Bound Of Time Delay Research Articles

Switching-like event-triggered control of uncertain NCSs under delay distribution and DoS attacks

The paper addresses the switching-like event-triggered control for uncertain networked control systems with time-varying delay under DoS attacks. First of all, to reduce the communication burden, a switching-like event-triggered mechanism is designed to automatically select the trigger condition according to whether the system is under DoS attacks, which have the advantage of reducing the number of data packets transmitted. Secondly, unlike the traditional assumption of time-varying delay, here it satisfies the condition that the probability is known, and combines the networked control systems to propose a novel time-delay system model, which can obtain a larger upper bound on the delay. Then, by using both the Lyapunov functional method and linear matrix inequality technique, we obtain sufficient conditions of uncertain networked control systems to achieve exponentially stable in the mean square sense. Furthermore, under the common limitations of the maximum continuous packet losses caused by the DoS attacks and delay, the stability criterion is derived, which can be used to estimate the communication parameters and security controller gain. Finally, through two simulation examples, the larger upper bound of time delay, less trigger times, faster convergence rate are obtained, which verify the validity of our theoretical analysis.

Event‐triggered output feedback H∞$$ H\infty $$ control for Markovian jump networked control systems with signal quantization

AbstractThis article studies the output feedback control problem for event‐triggered Markovian jump networked control systems with signal quantization. First, a Lyapunov–Krasovskii function is constructed, which contains time delay, upper bound of time delay and conditional transition probability information of Markovian jump systems. Second, when using the Wirtinger's inequality and the Reciprocally convex inequality to estimate the upper bound of the delay of the weak infinitesimal generator operator of the Lyapunov–Krasovskii function, the event‐triggered scheme and the signal quantization scheme are introduced. Finally, the stability criterion of the closed‐loop system of event‐triggered Markovian jump networked control systems and the design method of the output feedback controller of disturbance attenuation level are given in the form of linear matrix inequalities (LMIs). The effectiveness of the proposed method is verified by two numerical examples.

Fully Distributed Optimal Economic Dispatch for Microgrids under Directed Communication Networks Considering Time Delays

Distributed generation and demand-side management are expected to play a more prominent role in future power systems. However, the increased number of generations and load demands pose new challenges to optimal energy management in a microgrid. In this paper, an economic dispatch model for microgrids considering Traditional Generators (TGs), energy storage units, wind turbines (WTs), and flexible loads is established. To tackle the Economic Dispatch Problem (EDP) over directed communication networks, a fully distributed algorithm developed by leveraging a two-step state information exchange mechanism is proposed. In addition, by employing a fixed stepsize, the proposed algorithm demonstrates rapid convergence. Furthermore, our algorithm is well-suited for nonquadratic convex cost functions. Subsequently, we extend our algorithm to address imperfect communication scenarios. Even in the presence of arbitrarily large yet bounded time delays, our algorithm exhibits robustness. Finally, several numerical examples are given to verify the correctness and effectiveness of the developed results.

Design of structured [formula omitted] flight controllers: Passive fault-tolerant versus observer-based structures

This article presents the structured H∞ design and validation of two types of flight controller architectures: a passive fault-tolerant controller for the longitudinal motion and an active observer-based fault-tolerant controller for the lateral-directional motion. In the first, the controller follows the conventional Stability/Control Augmentation System (SCAS) structure, and its gains are obtained in continuous-time with the hinfstruct command by considering a set of elevator Loss-Of-Efficiency (LOE) faults. For the second, the conventional Luenberger observer-based controller structure is used, and the design aims to monitor the health of the aileron and rudder actuators in addition to provide active tolerance against LOE faults. Two different discrete-time designs are obtained for the latter, one focused on control performance optimization (using also the hinfstruct command), and the other on simultaneous control and observer performance optimization (using the systune command and under a slightly relaxed control performance constraint). For the two types of architectures, unmodeled dynamics are represented by uncertain bounded time delays modeled as pure delays or first-order Padé approximations. The resulting controllers are implemented on-board JAXA’s research airplane MuPAL-α, and not only is their practicality demonstrated but also control performance is validated via Aircraft-In-the-Loop (AIL) testing under gust-free and realistic gusty conditions. This demonstration is at a Technological Readiness Level (TRL) of 7–8, resulting in a high-level of confidence in the validity of the proposed flight control structures.

