Time-varying Delays Research Articles

A Sampled-Data-Based Secure Control Approach for Networked Control Systems Under Random DoS Attacks.

This article aims to analyze H∞ stability of a class of networked control systems (NCSs) under random denial of service (DoS) attacks and design a sampled-data-based state feedback security controller to mitigate the influence of attacks. Different from the existing random attacks, the information about the maximum duration time of DoS attacks can be captured by introducing a predesigned logical processor. Then, based on the periodic sampling technique, the probability of attack occurrence and the resultant number of maximum allowable consecutive packet dropouts can be calculated, which is quite significant to investigating the security problem of NCSs. A DoS-dependent security controller which makes full use of the attack probability information and the number of attack-induced packet dropouts is designed. A novel networked sampled-data system model is first established that enables us to deal with the random DoS attacks phenomena and the time-varying delay induced by attacks under a uniform framework. By structuring a suitable Lyapunov-Krasovskii functional, the relationship between mean square asymptotic stability and attack characteristics is obtained. Finally, the reliability and applicability of the presented control strategy in eliminating the influence of DoS attacks are validated by two practical engineering applications.

Switching adaptive dynamic event-triggered consensus of nonlinear multi-agent systems under DoS attacks and communication delay

This article addresses the issue of achieving security consensus in multi-agent systems (MASs) that are susceptible to denial-of-service attacks (DoS-As) and time-varying communication delays (TCD). We have developed a novel unified model to describe DoS-As and TCD. Firstly, a new switching adaptive dynamic event-triggered mechanism (SADETM) is proposed to conserve communication resources during DoS-As and TCD. The mechanism transforms into three event-triggered strategies adapted to highly dynamic MASs. Then, a consensus control protocol is designed through consensus errors based on SADETM. Finally, the sufficient conditions for ensuring the stability of MASs are solved by combining the Lyapunov-Krasovskii functional (LKF) method and the linear matrix inequality (LMI) technique. The effectiveness of this method is verified through simulation examples.

Observer-based guaranteed-cost bipartite time-varying formation tracking control for multiagent systems subject to communication delays

The paper centers on the guaranteed-cost bipartite time-varying formation tracking control for multiagent systems with nonuniform time-varying communication delays under the framework of a distributed observer. An integral quadratic cost function is presented, founded on formation tracking and observation error. Firstly, distributed state observers, using the relative measurement output between neighbors, are established so that the leader and follower can accurately estimate each agent's unmeasurable state. Subsequently, a bipartite formation tracking protocol is proposed, incorporating estimation information and nonuniform time-varying communication delays. This protocol aims to achieve bipartite time-varying formation tracking for multiagent systems. Next, a new augmented Lyapunov-Krasovskii functional with delay-product and triple integral terms is constructed. By integrating the second-order Bessel-Legendre inequality technique, the delay-dependent reciprocally convex combination inequality method, and the free weight matrix technique, a new guaranteed-cost bipartite time-varying formation tracking criterion is developed, offering less conservatism. Compared to certain existing delay conditions, the stability conditions assure a greater allowable upper bound of delay. Finally, a numerical example is conducted to confirm the validity and superiority of the theoretical findings.

New global exponential stability conditions for nonlinear delayed differential systems with three kinds of time-varying delays

For a class of nonlinear differential systems with heterogeneous time-varying delays, including distributed, leakage and transmission time-varying delays, a novel global exponential stability (GES) analysis method was developed. Based on the GES definition, some sufficient conditions and rigorous convergence analysis of nonlinear delayed differential systems are presented directly, which ensure all states to be globally exponentially convergent. The proposed analysis method not only avoids the construction of the Lyapunov–Krasovskii functional, but also uses some simple integral reduction techniques to determine the global exponential convergence rate. Furthermore, the main advantages and low calculation complexity are demonstrated through a theoretical comparison. Finally, three numerical examples are provided to verify the effectiveness of the theoretical results.

