We address formally the problem of opinion dynamics when the agents of a social network (e.g., consumers) are not only influenced by their neighbors but also by an external influential entity referred to as a marketer. The influential entity tries to sway the overall opinion as close as possible to a desired opinion by using a specific influence budget. We assume that the exogenous influences of the

In this paper, the pinning control problem is considered for the synchronization of a class of nonlinear discrete-time switched stochastic complex networks with identical nodes. The networks we considered are very general that account for nonlinear inner-coupling structures and nonidentical exogenous disturbances. In order to save the communication cost, a pinning controller under the event-triggered

This paper considers the global leader-following consensus of fractional-order multi-agent systems (FMASs), where the inherent dynamics is modeled to be discontinuous, and subject to nonlinear growth. Firstly, based on convex functions, three formulas on fractional derivative are established respectively. By applying the proposed formulas, a principle of convergence in finite-time for absolutely continuous

In this paper, the issue of asynchronous l1 control is discussed for a class of two-dimensional (2D) switched positive systems with polytopic uncertain parameters and impulses. By choosing a suitable co-positive Lyapunov function and utilizing the mode-dependent average dwell time technique, sufficient conditions can be derived under which the closed-loop system induced by a set of asynchronous state

In this study, distributed dynamic event-triggered controller containing Markov switching topologies is proposed in Markovian Complex Networks (MCNs). It is proved that the Zeno-behavior is avoided. Considering that the time delay and the controller vary with different modes in practical applications, two terms of the controller are designed to contain Markov switching. And mode-dependent Lyapunov–Krasovskii

The main concern of this paper is the study of degenerate sweeping process involving uniform prox-regular sets via an unconstrained differential inclusion by showing that the sets of solutions of the two problems coincide. This principle of reduction to unconstrained evolution problem can be seen as a penalization of the subdifferential of the distance function. Using this reduction technique, an existence

This article employs the hybrid-system-with-memory formalism to attain transmission intervals and delays that provably stabilize Networked Control Systems (NCSs). Nonlinear time-varying plants and controllers with variable discrete and distributed input, output and state delays along with nonconstant discrete and distributed network delays are considered. We bring together nominal system L2-stability

In this paper, a kind of event-based aperiodically intermittent pinning synchronization control strategies for linearly coupled complex networks over the directed topology is proposed. With the prescribed convergence performance dynamic, an event-triggered mechanism is presented to guarantee the globally exponential synchronization of the complex networks. Furthermore, a global and robust event-based

Due to the ability to handle uncertain nonlinear hybrid systems, barrier certificate based method has been widely used in safety verification problem. In this paper, an efficient framework, combining sum of squares programming with interval analysis, is proposed to generate barrier certificates for uncertain nonlinear hybrid systems. It utilizes the feature of bounded uncertainties to get a deterministic

This paper concerns with the mean square scaled consensus for multi-agent systems(MAS) with Markovian switching topologies and communication noises. A time-homogeneous Markov process governs the switching and each topology corresponds to a state of the process. Meanwhile, the communication noises are also considered for practical applications. We introduce a time-varying gain in control protocol which

We introduce an event-triggered algorithm for the stabilization of switched linear systems. We define a pseudo-Lyapunov function common to all the subsystems. The pseudo-Lyapunov function is compared, at every time instant, to an exponentially decreasing upper threshold. An event is generated when the two functions intersect, or when a new subsystem becomes active. The existence of a Lyapunov function

For a class of hybrid systems we introduce and characterize the almost always observability property, i.e. the possibility of reconstructing the current continuous component of the state, from the observed output, for almost all switching times. The optimal location of additional sensors that make the system almost always observable is investigated.

We present a new technique for calculating the Pötzsche, Siegmund, and Wirth’s region of exponential stability for a time scale, Sℂ(T). The approach taken here unifies and extends other results on this topic in the literature. We establish a tractable algorithm for computing Sℂ(T) in terms of the asymptotic extended graininesses of the time scale and their relative frequencies.

This paper establishes a novel non-fragile sampled data control framework for non linear multi-agent systems with additive time varying delays and Markovian jump parameters. The Laplacian matrix represents the interconnection between the agents which are denoted by an undirected graph. Relevant Lyapunov Krasovskii functional (LKF) is constructed which contain major information about the additive time-varying

We address the finite horizon control of a discrete time piecewise affine (PWA) system, which is affected by an additive bounded disturbance. The goal is to robustly drive the state of the system to some target region, while satisfying state and actuation constraints. This problem is challenging due to the mixed discrete and continuous dynamics, requiring the exploration of many mode sequences. We

This paper is concerned with the problem of event-triggered based asynchronous adaptive quantized sliding mode control (SMC) for Itoˆ stochastic control systems with semi-markovian switching and actuator failures. In this design work, the jump modes between plants and controller are asynchronous, which is represented by a hidden Markov model. The dynamical logarithmic quantizer is introduced in signal