Adaptive Consensus of the Stochastic Leader-Following Multi-Agent System with Time Delay

For the multi-agent system with time delay and noise, the adaptive consensus of tracking control problems is discussed by the Lyapunov function. The main purpose of this study is to design an adaptive control protocol for the system, such that even if there exists time delay among agents, the protocol can still ensure the consensus of the stochastic system. The main contribution is to revise the protocols that were previously only applicable to system without time delay. Because the system is inevitably disrupted by time delay and noise during the interactive process, achieving coordination and consensus is difficult. To enable the followers to track the leader, a novel adaptive law depending on the Riccati equation is firstly proposed, and the adaptive law is different from previous mandatory control law completely depending on a known function. The ability to be altered online based on the state of system is a major feature of the adaptive law. When there are interactive noise and time delay between the followers and leader of the system, a special Lyapunov function is constructed to prove the adaptive consensus. And the upper bound of time delay is obtained by using the Itô integral theory. Finally, if the time delay of the system approaches zero, it is shown that the adaptive law still ensures that each follower tracks the leader under simpler conditions.

Mean-square consensus of hybrid multi-agent systems with noise and nonlinear terms over jointly connected topologies

This paper studies the mean-square consensus of second-order hybrid multi-agent systems over jointly connected topologies. Systems with time-varying delay and multiplicative noise are considered. The date sampling control technique is adopted. Through matrix transformation, a positive definite matrix transformed by the Laplacian matrix is obtained, where the Laplacian matrix is a connected subgraph divided by the jointly connected topologies. By using graph theory, matrix theory and Lyapunov stability theory, sufficient conditions and the upper bound of time delays for the mean-square consensus are obtained. Finally, several simulations are presented to demonstrate the validity of the control method.

Data-sampled mean-square consensus of hybrid multi-agent systems with time-varying delay and multiplicative noises

This paper addresses the issue of dynamic mean-square consensus for second-order hybrid multi-agent systems. Time-varying delays and multiplicative noises are considered. New distributed control protocols are designed based on data-sampled information of neighbor agents. Equivalently using the error system based on Laplacian matrix, the method could make a dynamic consensus both under the fixed and switching topologies. By adopting stochastic system theory, Lyapunov stability method and linear matrix inequality theory, several sufficient conditions for the dynamic mean-square consensus are obtained. The upper bound of time delay and the discrete-time sampling period of hybrid multi-agent systems under a stochastic noises environment are inferred. Several simulations are presented to demonstrate the effectiveness of the proposed methods.

Hopf Bifurcation in a Reaction–Diffusion–Advection Population Model with Distributed Delay

The existence, direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady state of a reaction–diffusion–advection model with distributed delay and Dirichlet boundary condition are considered in this paper. By analyzing the characteristic equation and taking the bound of time delay as the bifurcation parameter, we show that Hopf bifurcation will occur when the shape parameter [Formula: see text], and the positive steady state is always stable when [Formula: see text]. The properties of Hopf bifurcations are then obtained by center manifold reduction and norm form methods. The effects of the distributed delay, shape parameter and advection on Hopf bifurcation values are also investigated. Finally, numerical simulations illustrate the effectiveness of the theoretical results.

Event‐triggered control for stochastic systems with multiple delays

AbstractThis paper investigates the stabilization problem for continuous‐time stochastic systems with multiple delays under continuous event‐triggered mechanisms, of which both static case and dynamic case are considered individually. In order to avoid zeno phenomenon in every sample path, a suspension time after each successful execution is forced for our event‐triggered mechanisms, resulting in intermittent detection of system states. Under such control strategy, we deduce mean square exponential stability of stochastic systems with multiple delays by means of Hanalay‐type inequality and obtain a delay‐dependent‐based and less‐conservative stabilization criterion without involving the upper bound of time delays. Besides, a co‐design procedure is proposed for linear controller and event‐triggered mechanisms. In the end, an illustrative example is presented to show effectiveness of the proposed co‐design procedure and contrasts the system performance under static and dynamic event‐triggered mechanisms.

