Exponential Mean Square Research Articles

Formation control and collision avoidance of unmanned water surface vehicles in maritime environments

The formation control of a team of unmanned water surface vehicles (USVs) experiencing maritime environmental disturbances is investigated. These perturbations include water waves, ocean current, wind gusts, communication and measurement errors, and other unmodeled dynamics that are captured through stochastic noise. A distributed control scheme leveraging local communication among team members is proposed to drive the group towards a set of waypoints while simultaneously achieving a desired spatial configuration and collision avoidance. The exponential mean square convergence of the proposed control scheme is shown under a version of the Lyapunov stability theory adapted to stochastic systems. Closed form expressions are proposed to estimate model parameters from experimental data collected in operating environments. The effectiveness of the proposed formation control scheme and collision avoidance method is assessed through numerical simulations demonstrating the interplay between the control parameters and the intensity of the noise. It also highlight the crucial role of the stochastic noise in resolving potential singularities or deadlocks in the vehicles’ motion , which originate from the collision avoidance forces.

Synchronization conditions for stochastic landslide chain model with delayed coupling

We examine the conditions for synchronization of landslide stochastic chain model with delayed coupling. Firstly, a new chain model for landslide dynamics is proposed, with the included effect of delayed coupling and background noise. The model is of the microscopic type, where the state of each block in the chain is influenced by the previous state of the same block and its neighbors as well as by noise. Secondly, we examine the stochastic synchronization of such a system of stochastic delay-differential equations. A sufficient condition for the exponential mean square stability of the synchronization is obtained. The sufficient condition indicates that the uni-directional asymmetric coupling induces the synchronization much more efficiently than the bi-directionally symmetric one. From the practical viewpoint, the results obtained confirm that different parts of the large unstable slope could exhibit synchronized activity under certain conditions, which indicates their possible larger influence on the structures (and generation of corresponding deformation) compared to the individual effect of unsynchronized activities.

Resilient adaptive event‐triggered synchronization control of piecewise‐homogeneous Markov jump delayed neural networks under aperiodic DoS attacks

SummaryUnder the aperiodic Denial‐of‐service (DoS) attacks, this paper studies the resilient adaptive event‐triggered synchronization control problem for a class of Piecewise‐Homogeneous Uncertain Markov Jump Neural Networks (PHUMJNNs) with time‐varying delays. First of all, a new way of carving DoS attacks is given from the defenders' perspective, that is, aperiodic DoS attacks based on fixed detection periods. Then, under such attacks, a new Resilient Adaptive Event‐triggered Communication (RAETC) is designed between sensor and controller, which has a threshold function based on the net change rate and is real‐time updated depending on the present sampling state. Next, a single functional is used in the construction of the Lyapunov‐Krasovskii functional, while a new looped functional is introduced that makes full use of the state information of the current instant , the trigger instant and the next trigger instant . Based on the constructed single functional, under the framework of the input delay method and the linear matrix inequality technique, the exponential mean square stabilization criterion of the error system is obtained, which makes the master system and the slave system synchronized. In the end, three simulation examples are used to illustrate the validity of the obtained results.

Lyapunov Characterizations of Exponential Mean Square Input-to-State Stability for Discrete-Time Markovian Switching Nonlinear Systems

Lyapunov Characterizations of Exponential Mean Square Input-to-State Stability for Discrete-Time Markovian Switching Nonlinear Systems

Fault-Tolerant Periodic Event-Triggered Consensus Under Communication Delay and Multiple Attacks

This article proposes a resilient strategy for leaderless and leader–following consensus in general linear multiagent systems under simultaneous presence of false data injection and denial-of-service (DoS) attacks. To save energy, local control updates and communication between the neighboring agents are based on a distributed periodic event-triggered scheme. Sufficient conditions to guarantee the exponential mean square bounded consensus are derived as linear matrix inequality (LMI) conditions obtained from some delay-dependent Lyapunov–Krasovskii functionals. The proposed design framework computes the required consensus control gain based on a desired level of resilience to DoS. The guaranteed level of resilience in our proposed LMI-based method is less conservative (more realistic) compared to the existing analytical solutions. Two physical constraints, namely nonuniform time-varying communication delay and actuator faults, are also included in the problem formulation to enhance the practicability of the proposed solution. Simulations results demonstrate the effectiveness of the proposed framework in the presence of the considered cyberthreats and physical constraints.