In this paper, we explain how, under the one-sided Lipschitz (OSL) hypothesis, one can find a mean square error bound for a variant of the Euler–Maruyama approximation method for stochastic switched systems. Subsequently, we explain how this bound can be used to control a stochastic switched system in order to make it reach a target zone with guaranteed minimum probability. The method is illustrated

This work investigates the problem of finite-time stochastic boundedness for a class of Markovian jump systems by synthesizing the sliding mode control and the transition rate matrix. First, a sufficient condition on the transition rate matrix is derived to guarantee the finite-time stochastic boundedness of the unforced Markovian jump systems. Moreover, a hybrid design scheme integrating the transition

This paper considers the mono/multi-periodicity problems in time-delayed memristor-based neural networks (MNNs) possessing impulsive effects, where the input–output activation functions are relaxed to be unbounded and nonmonotonic. Based on differential inclusions theory, several conditions are derived which ensure the existence and multiplicity of periodic positive solutions for impulsive time-delayed

This paper introduces the detectability notions and investigates the detectability properties for Boolean networks (BNs) and Boolean control networks (BCNs). A BN (BCN) possesses the property of detectability if the current state can be determined by limited observed data. According to different situations, three types of detectabilities are defined: strong detectability, detectability and weak detectability

This paper aims to propose dynamic consensus protocols for a class of non-linear saturated multi-agent systems. Due to the existence of non-linear dynamics of each agent, the system does not satisfy the condition named asymptotically null controllable with bounded controls (ANCBC). As a result, the widely-adopted method of low-gain feedback to solve consensus control problems for linear multi-agent

Cyber–physical Systems (CPS) involve a network of discrete controllers that control physical processes, e.g., pacemakers controlling the heart rhythm. The intuitive and formal Hybrid Automata (HA) based modelling approach for CPS is gaining momentum. HA combines the model of the plant along with its discrete controller resulting in a piece-wise continuous system with discontinuities. Accurate detection

Symmetries are ubiquitous in a wide range of nonlinear systems. Particularly in systems whose dynamics is determined by a Lagrangian or Hamiltonian function. For hybrid systems which possess a continuous-time dynamics determined by a Lagrangian function, with a cyclic variable, the degrees of freedom for the corresponding hybrid Lagrangian system can be reduced by means of a method known as hybrid

This paper investigates the stability and L∞-gain problems of positive linear systems with bounded time-varying delays on time scales. For such systems on time scales, the positivity conditions are firstly established. Then, in virtue of the monotonic and asymptotic properties of a positive linear system with the specified time delay, the stability condition is presented for positive systems with bounded

In this paper, we introduce and characterize the notion of approximate predictability for the general class of pseudo-metric systems, which are a powerful modeling framework to deal with complex heterogeneous systems such as hybrid systems. Approximate predictability corresponds to the possibility of predicting the occurrence of specific states belonging to a particular subset of interest, in advance

In a smooth dynamical system the characteristics of a given reference trajectory can be determined, to lowest order, by examining the linearised system about the reference trajectory. In other words, we can approximate the deviations of trajectories after a given time, with starting points in a neighbourhood of the reference trajectory, by multiplying the initial deviations by the corresponding fundamental

We develop a method for computing controlled invariant sets of discrete-time affine systems using Sum-of-Squares programming. We apply our method to the controller design problem for switching affine systems with polytopic safe sets but our work also improves the state of the art for the particular case of LTI systems. The task is reduced to a semidefinite programming problem by enforcing an invariance

In this paper, we propose an optimization-based design technique for constrained control and bounded-error state estimation for affine systems in the presence of intermittent measurements. We treat the affine system as a switched system where the measurement equation switches between two modes based on whether a measurement exists or is missing, and model potential missing data patterns with a finite-length

This paper presents a novel abstraction technique for analyzing Lyapunov and asymptotic stability of polyhedral switched systems. A polyhedral switched system is a hybrid system in which the continuous dynamics is specified by polyhedral differential inclusions, the invariants and guards are specified by polyhedral sets and the switching between the modes do not involve reset of variables. A finite

The event-based output-feedback control is studied for large-scale distributed networked nonlinear systems. All subsystems are described by interval type-2 (IT2) Takagi–Sugeno (T–S) model and communicate information to each other via distributed networks with time-varying transmission delays. The sampled rates of sensors and refresh rates of actuators are allowed to be different among subsystems. We

In this paper, a switched adaptive observer for a class of switched uncertain nonlinear systems is designed by using an average dwell time (ADT) method. Due to that switching unknown parameters lead to different coordinates transformation for different subsystems, some new dwell-time conditions are provided by an improved ADT method. Also, the boundedness of all signals is ensured by a well defined

