Maximum Sampling Period Research Articles

Distributed Dynamic Event-Triggered Control for Voltage Recovery in Islanded Microgrids by Using Artificial Delays.

This article tackles secondary voltage recovery problem in islanded microgrids with the aim of reducing communication frequency among distributed generation (DG) units, while maintaining desired performance and saving communication network workload. To pursue this objective, a distributed proportional-integral-derivative controller is first introduced, whose sampled-data implementation is enabled by leveraging the finite-difference approximation for the derivative action, which leads to a distributed proportional-integral-retarded (PIR) controller with a small enough sampling period . Then, the resulting fully distributed PIR control law is combined with a dynamic event-triggered mechanism (DETM), which embeds Zeno-freeness property and avoids the requirement of continuous transmission in triggering process. Thus, the communication burden is significantly mitigated and the waste of communication resources is avoided. By exploiting Lyapunov-Krasovkii method, we derive exponential stability conditions expressed as linear matrix inequalities (LMIs), whose solution allows evaluating the maximum sampling period and DETM parameters preserving the stability of the microgrid. A thorough numerical analysis, carried out on the standard IEEE 14-bus test system, confirms the theoretical derivation.

К выбору периода дискретизации нелинейных гибридных систем управления

Hybrid systems are often used in various technical applications, such as robotics, aviation, space, energy, etc. The emergence of hybrid control systems is due to the use of computers to implement control laws, including nonlinear ones. Digital means cannot implement continuous control laws. However, the known methods of design, especially of nonlinear systems, lead precisely to continuous controls, which caused the need to discretize the continuous control with the largest possible period. Solving the problem of determining the maximum permissible sampling period of a nonlinear control system is a rather complex stage of its creation. In this article the problem of definition of the maximum allowed sample period of the nonlinear hybrid system control and its dependence on the module of the maximum eigenvalue of the functional matrix of quasilinear model of the continuous system is also considered. The nonlinear hybrid system is created by discretizing the control of the nonlinear continuous system. This continuous system is synthesized using the algebraic polynomial and matrix method of the nonlinear control systems design in which quasilinear models are used. It has been is established that the value of the maximum permissible sample period depends not only on the module of the maximum eigenvalue, but also on initial conditions and external influences. These dependences are complex and it is difficult to find them theoretically. Experimentally, based on the example of the specific nonlinear hybrid control system it is shown that eigenvalues smaller on the module lead to larger values of the maximum of the permissible sample period. The problem of choosing the sample period of control laws of the real hybrid control systems can be solved in the similar way based on a compromise between the system high-speed performance and the sample period.

A Unified Distributed Digital Control Architecture for Secondary Control in Islanded Microgrids

Distributed control theory has gaining momentum for the global stability of modern Micro-grids (MGs), which can be hence regarded as a cyber-physical energy systems in a networked control systems perspective. Besides the benefits, the control over networks poses several issues and, among them, how to preserve stability despite the unavoidable sampling process is one of the most crucial to be addressed for the implementation in real-world scenarios. The paper addresses this concern by introducing a unified digital control architecture for secondary control of inverter-based MGs working in islanded mode, where both frequency and voltage regulations are ensured via fully-distributed sampled-data control protocols. By choosing a small-enough sampling period h > 0, the proposed strategies can ensure a reduction of the communication burden by avoiding a continuous interactions among electrical entities, thus enhancing the efficiency of the MG. Exponential stability of frequency and voltage closed-loop systems is analytically proven via Lyapunov-Krasovskii theory. The derived stability conditions are in the form of Linear Matrix Inequalities (LMIs) whose solution provides the maximum sampling period preserving the global stability. Simulation results, carried out in MATLAB/SimPower Systems, confirm the theoretical derivation.

Integrated Stabilizing Control for Sampled-Data NCSs With Intermittent Observation and Multiple Random Transmission Delays

In this paper, we study sampled-data networked control systems (NCSs) that operate over communication networks with multi-path channels. Due to limited bandwidth power, the delivery of observed state signals from the sensor to the controller may suffer packet loss possibility, which leads to intermittent observation. An unreliable multi-path routing network is responsible for the transmission of control signals from the controller to the actuator, subject to random transmission delays. These communication problems lead to degradation in system performance, which may even cause instability. By utilizing an idle-time-based scheduling policy with a pre-defined deadline constraint on the actuator side, we transform the affiliated integrated system into a stochastic model with constant input delay. For such implementation, we propose a set of Riccati-type stabilization conditions, which are necessary and sufficient. It is remarkable that the stabilizing control policy is designed based on the feedback of the optimal estimate with minimum mean square error. Moreover, for the scalar system, we study the uniqueness and existence property of the maximum sampling period, and derive its close form representation in terms of system parameters, service capability and packet dropout rate.

