This article develops a robust economic model predictive control (EMPC) scheme for load frequency control (LFC) in multiarea smart grids with load disturbances. The proposed approach integrates the optimization of the cost and the utilization efficiency of network resources within a single EMPC framework. An economic cost function, including the generation cost and the LFC cost, is designed to minimize the involved costs. To optimize the utilization efficiency of network resources while maintaining satisfactory control performance, a new dynamic memory event-triggered mechanism (DMETM) is designed. By introducing a dynamic variable and an adaptively adjusting variable, the proposed DMETM adaptively adjusts triggering conditions using historical triggering information, thereby conserving network resources and reducing communication burden. A “min–max” EMPC optimization problem (OP) is developed, and it is transformed into an auxiliary OP based on linear matrix inequalities. The recursive feasibility of the auxiliary OP is proved, and the closed-loop system is also proven to satisfy input-to-state practical stability, guaranteeing robustness against the load disturbances. At last, a case study on a three-area smart grids verifies the effectiveness and the advantages of the proposed DMETM-based EMPC scheme and demonstrates its potential in enhancing the optimization of the economic cost and the utilization efficiency of network resources.

This paper mainly focuses on fixed time control for interlayer synchronism problem under voltage-flux–time (VFT) delay deplux memristive neural networks (DDMNNs). Distinct from most previously reported achievements, continuous memristive VFT neural networks (MMNs) field with$2^{2{n^{2}} + n}$variables are considered, where the memristor is considered as a continuous time-varying uncertain parameter, and n is the number of states in DDMNNs. This memristor is a type of continuous system built on the HP memristor. To synchronize VFT DDMNNs, a fixed time control policy is proposed for interlayer synchronism of flux and voltage values under the VFT DDMNNs. According to the second method of Lyapunov, selecting appropriate Lyapunov functionals and using inequality techniques, the structure and parameters of a kind of fixed time controller are designed, and interlayer synchronism criteria for DDMNNs are obtained. Finally, a secure communication scheme based on interlayer synchronism is designed. It is found that the fixed settling time is relative to the constructive of DDMNNs and the parameters of the fixed time controller. Note to Practitioners—This work solves the fixed time interlayer synchronism control problem of VFT DDMNNs, which can be applied to some practical scenarios, such as information security communication and image encryption. When transmitting signals in computer networks, for security, encryption mechanisms are usually added to network communication protocols to achieve secure communication. In some encryption applications, there are special requirements for speed of encryption and decryption, which requires reducing encryption and decryption time and improving efficiency of encryption. This work provides a fixed time control strategy which can achieve synchrony for VFT DDMNNs under controllable time, thereby achieving encryption under controllable time. Meanwhile, improve encryption efficiency in secure communication.

The resilient control design for wireless networked control systems (WNCSs) under Denial-of-Service (DoS) attacks is investigated based on the sampled-data theory in this study. Firstly, by employing a logic processor module in the control center, WNCSs under DoS attacks are modeled as aperiodic sampled-data systems (SDSs). This integrates the duration of DoS attacks into the sampling intervals, simplifying the controller design without the need for additional handling of DoS attacks. Then, a sawtooth-characteristic-based hierarchical integral inequality is presented to leverage the underused sampling sawtooth characteristic in existing studies in WNCSs under DoS attacks. Next, a high-order two-sided looped-functional caters for the proposed hierarchical integral inequality is constructed and the sawtooth-dependent free-weighting matrices are introduced into the constraint of system equation to further preserve the information of SDSs. These improvements of methodological promote a reduction in the conservatism of the stability criteria. Consequently, a resilient controller design scheme is presented based on the system substitution-based de-coupling method, resulting in a controller that exhibits enhanced counteraction against DoS attacks. The efficacy of this controller design scheme is demonstrated through a satellite control system and a load frequency control power system, showcasing the advantages of the resilient controller. Note to Practitioners—This research offers significant insights into enhancing the resilience of WNCSs against DoS attacks, which is a prevalent challenge in industrial network security. The developed solution is particularly beneficial in industries where maintaining uninterrupted control communications is critical, such as satellite systems and power systems that are vulnerable to malicious DoS attacks. The logic processor module provides a practical approach to dynamically monitor the strength and duration of DoS attacks. Based on this, the relevant system is re-modeled as an aperiodic SDS. This integration with the existing sampling theories ensures that the system makes good use of current technologies and facilitates the design of resilient controllers that can withstand DoS attacks. On the one hand, the application of this enhanced control design allows for a more robust system that maintains functionality under cyber attack conditions, thereby protecting critical operations and potentially reducing downtime and associated costs. On the other hand, this approach reduces the conservatism of controller design guidelines, allows for more efficient utilization of network resources, and improves system response. However, this approach relies heavily on the accuracy and timeliness of the logic processor’s response to DoS attacks. This may not be entirely reliable in environments with highly irregular or complex network threats.

