Sampling Instants Research Articles

Aperiodic sampled-data control of distributed networked control systems under stochastic cyber-attacks

This paper examines the stabilization problem of a distributed networked control system under the effect of cyber-attacks by employing a hybrid aperiodic triggering mechanism. The cyber-attack considered in the paper is a stochastic deception attack at the sensor-controller end. The probability of the occurrence of attack on a subsystem is represented using a random variable. A decentralized hybrid sampled-data strategy is introduced to save energy consumption and reduce the transmission load of the network. In the proposed decentralized strategy, each subsystem can decide independently whether its state should be transmitted to the controller or not. The scheme of the hybrid triggering mechanism for each subsystem composed of two stages: In the first stage, the next sampling instant is computed using a self-triggering strategy. Subsequently, in the second stage, an event-triggering condition is checked at these sampling instants and the control signal is computed only if the event-triggering condition is violated. The self-triggering condition used in the first stage is dependent on the selection of event-triggering condition of the second stage. Finally, a comparison of the proposed approach with other triggering mechanisms existing in the literature is presented in terms of the sampling instants, transmission frequency and performance measures through simulation examples.

A Bayesian longitudinal model for quantifying students’ preferences regarding teaching quality indicators

The aim of the paper is to estimate the posterior mean values and analyze the posterior variation in students’ prioritization of teaching quality components within a 10-year frame. The results are based on longitudinal data gathered among Greek university students during the period of the national economic crisis in Greece spanned from 2009 to 2018. The analysis consists of fitting a Bayesian hierarchical beta regression model with a Dirichlet prior on the model coefficients that correspond to twenty quality attribute measures. Using this natural way to implement the usual constraints, the model coefficients can be interpreted as weights and thus they measure the relative importance that the students give to the different attributes. By estimating the posterior means and positioning measures of all consecutive sampling instances and summarizing posterior distributions of the differences between consecutive periods in the model weights, the study identifies and evaluates the major changes and patterns in students’ perception of academic quality over the ten-year sampling period.

Pull-Based Event-Triggered Containment Control for Multiagent Systems With Active Leaders via Aperiodic Sampled-Data Transmission

In this article, the containment control problem of multiagent systems (MASs) with active leaders under a directed communication graph is addressed. A novel pull-based event-triggered protocol combined with aperiodic sampled-data mechanism is first presented, where each agent merely updates controller at its own triggering instants. Under the proposed control protocols, the information is only exchanged and calculated at the aperiodic sampling instants, therefore, it can reduce communication congestion and save computing resources. Furthermore, the Zeno behavior is naturally excluded because the trigger instants are in the set of aperiodic sampled instants. By virtue of the algebraic graph theory and Lyapunov stability analysis, it is shown that the active leaders can reach their desired states predefined arbitrarily and all followers are driven to the convex hull formed by the leaders. Finally, an illustrative example is given to validate the theoretical results and emphasize the advantages of the proposed protocols.

An Industrial-Based Framework for Distributed Control of Heterogeneous Network Systems

In this paper, a novel control strategy for synchronization of heterogeneous network systems in industrial applications is proposed. Nonidentical nodes are adopted to describe the different industrial processes. The target trajectory is the output of an autonomous linear time-invariant system. The designed controller for each nonidentical node is distributed and calculated on the local information. Each distributed controller composes by the reference generator (RG) and the regulator (RE), where RG can copy the dynamics of the target trajectory and RE can ensure the synchronization. Limited to communication constraints, the time-varying sampled-data control strategy is utilized to reduce the updated frequency of the controller and communication burden of the network. The upper bound of the sampling instants is calculated by the theory of small gain theorem and the theory of integral quadratic constraints. Finally, a practical numerical example is presented to illustrate the effectiveness of the distributed controller design strategy.

Smoothing for continuous dynamical state space models with sampled system coefficients based on sparse kernel learning

A new smoother for a continuous dynamical state space model with sampled system coefficients is proposed. This is completely different from conventional approaches, such as Rauch–Tung–Striebel smoother. In the proposed method, the state vector as a continuous function of time is represented by kernel models. The state process model, namely the differential equation, is treated as part of the measurement model at the sampling instants of the system coefficients. Sparse solution of the kernel weights is obtained through a special regularization strategy called the Lasso estimator. The optimization problem appearing in the Lasso estimation is solved by the fast iterative shrinkage threshold algorithm. The hyperparameters involved, namely the kernel widths and the regularization coefficients, are selected objectively through generalized cross-validation or corrected Akaike information criterion tailored to the Lasso estimator. A simple two-dimension example is employed in the simulation to demonstrate the application and also the performance of the proposed method. It is shown that the proposed method could provide state vector estimates with satisfactory accuracy not only at the sampling instants of the observations but also at any other instants. The sparsity of the solution could also be clearly seen in the experiment. The proposed method can be viewed as an alternative smoothing method, rather than a replacement for conventional smoothers, due to the difficult model tuning and increased computation load.

