Delay-free System Research Articles

Optimal control for linear cyber physical systems under replay attacks via time delay estimation approach

We mainly study the optimal control problem for linear cyber physical systems under replay attacks in this paper. The methodological research mainly relies on the following two starting points: (1) Promptly detect and estimate the malicious replay attack behaviours hampering normal system procedures; (2) Design a resilient optimal control strategy to ensure the system regularly works as much as possible. Specifically, the linear cyber physical system becomes a time delay system after the replay attack, and then an algorithm is designed to transform the system into a delay-free system and ensure its stability. Finally, a numerical simulation is employed to demonstrate the practicality and efficacy of the proposed approach.

Almost Sure Stability of Complex-Valued Complex Networks: A Noise-Based Delayed Coupling Under Random Denial-of-Service Attacks.

This article is concerned with stability for stochastic complex-valued delayed complex networks under random denial-of-service (RDoS) attacks. Different from the existing literature on the stability of stochastic complex-valued systems that concentrate on moment stability, we investigate almost sure stability (ASS), where noise plays a stabilizing role. It is noted that, besides the vertex systems influenced by noise, the interactions among vertices are also at the mercy of noise. As a consequence, an innovative noise-based delayed coupling (NDC) in the presence of RDoS attacks is proposed first to accomplish the stability of complex-valued networks, where the RDoS attacks have a certain probability of triumphantly interfering with communications at active intervals of attackers. Namely, RDoS attacks considered are randomly launched at active periods, which is more realistic. In terms of the Lyapunov method and stochastic analysis theory, an almost sure exponential stability (ASES) criterion of the system discussed straightforwardly is developed by constructing a delay-free auxiliary system, while removing the traditional assumption of moment stability. The criterion strongly linked with topological structure, RDoS frequency, attack successful probability, and noise intensity reveals that the higher the noise intensity, the faster the convergence rate is for the stability of the network. In light of the criterion established, we present an algorithm that can be employed to analyze the tolerable attack parameters and the upper bound of the coupling delays, under the prerequisite of guaranteeing the stability of the network. Eventually, the theoretical results are applied to inertial complex-valued neural networks (ICNNs) and an illustrative example is presented to substantiate the efficiency of the theoretical works.

Cooperative target estimation of strap-down missiles considering random measurement delay

Aiming at the problem of cooperative target estimation for multiple strap-down missiles, this paper is concerned with developing a distributed cooperative estimation fusion algorithm considering the random transmission delay of observation data. As a stepping stone, the random measurement delay system with multiple strap-down missiles is transformed into a delay-free system with correlation noise in finite time intervals using the random observation delay model for strap-down missiles. Then, the distributed fusion technique without feedback is proposed based on the design of the best local filter for each strap-down sampling subsystem; To further enhance the robustness and stability of the cooperative target estimation system, the distributed fusion algorithm with feedback is suggested. Simulation in various cases and comparison studies are conducted to verify the effectiveness and robustness of the proposed scheme.

Stability of Delayed Homogeneous Positive Differential–Difference Systems

Stability theory of linear differential-difference system has been well-established, while fewer results can be found for nonlinear differential-difference systems. In this paper, stability and boundedness of homogeneous differential-difference system with bounded delay is studied based on the system positivity. At first, an exponential stability criterion is obtained, which is an extension of an existing result. Next, another boundary is computed under the previous condition, which proves to be tighter than the first result at least in some cases. Then a finite-time stability condition is achieved for the delay-free system, and an upper bound of the settling time and an explicit boundary of the state are derived. Finally, a numerical example is given to verify the results presented in this paper.

Necessary and Sufficient Conditions for Stabilizing an Uncertain Stochastic Multidelay System

We focus on the problem of asymptotically mean-square stabilization in discrete-time stochastic systems that exhibit plant uncertainty, multiple input delays, and multiplicative noises. Our innovative contributions are described as follows. First, we employ a reduction method to transform the original model into a delay-free auxiliary system, and establish an equivalent proposition for stabilization based on this reformulation. On the basis of the reformulated model, we propose two stabilization criteria for the uncertainty-free case, including both Lyapunov-type and Riccati-type criteria. More generally, we extend the stabilization result to the uncertain model, and propose a necessary and sufficient stabilization criterion utilizing matrix homogeneous polynomials. Finally, we explore the existence and uniqueness of a delay margin under certain structural restrictions, and provide a closed-form representation of this margin.