Distributed Event-Triggered Control for Multiagent Systems Under Denial-of-Service Attacked Topology: Secure Mode Strategy

In this article, the secure event-triggered control problem is investigated for multiagent systems (MASs) compromised by Denial-of-Service (DoS) attacks with multiple modes. With the rapid development of information technology, DoS attacks against communication topologies are more and more common in MASs with cyber-physical features. To actively reduce the influences caused by DoS attacks, a secure mode strategy is proposed to make agents switch into the secure mode when attacks occur. In this strategy, each agent accesses or terminates the secure mode with bounded time delays after DoS attacks begin or end. Based on the switched system theory, the secure mode strategy against DoS attacks is modeled as the asynchronous switching between agent models and topologies. Finally, we obtain the sufficient conditions on the frequency and duration of DoS attacks, under which the designed controller can guarantee the consensus of MASs. By practical examples, the MASs with the secure mode strategy are illustrated to have better attack-resistant effectiveness than the ones without the secure mode strategy.

Advanced controller design for uncertain linear systems with time‐varying delays via augmented zero equality approach

This paper deals with the stability analysis and controller design for linear systems with time‐varying delays and parameter uncertainties. By choosing appropriate augmented Lyapunov–Krasovskii functionals, a set of linear matrix inequalities is derived to get advanced feasible region of stability and controller gain matrices that guarantee the asymptotic stability of the concerned systems within maximum bound of time delays and its time derivative. To further reduce the conservatism of stabilization criterion, a recently developed mathematical technique that constructed a new augmented zero equality is applied. Finally, two numerical examples are utilized to show the validity and superiority of the proposed methods.

An efficient distributed algorithm for economic dispatch considering communication asynchrony and time delays

The increasing integration of distributed energy resources (DERs) to power grids has fostered the emergence of advanced control technologies for energy management. This study focuses on distributed solutions to economic dispatch considering asynchrony and non-ideal communications. A distributed consensus-based algorithm is developed for general directed networks, where heavy-ball momentum is incorporated into the algorithm design to accelerate convergency. Subsequently, an asynchronous version is proposed based on a general asynchronous communication model with unpredictable, non-uniform, and bounded time delays. Without a global clock in conventional synchronous distributed algorithms, distributed generators (DGs) are allowed to exchange information through local communications at any moment and use out-sync information to execute new updates. Simulations are presented to demonstrate the performance of the proposed algorithm and verify its robustness against time delays.

Stability analysis of proportional delayed projection neural network for quadratic programming problem

At present, projection neural network (PNN) with bounded time delay has been widely used for solving convex quadratic programming problem (QPP). However, there is little research concerning PNN with unbounded time delay. In this paper, we propose the proportional delayed PNN to solve QPP with equality constraints. By utilizing homeomorphism mapping principle, we prove the proportional delayed PNN exists with unique equilibrium point which is the optimal solution of QPP. Simultaneously, delay-dependent criteria about global exponential stability (GES) and global polynomial stability (GPS) are also acquired by applying the method of variation of constants and inequality techniques. On the other hand, when proportional delay factor [Formula: see text] is equal to 1, the proportional delayed PNN becomes the one without time delay which still can be utilized for solving QPP. But in most situations, [Formula: see text] is not equal to 1, and time delay is unpredictable and may be unbounded in the actual neural network, which causes instability of system. Therefore, it is necessary to consider proportional delayed PNN. A numerical example demonstrates that, compared with the proportional delayed Lagrange neural network, the proportional delayed PNN is faster in terms of convergence rate. The possible reason is that appropriate parameters make the model converge to the equilibrium point along the direction of gradient descent.

Minimal‐time complex consensus for multi‐agent systems with time delay

This paper studies the minimum time consensus problem for discrete-time multi-agent systems with complex Laplacian delay networks such that each agent can find its complex consensus value in a minimum number of steps using its local observations. The stability analysis is first provided and the convergence condition is derived for complex weighted networks with time delays. Specifically, the delayed multi-agent system is modeled by employing the augmented graph representation. Via adding virtual agents in the augmented systems, the complex consensus is obtained in the networks with bounded time delay if the communication topology digraph of the system has a spanning tree. A decentralized algorithm is proposed for the minimal-time computation of complex consensus based on the information from the robot itself without relying on the external environment. The algorithm hinges on the minimal polynomial of the matrix concerning the augmented graph. Furthermore, the rearrangement of the virtual agents in the augmented system provides an upper bound for the number of agents required to compute the consensus value. Simulation examples demonstrate the effectiveness of our results. The advantage of this approach is that it can be easily deployed on a group of agents to rapidly achieve a complex consensus setting within any delayed networks.

