feasible pair for the feedback control systems. Also, we apply our main results to obtain the optimal feedback control pair. Further, we investigate the time-optimal feedback control for our control system. In the end, an example is given to illustrate our theory.

New discussion on optimal feedback control for Caputo fractional neutral evolution systems governed by hemivariational inequalities

The main focus of this article is to investigate the existence of feedback optimal control for the neutral fractional evolution systems in Hilbert spaces in the sense of the Caputo fractional derivatives. In order to establish the necessary conditions for the proposed problem, we apply the semigroup property, the fixed point theorem of multivalued maps, and the properties of generalized Clarke's subdifferentials. Then, by using the Filippov theorem and the Cesari property, a set of sufficient conditions is formulated to ensure the existence of a feasible pair for the feedback control systems. Finally, we apply our main results to obtain the optimal feedback control pair. In the end, an example is given to illustrate our theory.

Almost output regulation for turbofan switched systems under multi‐source disturbances and time delay

AbstractIn allusion to the multi‐variable robust control for the turbofan engine with the large envelope, an almost output regulation (AOR) problem is discussed for a class of turbofan switched systems under multi‐source disturbances and time delay. The addressed disturbances include the regulated disturbance signal, the modeled disturbance from the input channel and the energy‐bounded disturbance. First of all, a disturbance observer is constructed to estimate the unknown disturbance in the system input. Then, by combining the output regulation method and the disturbance observer‐based control (DOBC) method, a switched composite regulation controller is developed to deal with the AOR problem of the turbofan switched systems and reject the adverse effects of disturbances. Through the multiple Lyapunov function method, a set of sufficient conditions are obtained to guarantee the AOR property with the performance and disturbance suppression ability. Finally, the validity of the proposed method is demonstrated by applying the composite anti‐disturbance regulator to the regulation of the speed and pressure ratio for the turbofan model.

Synchronization of coupled switched neural networks subject to hybrid stochastic disturbances

In this paper, the theoretical analysis on exponential synchronization of a class of coupled switched neural networks suffering from stochastic disturbances and impulses is presented. A control law is developed and two sets of sufficient conditions are derived for the synchronization of coupled switched neural networks. First, for desynchronizing stochastic impulses, the synchronization of coupled switched neural networks is analyzed by Lyapunov function method, the comparison principle and a impulsive delay differential inequality. Then, for general stochastic impulses, by partitioning impulse interval and using the convex combination technique, a set of sufficient condition on the basis of linear matrix inequalities (LMIs) is derived for the synchronization of coupled switched neural networks. Eventually, two numerical examples and a practical application are elaborated to illustrate the effectiveness of the theoretical results.

Event-Triggered Synchronization of Multiple Fractional-Order Recurrent Neural Networks With Time-Varying Delays.

This paper addresses the synchronization of multiple fractional-order recurrent neural networks (RNNs) with time-varying delays under event-triggered communications. Based on the assumption of the existence of strong connectivity or a spanning tree in the communication digraph, two sets of sufficient conditions are derived for achieving event-triggered synchronization. Moreover, an additional condition is derived to preclude Zeno behaviors. As a generalization of existing results, the criteria herein are also applicable to the event-triggered synchronization of multiple integer-order RNNs with or without delays. Two numerical examples are elaborated to illustrate the new results.

Equilibria and efficiency in a reinsurance market

We study equilibria in a reinsurance market with multiple reinsurers that are endowed with heterogeneous beliefs, where preferences are given by distortion risk measures, and pricing is done via Choquet integrals. We construct a model in the form of a sequential economic game, where the reinsurers have the first-mover advantage over the insurer, as in the Stackelberg setting. However, unlike the Stackelberg setting, which assumes a single monopolistic reinsurer on the supply side, our model accounts for strategic price competition between reinsurers. We argue that the notion of a Subgame Perfect Nash Equilibrium (SPNE) is the appropriate solution concept for analyzing equilibria in the reinsurance market, and we characterize SPNEs using a set of sufficient conditions. We then examine efficiency properties of the contracts induced by an SPNE, and show that these contracts result in Pareto-efficient allocations. Additionally, we show that under mild conditions, the insurer realizes a strict welfare gain, which addresses the concerns of Boonen and Ghossoub (2022) with the Stackelberg model and thereby ultimately reflects the benefit to the insurer of competition on the supply side. We illustrate this point with a numerical example.