Time delays modulate the stability of complex ecosystems

What drives the stability, or instability, of complex ecosystems? This question sits at the heart of community ecology and has motivated a large body of theoretical work exploring how community properties shape ecosystem dynamics. However, the overwhelming majority of current theory assumes that species interactions are instantaneous, meaning that changes in the abundance of one species will lead to immediate changes in the abundances of its partners. In practice, time delays in how species respond to one another are widespread across ecological contexts, yet the impact of these delays on ecosystems remains unclear. Here we derive a new body of theory to comprehensively study the impact of time delays on ecological stability. We find that time delays are important for ecosystem stability. Large delays are typically destabilizing but, surprisingly, short delays can substantially increase community stability. Moreover, in stark contrast to delay-free systems, delays dictate that communities with more abundant species can be less stable than ones with less abundant species. Finally, we show that delays fundamentally shift how species interactions impact ecosystem stability, with communities of mixed interaction types becoming the most stable class of ecosystem. Our work demonstrates that time delays can be critical for the stability of complex ecosystems.

Novel Stability and Stabilization Conditions of Linear Fractional-Order Time-Delay Systems Using Free Matrix Approach

The stability and stabilization problem of linear fractional-order time-delay systems is investigated. By introducing a free matrix, the linear fractional-order time-delay systems is transformed to a delay-free system interconnected with uncertainties. New stability and stabilization criteria are derived based on the small gain theorem. The criteria are formulated as linear matrix inequalities and are computationally efficient. Since the free matrix is utilized, the new conditions are less conservative than the existing ones. Two numerical examples indicate that the proposed criteria are less conservative than existing ones.

Stability analysis of nonstationary mechanical systems with time delay via averaging method

A linear mechanical system with constant matrix of dissipative forces and continuous and bounded matrices of positional forces is studied. It is assumed that there are a large positive multiplier at the vector of dissipative forces and a constant delay in positional forces. The case is considered where the associated delay-free averaged system is asymptotically stable. With the aid of the Lyapunov direct method and the averaging method, conditions are derived under which neither delay nor timevarying perturbations with zero mean values disturb the asymptotic stability. The developed approach is used in the problem of monoaxial stabilization of a rigid body.

Stabilization of Discrete-Time Systems with Random Delays and Packet Drops: A Predictor-Like Controller

In this paper, we study stabilization of discrete-time systems in which control inputs are transmitted over a random delay and packet drop channel. A predictor-like linear feedback controller is proposed by a reduction technique in which the reduced system has the same dimension as that of the original system. A necessary and sufficient condition to stabilize the original system in the mean-square sense is obtained based on an algebraic Riccati equation. Some necessary and sufficient stabilizability conditions based on the Lyapunov criterion are also presented. Interestingly, it is shown that the stabilization problem considered in this paper is equivalent to the stabilization problem of a particular delay-free system with control-dependent correlated noises. Simulation examples are provided to illustrate the effectiveness and advantages of the proposed stabilizing controller.

Global Hopf bifurcation of a two-delay epidemic model with media coverage and asymptomatic infection

The influence of media coverage on disease transmission has attracted more and more attention, but the impact mechanism of media coverage with asymptomatic infection needs to be studied urgently. Therefore, a SIsIaS−M model with two delays and asymptomatic infection is considered. The two kinds of delays are respectively caused by the lag time of media reports about the number of patients and the lag time of audience feedback after media coverage. By using the geometric approach based on the third compound matrix, the existence of a threshold for the average duration of media coverage ensures that the endemic equilibrium in delay-free differential system is globally asymptotically stable. In the delay system the uniqueness, positivity and boundedness of solutions are investigated, and the system is persistent when R0>1. Through stability analysis, we find that the disease can be eliminated when the proportion of symptomatic patients in total patients is above a threshold. By choosing the sum of two delays as a bifurcation parameter, we analyze the stability switches of the endemic equilibrium, and discuss the onset and termination of Hopf bifurcations of periodic solutions. The properties of local Hopf bifurcation are also obtained. Furthermore, the global Hopf bifurcations are unbounded and a sufficient condition for the system to have multiple periodic solutions is obtained. Three parameters related to media coverage are found in numerical simulations to have thresholds that guarantee the stability of the endemic equilibrium. In numerical simulations, if media coverage is highly responsive to the number of patients or it has a strong influence on individual behavioural changes, this can lead to periodic oscillations. Conversely, although this makes the disease stable, the number of patients who reach steady state is higher. This is the same result as for the dissipation rate of media coverage, and again there is a threshold that makes the endemic equilibrium stable.

