The stabilization problem of delay systems is studied under the delay-dependent impulsive control. The main contributions of this technical note are that, for one thing, it shows that time delays in ...impulse term may contribute to the stabilization of delay systems, that is, a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks; for another, it shows the robustness of impulsive control, that is, the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization. In this technical note, from impulsive control point of view we firstly propose an impulsive delay inequality. Then we apply it to the delay systems which may be originally unstable, and derive some delay-dependent impulsive control criteria to ensure the stabilization of the addressed systems. The effectiveness of the proposed strategy is evidenced by two illustrative examples.
Load frequency control (LFC) requires transmitting measurements from remote RTUs to control center and control signals from the control center to plant side. Constant delays exist in the conventional ...dedicated communication channels, while the future usage of open communication networks will introduce time-varying delays. Those delays would degrade the dynamic performance of LFC and in the worst case, cause instability. The maximal delay time which allows an LFC scheme embedded with controllers to retain stable is defined as the delay margin. This paper investigates the delay-dependent stability of the LFC scheme by using Lyaponuv-theory based delay-dependent criterion and linear matrix inequalities (LMIs) techniques. Case studies are carried out based on one-area and multi-area LFC schemes installed with proportional-integral (PI) controllers, respectively. Relationship between the gains of PI controller and the delay margin of the LFC scheme are investigated and results obtained can be used to tune the PI controllers to achieve a compromise between the dynamic performance and the delay margin. Both constant and time-varying delays are considered. The effectiveness of the criterion used is verified by simulation studies.
Load frequency control (LFC) of modern power systems tends to employ open communication networks to transmit measurement/control signals, which makes the LFC scheme more vulnerable to random time ...delays and time-delay attacks (TDAs). In this article, a resilient and active time-delay-compensation-based LFC scheme is proposed to compensate the random time delays and TDAs. At first, a state observer is employed to estimate the state of the LFC system. Then, a networked predictive control method is used to predict the control signals of the system in future moments. Next, an evaluation and compensation scheme for random time delays and TDAs is constructed in the actuator side of the LFC scheme based on the updating period of the actuator and the timestamp technique. Due to the stochastic characteristics of the random time delays or TDAs, the stability condition of the proposed scheme is developed with the aid of the mean-square stability theory. Moreover, a dual-loop open communication is employed in the proposed scheme to improve the reliability and resilience. At last, simulation and experiment tests are undertaken to demonstrate the effectiveness of the proposed scheme.
The extensive usage of open communication networks in power system control causes inevitable time delays. This paper studies impacts of such delays on the stability of one-area and two-area load ...frequency control (LFC) systems and proposes an analytical method to determine delay margins, the upper bound on the delay for stability. The proposed method first eliminates transcendental terms in characteristic equation of LFC systems without making any approximation and transforms the transcendental characteristic equation into a regular polynomial. The key result of the elimination process is that real roots of the new polynomial correspond to imaginary roots of the transcendental characteristic equation. With the help of new polynomial, it is also possible to determine the delay-dependency of system stability and root tendency with respect to the time delay. An analytical formula is then developed to compute delay margins in terms of system parameters. For a large set of controller gains, delay margins of LFC systems are computed to investigate the qualitative effect of controller gains on the delay margin. Finally, simulations studies are carried out to verify the effectiveness of the proposed method.
Time-delay systems Yi, Sun; Yi, Sun; Nelson, Patrick W ...
2010., 2010, 2010-06-25
eBook
This book comprehensively presents a recently developed novel methodology for analysis and control of time-delay systems. Time-delays frequently occurs in engineering and science. Such time-delays ...can cause problems (e.g. instability) and limit the achievable performance of control systems.