A waiting time based discrete event-triggered control for networked switched systems with actuator saturation

This paper studies the event-triggered control problem for networked switched systems with actuator saturation. An event-triggering strategy is developed based on discrete event-triggered samplings. By which, a waiting time is first ensured to avoid the Zeno-like behavior, and then the data transmission is carried out once a desired performance-dependent condition is satisfied. According to the implementation of the triggering strategy and considering the impacts of transmission delay and actuator saturation, a time-delay closed-loop switched system is developed. Subsequently, sufficient conditions to ensure stability of the closed-loop system are derived by making use of the average dwell time and multiple Lyapunov functions method. In particular, since the waiting time, periodic sampling instants, data updating instants and switching instants may be coupled with each other, typical cases are discussed thoroughly to analyze the system stability. Moreover, together with the estimation of domain of attraction, sufficient conditions for the design of the desired state-feedback sub-controller gains and event-triggering parameters are presented. Finally, the effectiveness of the proposed method is verified by numerical simulations.

Aperiodic Sampled-Data Control for Exponential Stabilization of Delayed Neural Networks: A Refined Two-Sided Looped-Functional Approach

This brief addresses the exponential stabilization of a class of delayed neural networks under the framework of aperiodic sampled-data control. Firstly, a two-sided looped-functional is precisely constructed to relax the stabilization conditions and to enlarge the maximum sampling period. It drops the common positive definiteness requirement and only requires it at the sampling instants. Combining the Gronwall-Bellman inequality with the reciprocally convex approach, a less conservative exponential stabilization criterion in terms of LMIs with fewer decision variables is presented. Meanwhile, an effective design algorithm for the feedback gain matrix is proposed. Finally, a simulation example is provided to illustrate the effectiveness and superiority of the main results over some popular ones.

Star-shaped control-vector sets of second-order systems with PWM-type input

This paper deals with second-order continuous-time linear time-invariant systems by means of a pulse-width modulation (PWM)-type input. In general, it is difficult to analyze and design a PWM system because of its nonlinearity in terms of the duty ratio. In this paper, it is shown that the nonlinearity appearing in the discrete-time model at the sampling instants can be eliminated by varying the location of the pulse as well as the duty ratio.

Consensus for hybrid multi-agent systems with pulse-modulated protocols

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 second-order HMASs are addressed, respectively. According to the model transformation, stochastic matrix theory and the mathematical analysis technique, some sufficient criteria for consensus of these two types of HMASs are derived where it shows that the consensus in the considered HMASs can be achieved when the network structure, pulse function and sampling period respectively satisfy some suitable conditions. And, an algorithm is presented to evaluate the maximum allowable sampling period for achieving consensus. Finally, three numerical simulation examples are performed to validate the main theoretical results.

Exponential Stabilization of Delayed Complex-valued Neural Networks with Aperiodic Sampling: A Free-matrix-based Time-dependent Lyapunov Functional Method

In this paper, the exponential stabilization of delayed complex-valued neural networks (DCNNs) is addressed via sampled-data control. First, aperiodic sampled-data control aimed at further reducing the frequency of data transmission is adopted, which covers the periodic sampling as a special case. Then, a free-matrix-based time-dependent Lyapunov functional is specially constructed for stability analysis of closed-loop DCNNs, in which two extra free matrices are introduced and the available information of system states at the sampling instants are fully utilized. Accordingly, some less conservative stability conditions are established. By resorting to a matrix transformation, the design scheme for the feedback gains can be obtained. Meanwhile, the qualitative relationship between the decay rate and the upper bound of the variable sampling period is established and the maximum allowable value of the variable sampling period is determined. Finally, an illustrative example is provided to demonstrate the feasibility of the proposed stabilization criteria.

Adaptive periodic event-triggered control for missile-target interception system with finite-horizon convergence

In this paper, the optimal control problem for finite-time missile-target interception systems is posed in a finite-horizon two-player zero-sum (ZS) differential game framework using a periodic event-triggered (PET) scheme. To solve the optimal control problem, a time-varying Hamilton-Jacobi-Issac (HJI) equation and a time-dependent cost function are constructed to deal with finite-horizon constraints, and an event-based periodic adaptive dynamic programming (ADP) algorithm is employed to find the Nash equilibrium solution for the designed HJI equation. Comparing with the traditional continuous event-triggered (ET) scheme, the proposed PET scheme only verifies the event-triggered conditions at periodic sampling instants, which reduces resource consumption in monitoring and excludes the Zeno behavior. A single critic neural network (CNN) is used to implement the proposed event-based optimal control algorithm, which reduces approximate errors bust also simplifies structures. Further, an additional error term is added in the designed weight updating law to such that the terminal constraint is also minimized over time. By resorting to Lyapunov function approach, some sufficient conditions are derived to achieve the uniformly ultimately bounded (UUB) of the ET closed-loop system and the estimation weight error of CNN. Finally, a missile-target interception system is introduced to illustrate the efficiency of the presented methods.