Bumpless transfer control for switched positive time-delay systems with linear-type dissipative inequalities

In this paper, a family of amplitude limited controllers and a hysteresis switching paradigm, for switched positive systems with time-varying delays, are simultaneously determined to achieve strict (q,r) -α-dissipativity. The concept of strictly (q,r)-α-dissipative, induced by linear-type dissipative inequalities, is introduced. The main feature of the presented method lies in two aspects. The first one is that the magnitude of controller discontinuities, at the occurrence of switching, is here restricted. The other one is that the high switching frequency is refrained commonly the appearance of in state-dependent switching schemes. Moreover, dissipativity analysis as well as feedback dissipativity are taken into account. Novel criteria are derived for the considered systems to be dissipativity by resorting to multi-linear copositive storage functionals. Eventually, the validity and superiority of the presented control strategy are demonstrated through two illustrative examples.

Relaxed mixed convex combination lemmas: Application to stability analysis of time-varying delay systems

Stability analysis of time-varying delay systems is a fundamental issue, and reducing the conservatism of stability criteria is the key. The high-order Bessel-Legendre inequality together with appropriate Lyapunov–Krasovskii functional (LKF) has the potential to reduce conservatism, but the reciprocally convex and quadratic correlation terms of time-varying delay appear in LKF derivative. This paper proposes the relaxed mixed convex combination lemmas, in which the reciprocally convex combination lemma introduces delay square terms in the LKF derivative, and the quadratic convex combination lemma relaxes the negativity condition for quadratic polynomial functions. The less conservative stability criteria of systems with time-varying delay satisfying two cases are derived, making the delay upper bound larger, and the design degree of freedom higher. Finally, two well-known numerical examples are presented to demonstrate the superiority of the lemmas and criteria over the previous works.

A predictive model with time-varying delays employing channel equalization convolutional neural network for NOx emissions in flexible power generation

This study aims to predict NOx (i.e. NO + NO2) emissions at the selective catalytic reduction inlet from coal-fired boilers. It develops a lightweight predictive model that can be adapted to the generation system dominated by renewable energy with fluctuating power. The random forest algorithm was first used to select the input variables from the auxiliary variables. The maximum information coefficient algorithm was then used to estimate the time delay between the input variables and the NOx emissions. Afterwards, to overcome the “channel collapse” issue in convolutional neural networks (CNNs), a Channel Equalization block (CE-Block) was proposed to activate the suppressed channels, and a lightweight network, referred to as CE-CNN, was designed by fusing a CNN with the CE-Block. Finally, a dynamic NOx emissions prediction model was developed employing the CE-CNN, and the model was evaluated using real data from a 600 MW down-fired boiler. The results showed that the dimensionality reduction policy decreased the model training time by 21.74 %, and the analysis of the time delay decreased the RMSE by 7.31 %. Compared to the baseline model 3-layer CNN, the proposed model achieves performance improvements of 20.97 %, 22.11 %, and 3.48 % in terms of RMSE, MAE, and R2, respectively.

Performance Guaranteed Robust Tracking Control of MIMO Nonlinear Systems With Input Delays: A Global and Low-Complexity Solution.

This article presents a global performance guaranteed tracking control method for a class of general strict-feedback multi-input and multi-output (MIMO) nonlinear systems with unknown nonlinearities and unknown time-varying input delays. By introducing a novel error transformation embedded with the Lyapunov-Krasovskii functional (LKF), the developed control scheme exhibits several appealing features: 1) it is able to achieve global prescribed performance tracking for uncertain MIMO systems with delayed inputs, while at the same time eliminating the constraint conditions imposing on initial values between the tracking/virtual error and the performance function; 2) there is no need for any a priori knowledge regarding the nonlinearities of the system nor a prior knowledge of time derivatives of the desired trajectory, making the resultant controller simpler in structure and less expensive in computation; 3) the control scheme includes a new differentiable time-varying feedback term, which gracefully compensates the unknown input delays and unknown control gain coefficient matrices; and 4) the controllability condition is relaxed, which enlarges the applicability of the proposed strategy. Finally, a two-link robotic manipulator example is provided to demonstrate the reliability of the theoretical results.

Adaptive event-triggered finite-time prescribed performance control of PMSM stochastic system considering time-varying delays

This paper investigates the finite-time prescribed performance tracking control problem of permanent magnet synchronous motor (PMSM) considering stochastic disturbances and time-varying delays under event-triggered mechanism. A quintuple polynomial finite-time prescribed performance function (FPPF) is introduced to ensure the transient and steady-state performance of the system output, and a nonlinear transformation function is employed to convert the constrained error into an unconstrained one. The Lyapunov-Krasovskii function is constructed to address time delays. And the system uncertainties are approximated by the radial basis function neural networks (RBFNN). For the “explosion of complexity” caused by backstepping method, a tracking differentiator (TD) is employed. By combining finite time control, command filtering backstepping control, and event-triggered mechanism, the effect of the filter errors is decreased, and the update frequency of the control signals are reduced. It is shown that the proposed controller can guarantee finite time convergence bounded of all signals in the closed-loop system, and the tracking error can converge in finite time. Finally, simulation results are presented to illustrate the effectiveness of the proposed controller.