Synchronization sampled-data control of uncertain neural networks under an asymmetric Lyapunov–Krasovskii functional method

This paper investigates the synchronization control of neural networks (NNs) considering parameter uncertainties by utilizing an improved asymmetric Lyapunov–Krasovskii functional (ALKF) method. Firstly, an uncertain NNs model with discrete and distributed delays is developed. To synchronize the master–slave system, a memory sampled-data controller is designed. Secondly, an improved ALKF is constructed, in which the positive-definite and symmetric restrictions of matrices are relaxed. Furthermore, improved synchronization criteria are established by linear matrix inequalities (LMIs), which are based on the ALKF method and the integral inequality technique. Finally, two simulation examples are conducted to demonstrate the feasibility and superiority of the established stability conditions in reaching a maximum sampling period.

On the stability of nonlinear sampled-data systems and their continuous-time limits

This work deals with the stability analysis of nonlinear sampled-data systems under nonuniform sampling. It establishes novel relationships between specific stability properties of the exact discrete-time model and stability properties of the continuous-time system that is obtained when the maximum admissible sampling period tends to zero. These results can be used to infer stability properties for the sampled-data system by direct inspection of the stability of the mentioned continuous-time system, a task which is typically easier than the analysis of the closed-loop sampled-data system. Compared to the literature, our results allow to prove stronger (asymptotic) sampled-data stability properties for nonlinear systems in cases for which existing results only guarantee practical stability.

Worries about the COVID-19 pandemic and the dynamic regulation of emotions in the general population: A network analysis study

BackgroundThe impact of the COVID-19 pandemic on mental health has been widely reported. Yet, little remains known about the psychological mechanisms associated with changes in mental well-being during the currently ongoing pandemic. MethodsHere, we use a network analysis to unravel complex relationships between COVID-19 related stressors and emotional states during the initial phase of the COVID-19 (April 2020). Adults living in the Netherlands and Belgium (N = 1145, age 16 and older) (repeatedly) completed an online survey (approximate survey completion rate = 66.2%) about COVID-19 (over a 5-day maximum sampling period). ResultsPartial correlations and contemporaneous networks illustrated that worries about the impact of the COVID-19 pandemic were primarily associated with distress and mood ratings, which were subsequently associated with other indicators of well-being. Temporal network analysis revealed that COVID-19 worries were selectively associated with the reciprocal interplay between high distress and low positive mood (https://osf.io/vtdkr/). LimitationsShort-term temporal intervals were evaluated. A small percentage of participants completed the survey repeatedly (35.63% of the total sample), yielding to a relatively small sample size for repeated measures online research. The sample was self-selected. ConclusionThese results may point to potential mechanisms by which initial worries about the COVID-19 pandemic may have impacted psychological well-being.

Distributed bipartite consensus of linear multi‐agent systems based on periodic event‐triggered mechanism

AbstractThis article considers the bipartite event‐triggered consensus problem for linear multi‐agent systems based on periodic sampling data. The cooperative and antagonistic communications are considered at the same time. The bipartite time‐triggered consensus with maximum sampling period is first addressed. Then, the bipartite periodic event‐triggered control strategy with two event‐triggered mechanisms is designed. Compared with previous control schemes, the proposed control method can realize intermittent communication, intermittent controller update and intermittent triggering condition monitoring. Moreover, considering the constraint of limited data rate, a quantized consensus with both state and input quantization is taken into account. The Zeno behavior is completely avoided due to the fact that the sampling time can be taken as the lower bound of trigger interval. Finally, three illustrative examples are provided to demonstrate the effectiveness of the proposed methods.

Stabilization Criteria for T–S Fuzzy Systems With Multiplicative Sampled-Data Control Gain Uncertainties

This study concerns the stabilization criteria of Takagi–Sugeno (T–S) fuzzy systems under the memory-based sampled-data control. Contrasted to the traditional sampled-data control strategy, a more general control scheme that admits the signal transmission delay and the multiplicative control gain uncertainties is designed. In order to indicate the perturbations of control gain, the Bernoulli sequence is applied to the designed control scheme. At the same time, the membership function dependent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index is introduced to attenuate the disturbances of continuous-time T–S fuzzy systems for the first time. By utilizing the novel <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> performance index together with the appropriate Lyapunov–Krasovskii functional, including the information of sampling period and signal transmission delay, the sufficient conditions are derived in the framework of linear matrix inequalities. These conditions ensure the stabilization of concerned T–S fuzzy systems and enlarging the maximum sampling period. At last, the advantages of the derived results are shown by the numerical examples.