Stabilisation of network-controlled aircraft pitch control system with time delay

This paper describes the stability assurance of network-controlled aircraft pitch control system with time delays. A frequency-domain method is used to determine the upper bound of time delay for aircraft pitch control system with gain and phase margin constraint. The effectiveness of proportional-integral (PI) and fractional-order PI controller on aircraft pitch control system stability and performance is investigated in presence of time delay. The parametric space of the PI and fractional-order PI controller are plotted in two-dimensional space to determine the stability region and controller is designed with concern to the time delay. The relation between controller parameters and time delay is estimated and these findings contribute significantly for the design of the controller for aircraft pitch control system. The accuracy of the proposed results is validated using simulation benchmark.

Pinning bipartite synchronization for coupled nonlinear systems with antagonistic interactions and time delay

This paper investigates the synchronization problem for coupled nonlinear systems in which antagonistic interactions and bounded time delay coexist. In order to make the network achieve bipartite synchronization, we design a pinning scheme to pin a part of agents such that the network is connected. Under the assumptions that the signed graph is structurally balanced, the nonlinear system satisfies one-sided Lipschitz and quadratic inner-boundedness conditions, we derive some bipartite synchronization conditions for non-differentiable and differentiable coupling delays respectively. All criteria are presented as linear matrix inequalities. Finally, we present two numerical examples about neural network to illustrate the effectiveness of the obtained results.

Mean-square tracking consensus of heterogeneous multi-agent systems with additive noise and time delay

This paper discusses the mean-square tracking consensus of heterogeneous multi-agent systems with additive noise and time delay both over fixed and switching topologies. To weaken the noises, consensus gain is introduced into the control protocol. By using graph theory, stochastic analysis, matrix theory and velocity decomposition approach, sufficient conditions as well as the upper bound of time delay for the mean-square tracking consensus are obtained. Several simulations are given to verify the potential correctness of the results.

Leader-following consensus of delayed multi-agent systems with aperiodically intermittent communications

In this paper, the leader-following consensus of nonlinear multi-agent systems with time delay and aperiodically intermittent communications is investigated. Compared with the intermittent communications for multi-agent systems in previous literature, we relax the periodicity or quasi-periodicity of the intermittent communications and render the intermittent communications to be completely aperiodic. The concepts of average communication ratio and average communication period are adapted to characterize the distributions of communication time and non-communication time. Then the consensus problem for the studied systems with large time delay and small time delay is studied, respectively. Especially, for the case of small time delay, the upper bound of time delay is assumed to be less than the average communication length (average communication ratio × average communication period), but can be larger than some communication lengths, which is less conservative. Finally, numerical examples are provided to show the effectiveness of the main results.

Delay-range-dependent ℋ∞ synchronization approaches for time-delay chaotic systems

The purpose of this paper is to investigate the problem of controller design for synchronization of the chaotic drive and response systems accompanied with bounded time delays limited by delay rates, uncertain parameters and admissible destabilization. An adequate condition is obtained employing the linear matrix inequality and a neoteric Lyapunov–Krasovskii functional to guarantee the global exponential synchronization of the studied chaotic systems. A control law is applied which would be added to the studied systems such that we can ensure the synchronization of the objective systems. The approach is proposed to solve the problem of the asymptotic synchronization of the studied systems. Numerical examples are illustrated to prove the feasibility and effectiveness of the current approach in this paper.

Aperiodically intermittent stabilization for complex-valued hybrid stochastic delayed systems: An average technique

This paper focuses on the stabilization problem of complex-valued hybrid stochastic delayed systems via aperiodically intermittent control (AIC). As for AIC in existing literature, strict conditions on the lower bound of control intervals and upper bound of control periods or the maximum proportion of rest intervals are required. In this paper, we relax these constraints by proposing average control ratio and average control period to describe the distribution of control and rest intervals of AIC, i.e., the lower bound of certain control widths can be arbitrarily small, upper bound of certain control periods can be very large and the proportion of rest widths can be any value in (0,1). Thus, the conservativeness is reduced compared with the existing related results. Then based on the complex generalized Itô’s formula, several novel stabilization criteria are obtained for small time delays and large time delays, respectively, which avoid splitting the real and imaginary parts. Especially, for the case of small time delays, the upper bound of time delays can be larger than the lower bound of all control widths, which has wider applications than previous results. Finally, two examples along with their numerical simulations are given to show the effectiveness and less conservativeness of our results.