Control for a Class of Unstable High-Order Systems with Time Delay Based on Observer–Predictor Approach

This work considers the stabilization of a high-order system with time delay; an observer–predictor scheme is designed to estimate an internal signal of the system that is not available for measurement: this internal signal is the output before being delayed. By using the estimated signal, it is possible to design a controller for the delay-free system. The key point to carrying out this estimation strategy is to obtain conditions assuring that the estimated signal converges to the internal variable of the system. A necessary and sufficient condition to achieve an appropriate convergence in the proposed observer–predictor scheme is given. In addition, an analysis of the disturbance rejection and robustness with respect to the delay term is provided. The correct functioning of this scheme is verified through an example.

Interval estimation for discrete-time linear time-delay systems based on state augmentation

This paper investigates an interval estimation method for discrete-time linear time-delay systems subject to unknown but bounded disturbances and noise. We utilize the state augmentation technique to decouple the time delays. The interval estimation problem for the time-delay system will be transformed into that for a delay-free state augmented system. We then propose a two-step method which consists of robust observer design and zonotope-based interval analysis to achieve interval estimation. In observer design, a T−N−L observer is used to provide more degrees of design freedom, whose robustness is characterized by H∞ performance. Finally, a numerical example is provided to demonstrate the effectiveness and superiority of the proposed method.

Stability of homogeneous systems with distributed delay and time-varying perturbations

For a class of nonlinear systems with homogeneous right-hand sides of non-zero degree and distributed delays, the problem of stability robustness of the zero solution with respect to time-varying perturbations multiplied by a nonlinear functional gain is studied. It is assumed that the disturbance-free and delay-free system (that results after substitution of non-delayed state for the delayed one) is globally asymptotically stable. First, it is demonstrated that in the disturbance-free case the zero solution is either locally asymptotically stable or practically globally asymptotically stable, depending on the homogeneity degree of the delay-free counterpart. Second, using averaging tools several variants of the time-varying perturbations are considered and the respective conditions are derived evaluating the stability margins in the system. The results are obtained by a careful choice and comparison of Lyapunov–Krasovskii and Lyapunov–Razumikhin approaches. Finally, the obtained theoretical findings are illustrated on two mechanical systems.

On Sontag’s formula for the sampled-data observer-based stabilization of nonlinear time-delay systems

In this paper, a new methodology for the design of sampled-data dynamic output feedback (DOF) stabilizers for control-affine nonlinear time-delay systems is proposed. In particular, the methodology here developed is based on the Artstein’s theory of control Lyapunov functions and related Sontag’s formula, here extended, for the first time in the literature, to the case of DOF controllers. Firstly, the new notion of Steepest Descent Error Dynamics (SDED) is introduced and used to suitably re-formulate the well-known Sontag’s universal formula for the case of DOF controllers. Then, it is shown that, under suitably fast sampling, a proposed sampled-data DOF controller based on the new provided version of Sontag’s universal formula ensures the semiglobal practical stability of the related sampled-data closed-loop system. Time-varying sampling intervals, as well as the intersampling system behavior, are taken into account. In the theory here developed, the case of delay-free systems is addressed as a special case. Applications are presented for the validation of the proposed theoretical results.

Delay compensation of linear systems with multiple distributed input delays via memoryless feedback

Time-delay systems are widely used in industrial applications, such as chemical process and aerospace. The predictor-based feedback method is one of the effective ways to deal with such systems. This paper studies the delay compensation problem for linear systems with multiple distributed input delays. A novel state vector associated with the future state of the system is constructed, which reduces the original linear time-delay system to a linear delay-free system. Memory feedback controller is then designed, and necessary and sufficient conditions for the stability of the closed-loop system are acquired in accordance with the stability of an integral delay system. To avoid the difficult implementation problem of memory feedback controller, the memoryless feedback controller is proposed instead to compensate the multiple distributed input delays. Finally, the proposed controllers are applied to the design of the linearized liquid-level control resonant circuit system.