Sampled‐data‐based H∞ load frequency control for power systems with wind power

AbstractLoad disturbances, the intermittent generation of wind power, and the uncertainty of sampling period will significantly affect the frequency stability of power system. This paper presents a sampled‐data‐based load frequency control (LFC) scheme for power systems with wind power (PSWPs), which aims to guarantee the stable operation of the systems under a sampling period as large as possible while retaining the desired robust performance. First, by considering the feature that power system plant operates in continuous‐time domain and LFC controller operates in discrete‐time domain, the closed‐loop PSWPs installed with a PI‐type LFC controller is modeled as sampled‐data control system with aperiodic samplings. Second, by utilizing an augmented two‐side looped Lyapunov functional and the linear matrix inequality (LMI), two sampling‐interval‐dependent stability criteria with less conservatism are derived for the studied systems, which guarantee that the presented LFC scheme operates in a large sampling period. Then, based on proposed stability condition, a sampled‐data‐based PI‐type LFC controller with the consideration of sampling period and performance index is obtained. Following this, an algorithm is given to obtain the gain of sampled‐data‐based PI‐type LFC controller and the admissible maximum sampling period while preserving the desired robust performance. Finally, case studies are carried out on the one‐area power system and three‐area PSWPs. The simulation results demonstrate the effectiveness of the presented LFC scheme, and robustness against load disturbances, wind power fluctuations and sampling period. It also shows that the designed LFC scheme can tolerate a larger sampling period while preserving the desired performance.

Hidden Markov model based non-fragile sampled-data control design for mode-dependent fuzzy systems with actuator faults

This paper investigates the dissipativity-based asynchronous sampled-data control design for a class of Takagi–Sugeno fuzzy Markovian jump systems along with time delay, gain fluctuations, and actuator failures. To do this, the hidden Markov model is introduced to describe the phenomenon of asynchronization between the controller and the given fuzzy jump systems. Then, a novel mode-dependent Lyapunov–Krasovskii functional is constructed to achieve the stability conditions and expand the maximum sampling period of fuzzy systems. The main purpose of this study is to design the asynchronous non-fragile reliable control with sampled-data information such that the mode-dependent fuzzy system is stochastically stable and possesses the dissipativity performance. For this, a sufficient condition is derived for the proposed system in the form of linear matrix inequalities. Meanwhile, the less conservative results and the desired controller are attained by solving the inequalities. At last, the validity and the superiority of our design technique are demonstrated by numerical examples.

Model‐based periodic event‐triggered stabilization for continuous‐time stochastic nonlinear systems

AbstractIn this paper, we investigate a model‐based periodic event‐triggered control framework for continuous‐time stochastic nonlinear systems. In this framework, an auxiliary approximate discrete‐time model of stochastic nonlinear systems is constructed in the controller module, which is utilized not only to design a discrete‐time controller but also as a state predictor within trigger intervals. This discrete controller design approach, the strategy of state prediction, and the periodic detection strategy for the trigger rule not only provide a manner of more direct and easier implementation on the digital platform but also effectively reduce the communication load while a satisfactory control performance is maintained. Additionally, the mean‐square exponentially stabilization for continuous‐time stochastic nonlinear systems is achieved, in which a guideline for determining the maximum admissible sampling period is provided and the periodic event trigger rule is designed. The final numerical simulation also supports the effectiveness of our proposed framework.

Onset and stabilization of delay-induced instabilities in piezoelectric digital vibration absorbers

The stability of a piezoelectric structure controlled by a digital vibration absorber emulating a shunt circuit is investigated in this work. The formalism of feedback control theory is used to demonstrate that systems with a low electromechanical coupling are prone to delay-induced instabilities entailed by the sampling procedure of the digital unit. An explicit relation is derived between the effective electromechanical coupling factor and the maximum sampling period guaranteeing a stable controlled system. Since this sampling period may be impractically small, a simple modification procedure of the emulated admittance of the shunt circuit is proposed in order to counteract the effect of delays by anticipation. The theoretical developments are experimentally validated on a clamped-free piezoelectric beam.