Fractional neutral functional differential equations driven by the Rosenblatt process with an infinite delay

Abstract This paper concerns a class of fractional impulsive neutral functional differential equations with an infinite delay driven by the Rosenblatt process. A set of sufficient conditions are established for the existence of new mild solutions using fixed point theory. Finally, an illustrative example is provided to demonstrate the applicability of the theoretical result.

Event-triggered control of Markov jump systems with partially unknown transition rates under time-varying delay and deception attacks

This paper investigates the event-triggered synthesis problem of Markov jump system with partially unknown transition rates under time-varying delay and deception attacks. A mode-dependent event-triggered scheme is adopted between sensor and controller to reduce the amount of signal transmission. A set of sufficient conditions, including constraints of deception attacks, is provided. Asymptotically stable criteria in mean square sense for Markov jump system with partially unknown transition rate under deception attacks are derived for the first time. Moreover, the parameters of mode-dependent event-triggered scheme and the gains of the controller can be obtained simultaneously. Finally, an illustrative example is provided to show the effectiveness of the proposed approaches.

Distributed event-based H∞ consensus filtering for 2-D T-S fuzzy systems over sensor networks subject to DoS attacks

This paper concentrates on the H∞ consensus filtering issue of a kind of nonlinear two-dimensional (2-D) systems over sensor networks, which are described by the Takagi-Sugeno fuzzy model. With consideration of the limited communication bandwidth and the malicious network attack behavior, a distributed event-triggered mechanism is considered for the sensor network under DoS attacks. Different from the implicit assumption of many previous results that detail information of the non-periodic DoS attacks is available, a switching-like distributed event-triggered mechanism is introduced under the 2-D framework, which could schedule the triggering strategy flexibly in the attack silent or active regions. By means of the switching system analysis method and the discontinuous Lyapunov functions, this paper aims to develop a proper distributed attack-resilient H∞ consensus filter based on the information from the local sensor and its neighbors. A set of sufficient conditions are presented so that the estimation error system can reach exponential stability and meet an expected H∞ performance. Finally, a numerical example is given to demonstrate feasibility of the filter designing method.

Existence and approximate controllability results for second-order impulsive stochastic neutral differential systems

This paper focuses on the existence and approximate controllability of second-order non-autonomous impulsive stochastic neutral differential systems in Hilbert spaces. First, by using Schauder's fixed-point theorem, stochastic analysis theory, and evolution operators, a new set of sufficient conditions are formulated, and we prove the existence of mild solutions of second-order non-autonomous impulsive stochastic neutral differential systems. Further, the result is extended to study the approximate controllability results for second-order non-autonomous impulsive stochastic neutral differential systems. Then, a set of sufficient conditions are derived for the approximate controllability of second-order non-autonomous impulsive stochastic neutral differential system by assuming the associated linear system is approximately controllable. The results are obtained with the help of Krasnoselskii's fixed point theorem. Finally, an example is given to illustrate our obtained results.

Existence Theoremsfor Solutions of a Nonlinear Fractional-Order Coupled Delayed System via Fixed Point Theory

In this paper, the problem of the existence and uniqueness of solutions for a nonlinear fractional-order coupled delayed system with a new kind of boundary condition is studied. For this reason, we transform the above problem into an equivalent fixed point problem using the integral operator. Moreover, by applying fixed point theorems, a novel set of sufficient conditions that guarantee the existence and uniqueness of solutions of the coupled system is derived. Eventually, an example is presented to illustrate the effectiveness of the obtained results.