This paper uses a proportional-integral (PI) controller to achieve the exponential synchronization of chaotic Lur’e systems under aperiodic sampled-data control. First of all, in order to achieve synchronization of the chaotic Lur’e systems, an aperiodic sampled-data PI controller is constructed. The controller in question incorporates a greater amount of information derived from the sampling sequence than the sampled-data proportional controller. Subsequently, a virtual variable is introduced based on an intermediate variable, thereby constructing a dimension-enhanced synchronization error system. A novel criterion is developed based on virtual variable-related equations for the design of sampled-data PI controllers, with the objective of achieving larger sampling periods and exponential convergence rates in the synchronization process. In the next, a numerical example of neural networks is presented, demonstrating how the developed method in this paper enhances the dynamic performance of the synchronization process in comparison to existing methods. Finally, the developed method is applied to Chua’s circuits, where the real-circuit experiment is made to show its effectiveness.

This article investigates the $H_{\infty }$ -based tracking control problem for nonlinear systems through the Takagi-Sugeno (T-S) fuzzy technique. A nonuniform sampled-time-dependent functional (NSTDF) is proposed, which removes the constraints of the conventional looped functional (LF) and relaxes the condition of the functional derivative. Combining the NSTDF with $H_{\infty }$ theory, a novel theorem for $H_{\infty }$ performance analysis of sampled-data systems is given, which loosens the positive-definite constraint on Lyapunov matrices in traditional LFs. By introducing the error integral state, an augmented system is constructed, and a proportional-integral (PI)-type controller that incorporates the external disturbance, transmission delay, and packet dropouts is designed to enable the tracking control. Thus, the $H_{\infty }$ -based tracking control issue is converted into an $H_{\infty }$ -based control problem for the augmented system, and the control conditions are derived via the proposed methods. Finally, the wind energy conversion system (WECS) and Rossler's system clarify the feasibility and merits of the provided methods.

The frequency stability of multiarea power systems is guaranteed by networked load frequency control (LFC). Time delays due to occasional congestions/attacks in the LFC are often much longer than those from signal transmissions during normal communication, which invalidates the previous stability assessment methods. In this article, a novel stability analysis method for this scenario via a segmented delay description and a switched system is proposed. First, a two-piecewise function is used to describe multisource-induced delays, including large delays under occasional harsh network conditions and small delays under smooth network conditions; thus, a multiarea LFC model with multisource-induced delay is established. The stability criteria, which is based on switched system theory, reveals the relationship between delay characteristics and system stability. Finally, the proposed method is used to assess the delay tolerance of the LFC in traditional/deregulated environments. The results show that even with a large delay causing instability, as long as it meets certain frequency and duration constraints, the LFC remains stable. This novel discovery reflects the essential improvements of the proposed method and is useful for designing better control strategies.

Smart grids usually apply digital load frequency controller to regulate the frequency via the wide-area communication network, where the data sampling and transmission delay of the signal transmission may degrade the frequency control performance. Plus, the inherent nonlinearity of frequency regulate may weaken the control performance. In this paper, a digital PID-type load frequency control (LFC) scheme based on warm up gray wolf optimization algorithm is designed for large-scale renewable energy grid-connected smart grids, considering the influence of data sampling, transmission delay and nonlinearity. First, a new digital PID-type LFC model considering data sampling, transmission delay and nonlinearity is established. Second, a novel warm-up gray wolf optimization method is proposed to optimize the parameters of the digital PID controller. The method can fully consider the nonlinearity of LFC and the influence of time delay and sampling, and the PID parameters with optimal control performance can be derived by taking the control performance as the objective function. Finally, simulation tests are undertaken on the three areas LFC systems. The simulation results illustrate the effectiveness and superiority of the proposed LFC scheme, and the necessity of control scheme design to consider the data sampling, transmission delay and nonlinearity.

The storage sources in auxiliary frequency regulation service (AFRS) for load frequency control (LFC) have a fast response time and are effective in smoothing wind power output. In this article, the disturbance suppression ability for delayed LFC is evaluated considering the participation of electric vehicle (EV) aggregators and redox flow batteries (RFBs)-based AFRS. First, a model for the delayed LFC with wind power is constructed, incorporating the EV aggregator and RFB participation. A criterion for evaluating the disturbance suppression ability of delayed LFC is presented, incorporating more system information to reduce conservativeness compared to existing methods. Finally, case studies show that the introduction of RFBs improves the disturbance suppression ability and the delay tolerance ability of LFC. Simulation and experimental tests demonstrate that the theoretical improvement produces more accurate evaluation results.