Fractional Power Spectrum and Fractional Correlation Estimations for Nonuniform Sampling

This letter proposes new estimations of fractional power spectral density (FrPSD) and fractional correlation function (FrCF) for nonuniform sampling of random signals with non-stationarity and limited bandwidths in the fractional Fourier domain. Unlike previous works, the developed FrPSD and FrCF estimations are capable of dealing with unknown sampling instants. In order to obtain them, we first formulate approximations of FrCF and FrPSD making use of uniform sampling instants. Then we convert the approximate FrPSD to a fractional filtered version of the FrPSD for the original random signal, which does not rely on the sampling instants. With such operations, we propose the FrPSD estimation to cancel the bias of FrPSD approximation by means of a fractional inverse filtering and thereby obtain a high accuracy of it. The FrCF estimation is proposed to be the inverse fractional Fourier transform of the FrPSD, and it serves as the fractional interpolation of the previously obtained approximation of the FrCF. Simulation results show the effectiveness of the proposed estimation methods.

Sampled-Data Set Stabilization of Switched Boolean Control Networks

In this paper, the set stabilization of switched Boolean control networks (SBCNs) under sampled-data feedback control is addressed. Here, the control input is switching signal-dependent, and SBCNs can switch only at the sampling instants. First, the sampled point control invariant subset (SPCIS) of SBCNs is defined, and an algorithm is provided to obtain the largest SPCIS under arbitrary switching signal. Based on the largest SPCIS, some necessary and sufficient conditions are presented for the set stabilization of SBCNs by switching signal-dependent sampled-data (SSDSD) state feedback control. Furthermore, a constructive procedure is given to design all possible SSDSD state feedback controllers. Finally, some examples are presented to illustrate the effectiveness of the obtained results.

Consensus of Hybrid Switched Multi-Agent Systems Under Different Topologies Via Impulsive Control

The consensus problem is studied in this paper for a class of hybrid switched multi-agent systems (HSMASs) consisted of continuous-time (CT) and discrete-time (DT) subsystems via impulsive control. Due to the complex dynamic characteristics of the system, how to deal with the connection between subsystems at each switching instant is one of the confronted difficulties. Based on the Lyapunov theory, some sufficient consensus criteria are derived under arbitrary switching signals, and we show that the consensus of HSMASs can be achieved with undirected, directed, and switching connected communication networks, respectively. Furthermore, relations between impulsive and sampling instants are discussed, including overlap, stagger, and incomplete overlap. Finally, two numerical examples are presented to illustrate the effectiveness of the main results.

Design of a Fault Tolerant Sampled-Data Fuzzy Observer With Exponential Time-Varying Gains

This paper deals with the sampled-data fuzzy observer design problem with time-varying gains under the sensor fault consideration. To this end, a nonlinear system with sensor fault is represented by a Takagi-Sugeno fuzzy model with immeasurable premise variables. The sensor fault considered in this paper is assumed to be a time-varying uncertain matrix included in measurements. The observer is designed to consist of gains varying exponentially between two consecutive sampling instants, by which the equilibrium point of the estimation error dynamics is asymptotically exponentially stabilized. In addition, the observer considered in this paper is assumed not to share the same premise variable with a system. Unlike previous studies, this paper proposes a method handling this mismatched premise problem by using an H-infinity criterion. The proposed observer design condition is formulated in terms of linear matrix inequalities, which is relaxed based on a novel fuzzified Lyapunov-Krasovskii functional and a matrix inequality. Finally, two simulation examples are given to validate the effectiveness of the proposed method.

On extending transitions logic in hybrid dynamic systems based on bond graph and Petri nets combination

In order to better take into account complexity of the heterogeneous dynamics in hybrid dynamic systems (HDS); we propose an unified and integrated fuzzy logic hybrid approach extending the concept of a classical switch bond graph modelling to a logical transition that takes into account a gradation instead of abrupt behavioural changes. It allows extension of the reachable states space where we propose real physical intermediate states (fluidification) that can be maintained with a sense. We also modify the mathematical structure of ideal primitive switching element (PSTS) by proposing a formula based on predictive and effective notions that fully comply with standard bond graph syntax and semantics as well as the Petri Nets, grants a freedom of the sampling instants according to the solver. We demonstrate the effectiveness of our approach on a flow control bi-tank and its usefulness both in academia and industrial field. Finally, we discuss some ideas about discrepancy between the level of mathematical abstraction and that of the physical level.