We propose an autonomous blockchain-based federated learning (BFL) design for privacy-aware and efficient vehicular communication networking, where local on-vehicle machine learning (oVML) model ...updates are exchanged and verified in a distributed fashion. BFL enables oVML without any centralized training data or coordination by utilizing the consensus mechanism of the blockchain. Relying on a renewal reward approach, we develop a mathematical framework that features the controllable network and BFL parameters (e.g., the retransmission limit, block size, block arrival rate, and the frame sizes) so as to capture their impact on the system-level performance. More importantly, our rigorous analysis of oVML system dynamics quantifies the end-to-end delay with BFL, which provides important insights into deriving optimal block arrival rate by considering communication and consensus delays. We present a variety of numerical and simulation results highlighting various non-trivial findings and insights for adaptive BFL design. In particular, based on analytical results, we minimize the system delay by exploiting the channel dynamics and demonstrate that the proposed idea of tuning the block arrival rate is provably online and capable of driving the system dynamics to the desired operating point. It also identifies the improved dependency on other blockchain parameters for a given set of channel conditions, retransmission limits, and frame sizes.<xref ref-type="fn" rid="fn1"> 1 However, a number of challenges (gaps in knowledge) need to be resolved in order to realise these changes. In particular, we identify key bottleneck challenges requiring further investigations, and provide potential future reserach directions. 1
An early version of this work has been accepted for presentation in IEEE WCNC Wksps 2020 <xref ref-type="bibr" rid="ref1">1 .
This book gathers a number of selected contributions aimed at providing a balanced picture of the main research lines in the realm of delay differential equations and their applications to ...mathematical modelling. The contributions have been carefully selected so that they cover interesting theoretical and practical analysis performed in the deterministic and the stochastic settings. The reader will find a complete overview of recent advances in ordinary and partial delay differential equations with applications in other multidisciplinary areas such as Finance, Epidemiology or Engineering
This paper aims at improving calculation accuracy and reducing calculation burden of delay-dependent stability analysis for large-scale multi-area load frequency control (LFC) schemes in traditional ...and deregulated environments. The special features of the LFC models have been exploited via model reconstruction technique to equivalently transform the original LFC model into a delay-free part and a delay-related part by a transition matrix. The improvement of the calculation efficiency is obtained by decreasing both the number of decision variables and the maximal order of the linear matrix inequalities. Based on the reconstructed model, a novel augmented Lyapunov functional is constructed mainly based on the delay-related part with much lower order and its derivative is bounded with the Wirtinger inequality to establish a stability condition with less conservatism. Case studies are based on two-area LFC systems to verify the effectiveness of proposed stability criteria based on the time-domain indirect method, with a great improvement of the calculation accuracy that can achieve almost accurate delay margins, such as the frequency domain method. Moreover, comparing with the criterion based on the original system model without reconstruction, the calculation efficiency has been greatly improved with the cost of small deduction of accuracy.
This technical note investigates the robust stabilization problem for uncertain linear systems with discrete and distributed delays under saturated state feedback. Different from the existing ...approaches, a distributed-delay-dependent polytopic approach is proposed in this technical note, and the saturation nonlinearity is represented as the convex combination of state feedback and auxiliary distributed-delay feedback. Then, by incorporating an appropriate augmented Lyapunov-Krasovskii (L-K) functional and some integral inequalities, the less conservative stabilization and robust stabilization conditions are proposed in terms of linear matrix inequalities (LMIs). The effectiveness and reduced conservatism of the proposed conditions are illustrated by numerical examples.
This paper is concerned with the delay-dependent stability analysis of linear systems with a time-varying delay. Two types of improved Lyapunov-Krasovskii functionals (LKFs) are developed to derive ...less conservative stability criteria. First, a new delay-product-type LKF, including single integral terms with time-varying delays as coefficients is developed, and two stability criteria with less conservatism due to more delay information included are established for different allowable delay sets. Second, the delay-product-type LKF is further improved by introducing several negative definite quadratic terms based on the idea of matrix-refined-function-based LKF, and two stability criteria with more cross-term information and less conservatism for different allowable delay sets are also obtained. Finally, a numerical example is utilized to verify the effectiveness of the proposed methods.