The time delay, disturbances, and parameters uncertainties brought by open communication networks and renewable energy source threaten the stable operation of the frequency control system (FCS) in microgrids (MGs). Plus, the low inertia of MGs exacerbates frequency fluctuations. In this article, the codesign of$ H_{\infty }$robust controllers for secondary frequency control (SFC) and virtual inertia control (VIC) in the delay-dependent FCS of MG is presented. First, the FCS of MG considering the VIC under the influence of the time delay is established. Second, based on Lyapunov stability theory, an$ H_{\infty }$performance analysis method is proposed for the FCS of MG with the time-varying delay. Then, with robust performance index as the design condition, the grey wolf optimizer is used to carry out the codesign of the SFC and VIC. Finally, the simulation test proves that the proposed control strategy can effectively codesign the SFC and VIC. The designed robust controllers can effectively deal with the problems of low inertia, time delay, disturbance, and parameters uncertainty in MG frequency control.

This article investigates the multistep model predictive load frequency control problem for multiarea smart grids (MASGs) with wind power and air conditioning loads under false data injection attack, where a control performance standards (CPSs)-dependent dynamic event-triggered mechanism (DETM) is considered to manage the data transmission. The CPSs-dependent DETM contains an adaptive adjustment variable related to two CPSs on the frequency deviation and area control error, which helps it to effectively reduce unnecessary transmission of data packets while promising the required frequency and tie-lie power of the MASGs. Two off-line optimization problems (OPs) are applied to design the terminal constraint set (TCS) and the approximate one step sets, respectively. The control laws designed by an online OP are utilized outside of the TCS. A CPSs-dependent DETM-based multistep MPC algorithm is proposed on the basis of the three OPs. The analyses of the feasibility of the algorithm and the stability of the closed-loop system are given. The effectiveness and superiority of the designed CPSs-dependent DETM and dynamic event-based multistep MPC algorithm are verified in two case studies of two-area and three-area smart grids.

The aim of this article is to investigate the stability of sampled-data systems (SDSs) by introducing a sawtooth-characteristic-based hierarchical integral inequality (SCBHII) and to obtain the maximum allowable sampling period that maintains the stability of the system. First, by associating the sawtooth characteristics of the input delay in SDSs with free matrices, an SCBHII is proposed; its accuracy improves as the hierarchy increases. Subsequently, a high-order two-sided looped-functional, which considers both the sampling multi-integral states and the sawtooth pattern, is introduced to cater to the aforementioned inequality. In addition, the system variables are augmented by sawtooth pattern-related terms, which eliminates the need for additional secondary processing when determining the negative-definiteness of derivatives with high-order terms. By combining the high-order two-sided looped-functional with the proposed SCBHII, a stability criterion for SDSs with reduced conservatism is achieved, presented in the form of linear matrix inequalities. The proposed inequality technique and the stability criterion are shown to be effective and superior through three numerical examples and a real-world simplified power market model.

Load frequency control (LFC) is crucial for ensuring the frequency stability of power system, and its control performance is often affected by nonlinearities in devices and multisource-induced hybrid delays in control signal transmission networks. This article investigates the LFC performance analysis and improvement of power systems under the nonlinearities and hybrid delays. First, the nonlinear part is approximated by a Takagi–Sugeno (T–S) fuzzy model and the hybrid delay is divided into two regions, thus establishing a T–S fuzzy LFC model with hybrid delays. Then, based on switched system theory, a delay-dependent weighted$H_\infty$performance analysis criterion for LFC system is proposed, giving the necessary conditions to achieve a certain robustness of the system against disturbances. On this basis, a controller design method is proposed to ensure the system have the optimal level of disturbance rejection under the designed controller. Finally, case studies based on single-area and three-area LFC demonstrate that, compared with previous methods, the proposed method can obtain a larger allowable upper bound of delays and better$H_\infty$performance estimation. Based on this, the designed controller enhances the robust performance of LFC, thereby ensuring the stable operation of power systems under nonlinearities and hybrid delays.