Linear superposition and interaction of Wronskian solutions to an extended (2+1)-dimensional KdV equation

&lt;abstract&gt;&lt;p&gt;The main purpose of this work is to discuss an extended KdV equation, which can provide some physically significant integrable evolution equations to model the propagation of two-dimensional nonlinear solitary waves in various science fields. Based on the bilinear Bäcklund transformation, a Lax system is constructed, which guarantees the integrability of the introduced equation. The linear superposition principle is applied to homogeneous linear differential equation systems, which plays a key role in presenting linear superposition solutions composed of exponential functions. Moreover, some special linear superposition solutions are also derived by extending the involved parameters to the complex field. Finally, a set of sufficient conditions on Wronskian solutions is given associated with the bilinear Bäcklund transformation. The Wronskian identities of the bilinear KP hierarchy provide a direct and concise way for proving the Wronskian determinant solution. The resulting Wronskian structure generates $ N $-soliton solutions and a few of special Wronskian interaction solutions, which enrich the solution structure of the introduced equation.&lt;/p&gt;&lt;/abstract&gt;

Global exponential periodicity of nonlinear neural networks with multiple time-varying delays

&lt;abstract&gt;&lt;p&gt;Global exponential periodicity of nonlinear neural networks with multiple time-varying delays is investigated. Such neural networks cannot be written in the vector-matrix form because of the existence of the multiple delays. It is noted that although the neural network with multiple time-varying delays has been investigated by Lyapunov-Krasovskii functional method in the literature, the sufficient conditions in the linear matrix inequality form have not been obtained. Two sets of sufficient conditions in the linear matrix inequality form are established by Lyapunov-Krasovskii functional and linear matrix inequality to ensure that two arbitrary solutions of the neural network with multiple delays attract each other exponentially. This is a key prerequisite to prove the existence, uniqueness, and global exponential stability of periodic solutions. Some examples are provided to demonstrate the effectiveness of the established results. We compare the established theoretical results with the previous results and show that the previous results are not applicable to the systems in these examples.&lt;/p&gt;&lt;/abstract&gt;

Design and experimentation of sampled-data controller in T-S fuzzy systems with input saturation through the use of linear switching methods

&lt;abstract&gt;&lt;p&gt;In this study, the stability and stabilization analyses are discussed for Takagi-Sugeno (T-S) fuzzy systems with input saturation. A fuzzy-based sampled-data control is designed to stabilize the T-S fuzzy systems. Based on the Lyapunov method and some integral inequality techniques, a set of sufficient conditions is obtained as linear matrix inequality (LMI) constraints to guarantee the asymptotic stability of the considered system. In this process, the linear switching method is utilized to design a controller that is dependent on the membership function, and an integral inequality is utilized. Additionally, determination of the controller parameters is achieved by resolving a series of LMI constraints. The effectiveness of these criteria is demonstrated through a real system that is modeled by the T-S system.&lt;/p&gt;&lt;/abstract&gt;

Event-Based Bipartite Consensus of Multi-Agent Systems Subject to DoS Attacks

This paper investigates the event-triggered bipartite consensus control of multi-agent systems subject to DoS attack. Existing results of relevant issues are usually confined by an implicit assumption that the real-time information of DoS attack is available for the construction of triggering strategy. However, some practical systems may not be equipped with elaborated attack detection mechanism, which means the trigger may not be notified the emission and suspension instants of attack timely. To settle with this scenario, we develop a novel distributed hybrid event-driven strategy which schedules the ordinary and attack-affected triggering laws by judging whether the previous transmission attempt of corresponding follower is successful, rather than utilizing detailed attack information directly. Furthermore, taking antagonistic interactions among agents into consideration, a resilient event-based control scheme is developed over signed digraph. Then, based on the analysis of hybrid Lyapunov functions exhibiting discontinuous property at practical triggering instants, a set of sufficient conditions which can ensure the exponential leader-following bipartite consensus of the investigated systems are presented. We also prove that Zeno behavior is excluded for triggering attempt sequences. Besides, the developed results are further extended to a self-triggered case. Finally, simulation results are provided to verify the effectiveness of the proposed control scheme.