Fault detection filtering for MNNs with dynamic quantization and improved protocol

This paper concerns the fault detection filtering problem for discrete-time memristive neural networks with mixed time delays. An improved dynamic event-triggering protocol, whose multiple threshold functions are dynamically adjustable, is presented to decrease the utilization of limited resources and achieve desired performance. Two mutually independent Bernoulli variables are given to depicting the randomly occurring cyber-attacks. Meanwhile, a dynamic quantizer is established to account for restricted bandwidth efficiently. Based on the Lyapunov theory, sufficient conditions are derived to ensure the filtering error system is exponential mean square stable and desired performance. In the end, a numerical example is provided to verify the effectiveness of the proposed methodology.

Stability results on random impulsive control for uncertain neutral delay differential systems

This study addresses the delay-dependent criteria like mean square robust exponential stability and mean square exponential stability for the uncertain neutral discrete time-varying and distributed delay differential systems under random impulsive control. By employing the random impulsive control, descriptor model transforms, and Lyapunov functional approach, we achieved the desired performance for the given system in the way of Linear matrix inequality. Finally, we justify the proposed results through numerical examples and their simulations.

Dynamic event-triggered state estimation for time-delayed spatial-temporal networks under encoding-decoding scheme

This paper is concerned with the dynamic event-triggered state estimation problem for a class of spatial-temporal networks (STNs) with time-varying delays under an encoding-decoding strategy. For the sake of reducing the unnecessary resources wastes, we establish a dynamic event-triggered mechanism to determine whether the current measurement output data is transmitted to the filter, where the threshold is dynamically adjusted according to a certain rule. In order to enhance the robustness of signal transmission, an encoding-decoding strategy is exploited in the process of the data transmission. To be specific, the original signals encoded as a bit string are transmitted through binary symmetric channels with certain crossover probabilities and then restored by a decoder at the receiver. By constructing Lyapunov-Krasovskii functional, we obtain a sufficient condition to ensure that the estimation error system is exponential mean square ultimately bounded. Subsequently, the desired state estimator is designed in terms of the solution to a certain matrix inequality. Finally, a numerical example is shown to demonstrate that the proposed state estimator is valid for time-delayed STNs.

Delayed impulsive SDEs driven by multiplicative fBm noise and additive fBm noise

The problems of stability and boundedness for delayed impulsive SDEs driven by fBm are studied in this paper. Two kinds of noises, i.e., additive fBm noise and multiplicative fBm noise, are both taken into consideration. By using stochastic Lyapunov technique and impulsive control theory, sufficient criteria for pth moment exponential stability and mean square ultimate boundedness are derived, for two kinds of fBm‐driven delayed impulsive SDEs, respectively. As applications, the obtained results are used to do practical synchronization w.r.t. a class of chaotic systems, in which the response systems are perturbed by additive fBm noises. Finally, a Chua chaotic oscillator is given to verify the validity and applicability of the derived results.

Mean square exponential stabilization of uncertain time‐delay stochastic systems with fractional Brownian motion

AbstractThis article is concerned with exponential mean square stabilization of stochastic systems driven by fractional Brownian motion subject to state‐delay and uncertainties by sliding mode control. By applying the proposed method, the states of the system reach the sliding surface in finite time. Then, some sufficient conditions are given in terms of linear matrix inequalities (LMIs) to guarantee the mean‐square exponential stability of the sliding motion. The LMI conditions for mean‐square exponential stability of the sliding mode dynamics are derived by constructing a novel Lyapunov functional. Finally, a simulation example is presented which corroborates the accuracy of the results.

The exponential behavior and stabilizability of quasilinear parabolic stochastic partial differential equation

In this paper, we study the stability of quasilinear parabolic stochastic partial differential equations with multiplicative noise, which are neither monotone nor locally monotone. The exponential mean square stability and pathwise exponential stability of the solutions are established. Moreover, under certain hypothesis on the stochastic perturbations, pathwise exponential stability can be derived, without utilizing the mean square stability.