Semiglobal exponential input-to-state stability of sampled-data systems based on approximate discrete-time models

Exact discrete-time models of nonlinear systems are difficult or impossible to obtain, and hence approximate models may be employed for control design. Most existing results provide conditions under which the stability of the approximate model in closed-loop carries over to the stability of the (unknown) exact model but only in a practical sense, i.e. the trajectories of the closed-loop system are ensured to converge to a bounded region whose size can be made as small as desired by limiting the maximum sampling period. In addition, some very stringent conditions exist for the exact model to exhibit exactly the same type of asymptotic stability as the approximate model. In this context, our main contribution consists in providing less stringent conditions by considering semiglobal exponential input-to-state stability (SE-ISS), where the inputs can successfully represent state-measurement and actuation errors. These conditions are based on establishing SE-ISS for an adequate approximate model and are applicable both under uniform and nonuniform sampling. As a second contribution, we show that explicit Runge–Kutta models satisfy our conditions and can hence be employed. An example of control design for stabilization based on approximate discrete-time models is also given.

Aperiodic Sampled-data Control for Exponential Synchronization of Chaotic Delayed Neural Networks with Exponentially Decaying Gain

This paper studies the exponential synchronization of chaotic delayed neural networks (CDNNs) under aperiodic sampled-data control. First, an aperiodic sampled-data controller with exponentially decaying gain is designed to enlarge the maximum sampling period and the maximum allowable delay while still preserving the stability of the closed-loop system. Then, a novel time-dependent Lyapunov functional that consists of the information of the exponential decay rate η is elaborately designed to analyze the stability of the closed-loop system instead of using the common “change of coordinates” method.With the aid of Lyapunov theory and some inequality techniques, the sufficient conditions are established to guarantee the exponential synchronization of master-slave CDNNs. Based on matrix transformation, the equivalent conditions in LMI form are established to design the feedback gain. Finally, an illustrative example is given to demonstrate the effectiveness of the proposed controller and the obtained synchronization criteria.

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.

Dissipativity-Based Sampled-Data Control for Fuzzy Switched Markovian Jump Systems

In this article, the dissipativity-based sampled-data control problem is studied for the fuzzy switched Markovian jump systems (FSMJSs). By considering the problem of the asynchronous switching caused by the subsystems' switching occurred during the sampling intervals, constructing novel time-dependent Lyapunov functional, and using average dwell time (ADT) approach, sufficient mean-square exponential stability criteria, and strictly ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> )-γ- dissipativity criteria are proposed under the constraints that the maximum sampling period is no larger than the dwell-time between the transition rates switching instants. Meanwhile, a relationship between ADT and sampling period is revealed for FSMJSs. Based on the strictly ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Q</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">S</i> , <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</i> )-γ- dissipativity criteria, the sampled-data controller is designed for FSMJSs. A circuit simulation example is provided to illustrate the effectiveness of the proposed method.

Consensus of Upper-Triangular Multiagent Systems With Sampled and Delayed Measurements via Output Feedback

This paper investigates the sampled-delayed-data-based consensus problem for upper-triangular multiagent nonlinear systems via output feedback. The sampled-delayed outputs are directly utilized to design observer-based piecewise continuous output feedback controllers. By properly constructing a Lyapunov–Krasovskii function, we obtain a parametric sequence and prove that it is convergent. Then, sufficient conditions are presented to guarantee the considered multiagent systems achieve global and exponential consensus. We also give the maximum admissible sampling period and transmission delay. Finally, simulation results show the validity and effectiveness of the newly proposed methods.

A sampled-data control problem of neural-network-based systems using an improved free-matrix-based inequality

In this work, a sampled-data control problem for neural-network-based systems with an optimal guaranteed cost is investigated. By constructing suitable time-dependent functionals and utilizing an improved free-matrix-based integral inequality, a sampled-data stability criterion for neural-network-based systems is derived. Based on a first result, a sampled-data controller design method for neural-network-based systems that meets the maximum sampling period and minimum guaranteed cost performance is proposed. The superiority and validity of the results will be verified by comparing with the existing results in a numerical example.

Global sampled-data output feedback stabilization for a class of switched stochastic nonlinear systems with quantized input and unknown output gain

This paper aims at addressing the sampled-data output feedback control problem for a class of uncertain switched stochastic nonlinear systems, whose control input is quantized by a logarithmic quantizer and the output gain cannot be precisely known. We design a compensator with the quantized information. With the help of the feedback domination approach and the backstepping design method, a sampled-data output feedback controller is constructed with appropriate design parameters and a maximum sampling period to guarantee the global exponential stability in mean square of the closed-loop system under arbitrary switching. Finally, a numerical example is given to illustrate the effectiveness of the proposed scheme.