A general approach to smoothing nonlinear mixed traffic via control of autonomous vehicles

Stop-and-go waves are easily caused by unstable traffic due to the collective behavior of human drivers, resulting in higher vehicle fuel consumption and emissions. In this article, we develop a general approach to synthesizing feedback controllers of autonomous vehicles (AVs) for smoothing unstable nonlinear mixed traffic flow, consisting of AVs and human-driven vehicles (HVs). In the context of traffic smoothing and stabilization, prior studies have mainly focused on analyzing string stability of specific car-following models linearized at flow equilibrium points. By contrast, we are interested to analytically synthesize appropriate feedback controllers of AVs for smoothing nonlinear mixed traffic in its general functional forms, covering a broad class of deterministic car-following models commonly seen in the literature. Specifically, by leveraging feedback control theory AVs are controlled to operate in such a way that they closely track a virtual speed profile, i.e., a subtler version of the disturbance resulting from the immediate preceding vehicle. Thus, traffic waves are reduced when propagating backward across controlled AVs. Based on the general functional form of car-following dynamics, we derive a class of effective additive AV controllers that are proven to be able to ensure convergence in tracking desired speed profiles, leading to smoother traffic. In addition, a set of sufficient conditions is devised for guaranteeing car-following safety. More importantly, head-to-tail string stability of the mixed traffic is likely to be achieved with a sufficient market penetration rate (MPR) of AVs. Notably, unlike many existing studies the feedback controllers synthesized for AVs require only local traffic information without having to rely on high degrees of vehicle connectivity, and the rate of smoothing mixed traffic is readily tunable, which is useful for practical implementations. The proposed approach is further illustrated with a theoretical intelligent driver model (IDM) and commercially available adaptive cruise control (ACC) vehicles represented by a well calibrated IDM. Extensive numerical results are presented to show the effectiveness and robustness of the feedback controllers synthesized for AVs on smoothing nonlinear mixed traffic.

Multistability of Switched Neural Networks With Gaussian Activation Functions Under State-Dependent Switching.

This article presents theoretical results on the multistability of switched neural networks with Gaussian activation functions under state-dependent switching. It is shown herein that the number and location of the equilibrium points of the switched neural networks can be characterized by making use of the geometrical properties of Gaussian functions and local linearization based on the Brouwer fixed-point theorem. Four sets of sufficient conditions are derived to ascertain the existence of 7^p₁5^p₂3^p₃ equilibrium points, and 4^p₁3^p₂2^p₃ of them are locally stable, wherein p₁ , p₂ , and p₃ are nonnegative integers satisfying 0 ≤ p₁+p₂+p₃ ≤ n and n is the number of neurons. It implies that there exist up to 7ⁿ equilibria, and up to 4ⁿ of them are locally stable when p₁=n . It also implies that properly selecting p₁ , p₂ , and p₃ can engender a desirable number of stable equilibria. Two numerical examples are elaborated to substantiate the theoretical results.

Longitudinal flight dynamics modeling and a flight stability analysis of a monocopter

A monocopter, which is a biology-inspired aircraft based on the samara, has been proved to have passive flight stability. However, due to the asymmetry of its configurations and the constant rotation during flight, its flight dynamics equation is complex. In this paper, the longitudinal stability of a monocopter is systematically analyzed. The longitudinal motion of the monocopter is used as the main research object in this paper. By transforming the body axis coordinate frame to the semi-body axis coordinate frame, its longitudinal dynamics equation is greatly simplified. Then, a fourth-order state space matrix of the longitudinal motion of the monocopter is established, and its longitudinal stability is analyzed at different pitch angles of the wing. Furthermore, the fourth-order state space matrix is simplified into a third-order matrix, and the Rouse criterion is used to analyze the stability of the simplified state space. A set of sufficient conditions is obtained as the criterion for longitudinal stability. Based on this criterion, it is found that the product of inertia Iyzb is a very important factor affecting the stability. Then, the inertial parameters of the aircraft are modified, which greatly expands the range of the pitch angle that maintains longitudinal stability. Finally, the six-degree-of-freedom nonlinear flight dynamic simulation is performed to verify the rationality of the longitudinal stability criterion.