$H_{\infty }$ State Estimation for Coupled Stochastic Complex Networks With Periodical Communication Protocol and Intermittent Nonlinearity Switching

In this paper, an $H_{\infty }$ estimation approach is given for an array of coupled stochastic complex networks with intermittent nonlinearity switching. A set of binary random variables are adopted to characterize the intermittent switching behavior of the involved nonlinearities. To effectively alleviate data collisions and save energy, the Round-Robin protocol is utilized to curb network congestions in data communication. For the coupled stochastic complex networks, we design a protocol-based $H_{\infty}$ estimator that not only resists stochastic disturbances, but also ensures the exponential mean square stability of the desired error system under a given disturbance attenuation level. With the help of the Lyapunov stability and convex optimization theories, sufficient conditions are provided for the expected estimator. Simulations are provided to illustrate the reasonability of our $H_{\infty }$ approach.

Lyapunov stability analysis for nonlinear delay systems under random effects and stochastic perturbations with applications in finance and ecology

This manuscript is involved in the study of stability of the solutions of functional differential equations (FDEs) with random coefficients and/or stochastic terms. We focus on the study of different types of stability of random/stochastic functional systems, specifically, stochastic delay differential equations (SDDEs). Introducing appropriate Lyapunov functionals enables us to investigate the necessary conditions for stochastic stability, asymptotic stochastic stability, asymptotic mean square stability, mean square exponential stability, global exponential mean square stability, and practical uniform exponential stability. Some examples with numerical simulations are presented to strengthen the theoretical results. Using our theoretical study, important aspects of epidemiological and ecological mathematical models can be revealed. In ecology, the dynamics of Nicholson’s blowflies equation is studied. Conditions of stochastic stability and stochastic global exponential stability of the equilibrium point at which the blowflies become extinct are investigated. In finance, the dynamics of the Black–Scholes market model driven by a Brownian motion with random variable coefficients and time delay is also studied.

Event-triggered [formula omitted] state estimation for discrete-time delayed switched stochastic neural networks with persistent dwell-time switching regularities and sensor saturations

In this paper, the H∞ state estimation problem is considered for a class of the discrete-time delayed switched stochastic neural networks with sensor saturations. In order to improve the resource utilization efficiency, an event-triggered H∞ state estimator is designed to regulate the transmission of the measurement outputs. The persistent dwell-time switching strategy is adopted in this paper which is more general and less conservative. By utilizing a proper Lyapunov–Krasovskii functional, some criteria are presented to ensure the exponential mean square stability of the estimation error system and the prespecified H∞ level of disturbance attenuation. Finally, a numerical example is given to illustrate the effectiveness of our results.

Improved robust H∞ exponential mean square stabilization for uncertain Markov jump delay systems based on memory‐state feedback control

Improved robust H∞ exponential mean square stabilization for uncertain Markov jump delay systems based on memory‐state feedback control

Inversely Calibrated Curvilinear Artificial Neural Network Model for Simultaneous Assay of Ternary Cardiovascular Drug Mixture

Novel chemometric design, tailored for pre-clinical multiple drug screening, goals for bioanalytical future scope. A highly sensitive, non-linear multivariate Artificial Neural Network (ANN) is developed and applied for simultaneous spectrophotometric determination of three commonly concomitant cardiovascular drugs in laboratory made mixtures and spiked human plasma samples. Ticagrelor, Irbesartan and Hydrochlorothiazide have been simultaneously quantified in the curvilinear ranges of 0-30 µg/mL, 0-10 µg/mL and 0-3 µg/mL respectively. Highly overlapping Near UV absorption spectra of three drugs, in the region of 215-280 nm, have been recorded 1-nm range in synthetic ternary mixtures and trained iteratively. By inversely relating the concentration matrix (x-block) with its corresponding absorption one (y-block), gradient-descent back-propagation ANN calibration could be computed and optimized. All proposed mathematical modeling was manipulated using MATLAB® 2007, reaching down to sixth order exponential Mean Square Error, MSE. To validate, independent set of ternary synthetic mixtures has been constructed and examined, where excellent recovery results has been obtained. Furthermore, application of suggested model to varying ratios synthetic ternary mixtures as well as spiked plasma samples has resulted in accurate, precise and robust estimations with no background interference. ANN method was compared to a reference HPLC method; Student’s t-test and F-variance ratio were calculated and showed insignificant difference. This chemometric approach is an eco-friendly green assay, time-saving, and economic method. It initiates a pathway for clinical drug screening through affordable spectroscopic instrumentation.