In this paper, the problems of robust finite-time fault-tolerant stochastic stability and stabilization of networked control systems (NCSs) in the presence of random delays and actuator faults are investigated. First, sensor-to-controller and controller-to-actuator random delays are modeled as a Markov chain. Since in the network environment, the accurate access to the transition probabilities (TPs)

In this paper, the design of finite-time mixed H∞ and passive asynchronous filter for T–S fuzzy singular Markov jump systems with general transition rates under the dynamic event-based scheme is discussed. An asynchronous filter is considered such that the phenomena of asynchronous modes between the original singular Markov jump systems and the considered filter is modelled as a hidden Markov model

An immersion and invariance (I&I) stabilization theorem for nonlinear switched systems with average dwell time is set up which provides a tool for analyzing the behavior of switched systems. Also, a method integrating the I&I technique and viability method is proposed to stabilize nonlinear switched systems with state constraints. Based on the proposed theorem, this paper further investigates the problem

In this paper, we will study the problem in fed-batch culture of glycerol producing 1,3-propanediol induced by Klebsiella pneumonia. In practice, the concentrations of intracellular substances are difficult to be measured. To address this problem, quantitative biological robustness is introduced to identify the unknown parameters related to the concentrations of intracellular substances. The problem

In this article, a new hybrid controller is designed, which consists of sampled-data controller and impulsive controller with actuator saturation. Firstly, by applying polytopic representation approach and establishing an appropriated Lyapunov function, some established linear matrix inequalities (LMIs) are obtained to guarantee exponential stabilization of a class of nonlinear dynamical systems. It

This paper introduces operators, semantics, characterizations, and solution-independent conditions to guarantee temporal logic specifications for hybrid dynamical systems. Hybrid dynamical systems are given in terms of differential inclusions – capturing the continuous dynamics – and difference inclusions – capturing the discrete dynamics or events – with constraints. State trajectories (or solutions)

We consider consensus in this paper for hybrid multi-agent systems (HMASs) consisting of continuous-time dynamic agents and discrete-time dynamic agents via designing pulse-modulated protocols. By assuming all the agents communicate with its neighbors only at some sampling instants, and the input of each continuous-time agent is determined by a pulse function, the consensus for first-order HMASs and

This work investigates the observability analysis and the observer synthesis for Linear Hybrid Systems (LHS’s) considering both known and unknown inputs and constrained discrete dynamics. In this framework, none assumption is made over the unknown inputs (that can represent faults or disturbances), moreover, the discrete dynamics are represented by a Petri net, whose behaviour constraints the possible

In this paper, we propose a compositional approach for the construction of finite abstractions (a.k.a. finite Markov decision processes (MDPs)) for networks of discrete-time stochastic control subsystems that are not necessarily stabilizable. The proposed approach leverages the interconnection topology and a notion of finite-step stochastic storage functions, that describes joint dissipativity-type

For a practical system with switching actions, it is necessary to restrict the switching frequency under the limit of its physical constraints, avoiding potential damage to the equipment. In this paper, a mixed switching scheme with both state-dependent and time-dependent functions is designed to reduce the switching frequency. First, a constant dwell-time constraint is considered and a switching logic

This paper mainly investigates the global stability (stabilization) of switched logical (control) networks at one of attractors. Firstly, the switched Boolean (control) networks are transformed into a discrete-time algebraic system by using semi-tensor product (STP) method of matrices. Then, based on this algebraic system, the global stability (stabilization) problem of switched Boolean (control) networks

This paper investigates the stability of totally positive switched linear systems (TPSLSs), for the continuous-time case and the discrete-time case. The multiple linear copositive Lyapunov function (MLCLF) is used to study exponential stability of the considered system with average dwell time. Then the case with common linear copositive Lyapunov function (CLCLF) is also established. Sufficient conditions

Model Predictive Control is a well consolidated technique to design optimal control strategies, leveraging the capability of a mathematical model to predict a system’s behavior over a time horizon. However, building physics-based models for complex large-scale systems can be cost and time prohibitive. To overcome this problem we propose a methodology to exploit machine learning techniques (i.e. Regression

In this paper, the finite-time event-triggered and guaranteed non-fragile cost control problem is discussed for a class of uncertain switched nonlinear networked control systems (SNNCS) which involves parameter uncertainties and time-varying transmission delays. The main aim of this work is to synthesize finite-time event-triggered and guaranteed cost non-fragile controller for ensuring the finite-time

The literature has proven that attaining good transient behavior in leakage-based robust adaptive control of uncertain switched systems is intrinsically challenging. In fact, because the gains of the inactive subsystems must exponentially vanish during inactive times as an effect of leakage action, new learning transients will repeatedly arise at each switching instant. In this paper, a new leakage-based

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