Reachable Set Estimation for Neutral Markovian Jump Systems with Time-varying Delay and Distributed Delay

Reachable Set Estimation for Neutral Markovian Jump Systems with Time-varying Delay and Distributed Delay

Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative

Finite-time stability analysis of fractional fuzzy differential equations with time-varying delay involving the generalized Caputo fractional derivative

Parameter-dependent conditions for H ∞ stabilisation of polynomial parameter-varying system with delay

This paper considers the problems of achieving exponential stability and H ∞ stabilisation for polynomial parameter-varying system with time-varying delay. Unlike some existing linear parameter-varying results that treat system parameters as time invariant factors, this paper makes full use of the nonlinearity and time-varying characteristics of system through introducing a novel delay-and-parameter-dependent Lyapunov function. The main conclusions are discussed in three cases (system without input, system with disturbance input, system with disturbance input and control input). And the H ∞ stabilisation problem is solved by constructing a controller which is inserted with system parameters and their derivatives. The structures of Lyapunov function and controller lead to that the derived criteria for exponential stabilisation are expressed by state-and-parameter-dependent linear matrix inequalities, which are efficiently solved by sum-of-squares program. The effectiveness and superiority are verified through two numerical examples.

Stability analysis for neutral stochastic time-varying systems with delayed impulses

This article investigates the stability of stochastic neutral delayed systems (SNDS) with delayed impulses, which includes the stability in input-to-state exponentially stable in pth moment (p-ISES), integral ISES in pth moment (p-iISES) and eλt-weighted ISES in pth moment (eλt-p-ISES). Compared with the existing works, we allow the neutral term, delayed impulses, time-varying coefficients in the diffusion condition, bounded time-varying delay (BTVD) to be in a stochastic system, which arise the difficulty. By utilizing the techniques of Lyapunov-Krasovskii (L-K) function, generalized delay integral inequality and average impulsive interval (AII), some desired results are obtained by surmounting the underlying difficulty. Finally, an example is given to show the validity of our work.

Stability and stabilization of fractional-order singular interconnected delay systems

An analytical approach based on fractional calculus and singular value theory to finite-time stability and stabilization of fractional-order singular interconnected delay systems is proposed. Particularly, we study fractional singular equations with interval time-varying delays. We first give new sufficient conditions for finite-time stability of such equations. Then, the feedback stabilizing controllers are designed via solving a tractable linear matrix inequality (LMI) and Mittag-Leffler function. Finally, numerical examples with simulations are given to illustrate the feasibility and effectiveness of the proposed results.

Distributed consensus control based on double event-triggered mechanism for multi-agent systems with irregular switching topologies under malicious attacks

This paper studies the consensus control of leader-following multi-agent systems (MASs) with irregular switching communication topology and time-varying delay under malicious attacks. The Markov stochastic process is used to describe the irregular switching of the communication topology caused by random factors, and it is verified that the communication protocol is still feasible when the communication channel is partially broken. At the same time, in order to filter out more efficient status signals and reduce the burden of network communication resources under malicious attacks, the double event-triggered mechanism (DETM) are adopted to make the number of state signals reaching the actuator much less and the state signals more efficient. Then, using the Lyapunov–Krasovskii functional (LKF) and integral inequality methods, the LKF contains the information of the lower bound of delay. Lastly, the stability criterion of MASs stochastic asymptotic consensus with time-varying delay is given, the gain of the consistent controller and the event triggered matrix parameters are solved by using the linear matrix inequality toolbox. Finally, four numerical simulations are given to verify that the MASs with irregular switching topology under malicious attacks can still achieve leader-following consensus.