Fractional Spectrum Analysis for Nonuniform Sampling in the Presence of Clock Jitter and Timing Offset

This paper focuses on analyzing the fractional spectrum of nonuniform sampling which is affected by clock jitter and timing offset. Both cases of single-channel and recurrent samplings with limited bandwidth in the fractional Fourier domain are considered, for which we study two types of discrete-time fractional Fourier transforms (DTFrFTs). For the first-type DTFrFTs, we perform their statistical analyses, and meanwhile establish relationships between the fractional spectra of the input and output signals of non-ideal single/multi-channel analog-to-digital converter. Such relationships indicate that the statistical mean of each fractional spectrum contains periodic replicas of the spectrum for the input signal, and these replicas are particularly modulated by the characteristic function of the perturbations introduced by the clock jitter. Moreover, we interpret the first-type DTFrFTs from the perspective of linear frequency modulation signal decomposition for nonuniform sampling. The second-type DTFrFTs serve as approximate DTFrFTs, and they especially deal with the general situation when the nonuniform sampling instants are unknown. To this end, we study modified forms of the first-type DTFrFTs with known inputs in kernels, based on which the statistical mean of the approximate fractional spectra for both cases are derived. Then we compensate the fractional spectrum bias with high accuracy by developing optimal filters that minimize the mean square error between the original and the compensated fractional spectra for both cases. Different from single-channel sampling, the compensation for recurrent sampling involves an additional step before optimal filtering, which gives better accuracy. Simulation results show that the proposed methods outperform existing methods.

Novel Equalities for Stability Analysis of Asynchronous Sampled-Data Systems

This paper is concerned with the stability analysis problems of asynchronous sampled-data systems with use of a input-delay approach, where a sampled-data system can be reformulated into a time-delay system having incremental delays. For these systems, this paper introduces a new looped-functional to utilize both integral states and their interval-normalized ones. Utilization of these two types of integral state variables in a construction of stability conditions has been effective in reducing the conservatism. Further, generalized equalities are proposed for the case utilizing these two types of integral states. The sampled-data system formulation consists of a sampled state, a system state and its derivative. Here, the sampled state between two consecutive sampling instants is a constant value and thus can be eliminated by an integration with Legendre polynomials of positive degrees. Consequently, the system formulation turns into the equalities consisting of state variables, sampled-state variables, integral state variables and their interval-normalized ones without additional slack matrices. Based on the proposed equalities, a large computational burden can be reduced while reducing the conservatism. The effectiveness of the proposed approaches is demonstrated via three numerical examples for the stability analysis of asynchronous sampled-data systems.

Distributed Tracking in Heterogeneous Networks With Asynchronous Sampled-Data Control

This article investigates distributed coordinated tracking problems of networked heterogeneous systems. Based on asynchronous sampling information, distributed sampled-data protocols are employed to realize leader-following synchronization and containment tracking in networked heterogeneous systems. In asynchronous sampled-data protocols, each node has different sampling instants with other nodes and only samples itself information at its own sampling instants. By utilizing the input-delay approach and Lyapunove–Krasovskii functional approach, some sufficient conditions for guaranteeing the coordinated tracking are presented. First, quasi-synchronization criteria are obtained for networked heterogeneous oscillator systems with a dynamic leader over the directed graph. Second, in the presence of multiple heterogeneous leaders for networked heterogeneous systems, sufficient conditions of quasi-containment tracking are derived. In a word, all followers can converge into a bounded level of convex hull spanned by the leader(s). The upper bounds of tracking errors are estimated for both quasi-synchronization and quasi-containment tracking. Finally, two numerical examples are given to verify the theoretical results.

Design of state and output feedback pole placement controller in the presence of slow-rate integrated measurement

Lab measurements in the industrial processes are either through instantaneous measurement at a specific time instance, known as Slow-Rate inStantaneous Measurement (SRSM), or through Slow-Rate inTegrated Measurement (SRTM), in which some amount of material is gradually collected for a period of time; so, the average of the collected material during that period is measured. In this paper, control of a system under SRTM is studied for the first time. Pole placement state feedback with feedforward controller is proposed so that both SRTM and conventional fast-rate output can track their step reference input. This controller comprises a periodically time-varying gain and an observer to estimate the slow-rate instantaneous state variable at the sampling instances. An observability condition is studied, and a modified Kalman filter is established to estimate slow-rate instantaneous state variable using SRTM. In the next step, two modified pole placement output feedback controllers are designed using SRTM. In the first control system, the aim is to track a slow-rate integrated reference input. In the second controller, fast-rate reference input is introduced to the control system. The performance of the proposed methods is evaluated through both simulation study in a pH neutralization process plant and experimental implementation on a laboratory scale Quadruple Tank pilot plant.