Event‐triggered mean square consensus of linear multiagent systems with measurement noises

SummaryThis article investigates mean square consensus of linear multiagent systems with measurement noises based on event‐triggered control. Considering various uncertain factors in the communication environment, multiplicative noises exists in the information that each agent measures from its neighbors. In order to save limited resources and to exclude the Zeno phenomenon, the update of the controller for each agent is driven by properly defined event‐triggered condition. Sufficient conditions are given to ensure exponential mean square consensus of multiagent systems with multiplicative noises by utilizing static and dynamic event‐triggered scheme. The interevent times of static event‐triggered mechanism is less than those of corresponding dynamic case for each agent. Finally, validity of the theoretical results is illustrated through a simulation example.

Protocol‐based collaborative design for discrete‐time switched systems with sojourn probabilities

SummaryThis article focuses on the collaborative design of a class of discrete‐time switched systems with sojourn probabilities. For the purpose of preventing the data collision, the Try‐Once‐Discard (TOD) protocol is employed to govern the information transmission between sensors and the controller. Moreover, it is worth noting that the values of sojourn probabilities, which are not given ahead, have an effect on the system stability. As a consequence, a novel collaborative design framework is established, in which the sojourn probability and static output‐feedback controller are to be designed simultaneously. By considering the effect from the TOD protocol and using the Lyapunov function related to the mode and protocol, a sufficient condition is derived to guarantee the exponential mean square stability of the closed‐loop system with a prescribed lower bound on the decay rate. Then, the desired sojourn probabilities and controller gains dependent on the corresponding mode and protocol are obtained in terms of convex optimization method with equality constraints. Subsequently, an estimation approach is provided to estimate the decay rate and decay coefficient of the closed‐loop system. Finally, one numerical example is given to testify the effectiveness of the proposed design approach.

Dynamic event-triggered [formula omitted] state estimation for delayed complex networks with randomly occurring nonlinearities

This paper aims to iron out the dynamic event-triggered (ET) H∞ state estimation issue for a class of discrete time-delay complex networks (CNs) with randomly occurring nonlinearities (RONs). In the signal transmission among the nodes, the effect of time-varying delays is examined. The RONs under consideration is modelled by a series of random variables obeying Bernoulli distribution. In the design of state estimators, a dynamic ET scheme is utilized with the hope of improving the energy utilization efficiency. A sufficient condition is first derived to ensure the exponential mean-square (EMS) stability and H∞ performance index of the estimation error systems. Then, by using the matrix inequality technology, the desired state estimators are designed. Lastly, a numerical simulation example is given to show the usefulness of the proposed estimator design algorithm.

Robust l2−l∞ dynamic output feedback control design for uncertain discrete‐time switched systems with random time‐varying delay

SummaryThis article deals with the problem of robust output feedback control design for a class of switched systems with uncertainties and random time‐varying delay. Our purpose is focused on designing a full order dynamic output feedback controller and an appropriate switching rule to ensure the exponential mean square stability of the resulting closed‐loop switching system with an l2−l∞ performance level. The appealing aspects of the proposed control scheme include: (a) the development of LMI based delay‐dependent sufficient conditions for the exponential stability analysis of the stochastic hybrid systems using the appropriate choice of the augmented Lyapunov–Krasovskii functional, the partitioning technique and the average dwell time, (b) conservatism reduction of the unified design conditions, and (c) the controller designed exhibiting robustness with l2−l∞ performance against uncertainties and external disturbance. Finally, representative examples are given to demonstrate the validity and the merit of the proposed design technique.