Strong stability with impact of maturation delay and diffusion on a toxin producing phytoplankton–zooplankton model

Plankton species is backbone for any healthy aquatic system, but a global increment in toxin phytoplankton blooms is a major threat to aquatic systems. As toxic phytoplankton Microcystis aeruginosa becomes too high, Artemia salina a zooplankton species avoids to consume it and more inclines towards a non-toxic phytoplankton Chaetoceros gracilis for food. Considering this fact, additional food is provided to zooplankton species to survive when non-toxic species is insufficient for the zooplankton and toxin phytoplanktons are harvested linearly to control toxicity level in the system. Also, increasing of phytoplankton may increase competitive behaviour between toxic and non-toxic phytoplanktons due to limited resources. Keeping these in mind, we propose a three populations reaction–diffusion delay model. In this study, existence of feasible equilibria has been studied. Conditions for Turing instability of delayed and non-delayed system have been discussed analytically. Strong stability analysis with respect to both delay and diffusion is performed and excitable nature through Hopf bifurcation is also examined. It has been investigated that if the delay spatial system shows diffusion driven instability, then it is also shown by the delay free system for the same parameters. The study explores that the model depicts strong stability with respect to both delay and diffusion. Movements of the species are responsible for the occurrence of planktonic bloom via Hopf bifurcation due to diffusion and affect the critical value of the time delay. This study suggests that a specific amount of harvesting ensures the long-term sustainability. It is also inspected that considerable amount of alternative food supply supports the zooplankton for its growth. Turing patterns like spots are observed. The behaviour of the system depends on the both variation of delay and choice of initial population. This study says that maturation delay stabilizes the system more quickly in the presence of diffusion than in the absence of diffusion.

Stability of homogeneous positive systems with time-varying delays

Stability analysis of positive linear systems has been well-developed, while attention to positive homogeneous nonlinear systems is notably less paid. This note deepens and extends some previous results on stability of homogeneous systems with bounded time-varying delays. Based on positivity property, exponential stability of a class of delayed homogeneous system with degree confined to an interval is studied, and its state boundary is further investigated in any fixed time, which is more precise than the former result in some cases. Additionally, finite-time stability is obtained for a delay-free homogeneous system and an explicit boundary is presented.

Distributed control for spatially interconnected time-varying delay systems under input saturation

This paper presents the distributed control design for a class of spatially interconnected continuous-time time-varying delay (SICTD) systems under input saturation. A distributed controller and distributed anti-windup compensator (AWC) are proposed based on the distributed structure of the SICTD system. Then, a sufficient condition is derived to guarantee the asymptotic stability and H∞ performance of the closed-loop system under the saturation constraints. We have also provided an algorithm for obtaining the AWC parameters by employing the elimination lemma and the cone complementary linearization approach. The proposed anti-windup compensation methodology can also be employed to compensate for the actuator saturation of the spatially interconnected delay-free systems. Finally, two practical examples are presented to verify the effectiveness of the proposed AWC design method.

Anti-windup ADRC design for temperature control systems with output delay against asymmetric input constraint

To tackle the asymmetric input constraint typically involved with industrial temperature control systems, e.g., there is a tuning range from 0 to 100% in the heating power, an anti-windup active disturbance rejection control (ADRC) is proposed for the practical application, in particular for dealing with output delay. Based on an artificial symmetric transformation for the asymmetric input constraint along with a delay-free output prediction, an anti-windup extended state observer (AESO) is firstly constructed to simultaneously estimate the delay-free system state and external disturbance for control design. When the input saturation constraint occurs, the proposed AESO could also offer anti-windup compensation. Then, a feedback controller is analytically derived by assigning repetitive-type poles for the characteristic equation of the closed-loop structure, followed by a set-point prefilter design to ensure no overshoot and output tracking deviation. Tractable linear matrix inequality based conditions are rigorously established to guarantee the asymptotic stability of the resulting closed-loop system under a specified initial condition. A benchmark example from a recent reference is used to verify the superiority of the proposed control method over some existing anti-windup control designs. Moreover, a real application to the temperature control of a jacketed crystallizer is shown in comparison with a recently developed control method with no anti-windup compensation.

Robust Regulator for Markov Jump Linear Systems with Random State Delays and Uncertain Transition Probabilities

The recursive robust regulation problem for Markov jump linear systems with state delay is investigated. The random delay belongs to a known interval and its maximum variation rate is considered. The transition probabilities matrix is subject to polytopic uncertainties. We model the delay by a Markov chain and obtain a delay-free Markovian system, through the augmented system approach. Based on combination of regularized least-squares with polytopic uncertainties and penalty function method, we propose a mode-dependent state-feedback control. The solution is given in terms of coupled Riccati equations presented in a symmetric matrix arrangement. With a numerical example, we compare our approach with other robust controllers from the literature.