The future power systems with renewable energy sources (RESs) and electric vehicles (EVs) are usually subject to strong uncertainties in system parameters, communication network, and disturbances, which may severely degrade the frequency control performance. This article proposes a performance enhancing load frequency control (LFC) scheme for future power systems with strong uncertainties based on the Kalman-filter (KF) control compensation method. First, the LFC of a multiarea interconnected power system (MAIPS) with RESs and EVs is conceptualized as a linear stochastic and discrete model. Then, KF is introduced to evaluate the unmeasurable states of the LFC, so as to design an additional KF-based state feedback control law. The KF-based control loop serves as compensation for the original controller of the LFC system. Next, an optimal compensation control gain of the KF-based control loop is derived based on a differential optimal calculation method to enhance the control performance of the LFC of MAIPS under strong uncertainties. Finally, simulation results are conducted on a typical three-area LFC systems that integrate RESs and EVs, which demonstrate that the proposed control strategy can provide better control performance and robustness than the original LFC strategy when the systems are subject to strong uncertainties.

This paper investigates the problem of stability analysis for the uncertain linear systems with time-varying delay. Firstly, an uncertain linear system model considering time-varying delay is established. Then based on the Lyapunov-Krasovskii functional (LKF) method, a novel robust delay-dependent stability criterion is proposed, which is benefited by a new augmented LKF with more effective time-delay information and the use of a tighter integral inequality to estimate functional derivative. The stability criterion obtained is less conservative. At last, a numerical example shows the superiority and effectiveness that the method used in this paper.

This work focuses on the input-to-state stability (ISS) of digital filters with disturbances and time-varying delay in the presence of generalized overflow arithmetic. First, an extra-freedom-based lemma is derived to consider the information about the overflow arithmetic connecting the digital filter's state. Then, a novel delay-dependent ISS criterion of the digital filter is established based on the given lemma, which has less conservatism than the criterion described in the existing results. At last, the feasibility and advantages of the presented ISS analysis methods are demonstrated using a numerical simulation.

This article presents a novel reconstructed model for the delayed load frequency control (LFC) schemes considering wind power, which aims to improve the computational efficiency for PID controllers while retaining their dynamic performance. Via fully exploiting system states influenced by time delays directly, this novel reconstructed method is proposed with a controller isolated. Hence, when the PID controllers are unknown, the stability criterion based on this model can resolve controller gains with less time consumed. For given PID gains, this model can be employed to establish criteria for stability analysis, which can realize the tradeoff between the calculation accuracy and efficiency. The case study is first based on a two-area traditional LFC system to validate the merits of a novel reconstructed model, including accurately estimating the influence of time delay on system frequency stability with increased computational capability. Then, under traditional and deregulated environments, case studies are carried out on the two-area and three-area schemes, respectively. Through the novel reconstructed model, the efficiency of obtaining controller parameters is highly improved while their robustness against the random wind power, tie-line power changes, inertial reductions, and time delays remains almost unchanged.

This article proposesa control performance standard (CPS)-based fuzzy event-triggered scheme for load frequency control (LFC) of power systems with a limited communication bandwidth. First, a CPS-based fuzzy LFC system is established to reduce the wear and tear of the generating unit equipment. Then, based on the Lyapunov stability theory, a stability criterion of the LFC system is proposed to ensure the stable operation of the LFC system, which considers the threshold parameter of the event-triggered condition and the fuzzy gain in the fuzzy LFC system. Next, based on the stability criterion and the Gaussian-type curve-fitting method, a functional expression between the fuzzy gain and the threshold parameter is obtained. According to the expression, the threshold parameter is updated in real time with the change of fuzzy gain, so as to further save usage of the communication network bandwidth. Case studies based on a one-area power system and an IEEE 39-bus benchmark test system are undertaken. Simulation results show that the proposed scheme achieves three objectives: 1) to comply with CPS1 and CPS2 in the North American Electric Reliability Council; 2) to reduce wear and tear of the generating unit equipment; and 3) tosave more communication network resources.

Uncertain transmission delays, sampling periods, parameters uncertainties regarding the power system, load fluctuations, and the intermittent generation of renewable energy sources (RESs) will significantly influence a power system's frequency. This article designs a robust delay-dependent PI-based load frequency control (LFC) scheme for a power system based on sampled-data control. First, a sampled-data-based delay-dependent LFC model of power system is constructed. Then, by applying the Lyapunov theory, and the linear matrix inequality technique, a novel stability criterion is developed for the LFC of the power system by considering the sampling period, and transmission delay of the communication network, which ensures that the proposed scheme operates in large sampling periods, and under transmission delays. Next, an exponential decay rate (EDR) is introduced to guide the design of a robust PI-based LFC scheme. The LFC scheme with robustness is designed by setting a small EDR. The values of EDR are adjusted by the given robust performance evaluation conditions of parameter uncertainties, and$H_\infty$performance. Finally, case studies are carried out based on a one-area power system, and a three-area power system with RESs. Simulation results show that the proposed LFC scheme performs strong robustness against parameter uncertainties regarding the power system, and communication network, load fluctuations, and the intermittent generation of RESs.