Stability of highly nonlinear stochastic systems with non-random switching signals and multiple delays

The situation of multiple delays often occur in hybrid stochastic systems. In this paper, multiple time-varying delays are considered for highly nonlinear switching stochastic systems. The function of time-varying delays is differentiable, and its derivative is a positive constant less than 1. By the Lyapunov functional method and the mode-dependent average dwell time approach, existence and uniqueness of solution, asymptotic stability and pth moment exponential stability for highly nonlinear switching stochastic multiple delays systems are obtained. Finally, an example is afforded to explicate the effectiveness our theoretical analysis results.

Enhancing Stability Criteria for Linear Systems with Interval Time-Varying Delays via an Augmented Lyapunov–Krasovskii Functional

This work investigates the stability conditions for linear systems with time-varying delays via an augmented Lyapunov–Krasovskii functional (LKF). Two types of augmented LKFs with cross terms in integrals are suggested to improve the stability conditions for interval time-varying linear systems. In this work, the compositions of the LKFs are considered to enhance the feasible region of the stability criterion for linear systems. Mathematical tools such as Wirtinger-based integral inequality (WBII), zero equalities, reciprocally convex approach, and Finsler’s lemma are utilized to solve the problem of stability criteria. Two sufficient conditions are derived to guarantee the asymptotic stability of the systems using linear matrix inequality (LMI). First, asymptotic stability criteria are induced by constructing the new augmented LKFs in Theorem 1. Then, simplified LKFs in Corollary 1 are proposed to show the effectiveness of Theorem 1. Second, asymmetric LKFs are shown to reduce the conservatism and the number of decision variables in Theorem 2. Finally, the advantages of the proposed criteria are verified by comparing maximum delay bounds in four examples. Four numerical examples show that the proposed Theorems 1 and 2 obtain less conservative results than existing outcomes. Particularly, Example 2 shows that the asymmetric LKF methods of Theorem 2 can provide larger delay bounds and fewer decision variables than Theorem 1 in some specific systems.

Decay rate of discrete-time homogeneous delayed systems with cone invariance

This paper is dedicated to analysing the decay rate of discrete-time homogeneous delayed systems that exhibit order preservation within a proper cone. First, a sufficient criterion ensuring the cone invariance of the system is introduced. By exploring the monotonicity of system trajectories, a condition that is both sufficient and necessary for guaranteeing the asymptotic stability of the system is presented. Importantly, under a weak assumption for the growth rate of time-varying delays, a universal framework is provided for characterising the decay rate of the system. Furthermore, typical examples of decay rate analysis are presented when delays are bounded or experience linear, sublinear, or logarithmic growth rates. Eventually, the rationality of the results is illustrated through a numerical simulation.

Stability analysis of homogeneous cooperative positive differential systems with time-varying delays and its generalization

This article is devoted to studying the asymptotic behavior of differential systems with bounded delays. We first focus on the analysis of homogeneous cooperative positive systems. Under the assumption that the vector field is homogeneous of a degree greater than 1, we show that the non-trivial solutions of the system converge to the origin at a polynomial rate. In the case when the degree of homogeneity equals 1, we prove that the solutions will decay at an exponential rate. As a generalization of these results, we consider nonlinear non-autonomous differential systems with time-varying delays that are bounded above by stable homogeneous positive systems. By some additional imposed conditions, in light of the comparison principle, we obtain the locally exponential stability and polynomial stability of the equilibrium point to these systems. Finally, specific examples and discussions are provided to illustrate the validity of the proposed theoretical results.

Combustion instability characteristics via fuel nozzle modification in a hydrogen and natural gas Co-firing gas turbine combustor

In this study, three premixed swirl gas turbine nozzles with different fuel injection hole sizes were designed to optimize combustion characteristics influenced by changes in the hydrogen mixing ratio. Experiments involved increasing the hydrogen volume fraction of the fuel from 0 to 60%. The amount of fuel supplied through the pilot flow was increased to suppress combustion instability. The OH* chemiluminescence technique was introduced to analyze flame structure. To understand combustion instability, time delay and time-delay distribution were derived from flame structure analysis and applied to the 1D thermoacoustic model. The results indicated that the amount of fuel required for pilot injection with increasing hydrogen ratio varied with fuel hole size. It was also observed that changes in fuel hole size significantly affected flame characteristic length. Findings from the 1D thermoacoustic analysis confirmed that fuel hole size variation altered combustion instability characteristics by influencing time delay and time-delay distribution variation.