Krasovskii Functionals Research Articles

Integrated Security Control for Nonlinear CPS with Actuator Fault and FDI Attack: An Active Attack-Tolerant Approach

This paper investigated the co-design problem of less conservative integrated security control and communication for a nonlinear cyber-physical system (CPS) with an actuator fault and false data injection (FDI) attacks. Firstly, considering the efficient utilisation and allocation of computing and communication resources, an integrated framework was proposed from the perspective of active defence against FDI attacks. Secondly, the actuator fault and FDI attacks were augmented as a vector, and a robust observer was proposed to estimate the system state, actuator fault and FDI attacks. Furthermore, based on the obtained estimation results and the location of the FDI attack in the dual-end network, we designed an integrated security control strategy of active attack tolerance and active fault tolerance and, by constructing Lyapunov–Krasovskii functions and using time-delay system theory and the affine Bessel–Legendre inequality, a less conservative co-design method for integrated security control and network communication resource saving was developed. Finally, a simulation experiment of a quadruple tank was carried out to demonstrate the effectiveness of the proposed method.

Mean-Square Stability of Uncertain Delayed Stochastic Systems Driven by G-Brownian Motion

This paper investigates the mean-square stability of uncertain time-delay stochastic systems driven by G-Brownian motion, which are commonly referred to as G-SDDEs. To derive a new set of sufficient stability conditions, we employ the linear matrix inequality (LMI) method and construct a Lyapunov–Krasovskii function under the constraint of uncertainty bounds. The resulting sufficient condition does not require any specific assumptions on the G-function, making it more practical. Additionally, we provide numerical examples to demonstrate the validity and effectiveness of the proposed approach.

Event-triggered tracking control for nonlinear time-varying delay systems with full state constraints and unknown control coefficients

This paper addresses the problem of event-triggered control for a class of nonlinear systems with unknown control coefficients, time-varying delays, full state constraints and external disturbances, simultaneously. Firstly, based on integral Barrier-Lyapunov Functionals, an adaptive event-triggered controller is designed to account for the impacts of complete state constraints, unknown time-varying delays and external disturbances. Using fuzzy logic systems, the unknown functions of systems are then roughly estimated. The system redundancy can be significantly reduced by implementing the event-triggered control technique in the meanwhile. By introducing the separation technique and Lyapunov–Krasovskii functionals, it is shown that the strategy can ensure tracking performance greatly and all the closed-loop signals of the system are bounded. Compared with the existing results, the proposed design scheme is less conservative and has a wilder application range. Finally, the simulation results show the effectiveness of the proposed approach.

H∞ cruise control for high-speed trains with process and data transmission time-varying delay

This paper investigates an H∞ cruise control strategy for uncertain high-speed trains (HSTs) with two time-varying delays. The multibody model of the cascading car is established, taking into account the influence of the flexible coupler and the basic resistance (rolling mechanical resistance + aerodynamic resistance) in the actual operation process. There are many uncertainties in the actual operation of the train, such as disturbances caused by gusts and track irregularities and time-varying delays caused by flexible couplers. Based on the above factors, this paper fully considers and supplements the multibody model. A cruise control strategy based on Lyapunov stability theory and linear matrix inequality (LMI) is proposed. The state feedback control rate with input short time delay is designed, and a cruise control method with double time-varying delays is proposed by sampling data. Constructed Lyapunov–Krasovskii function (LKF) with time-delay parameters for time-delay systems to fully introduce the information of time delays. In view of the disturbance effect, the sufficient condition to suppress the disturbance is given. The proposed H∞ cruise control method controls the fluctuating speed and displacement of the train to quickly converge to the steady state. The HST at equilibrium tracks the desired velocity and ensures a stable relative displacement. The specified H∞ interference attenuation level is achieved to ensure safe and comfortable operation. Two numerical simulations are carried out to illustrate the effect of state time-varying delay and disturbance on train stationarity, which proves the superiority of the proposed method.

BLF-based neural dynamic surface control for stochastic nonlinear systems with time delays and full-state constraints

This paper investigates the adaptive neural tracking control problem for a class of stochastic nonlinear systems with time delays and full-state constraints in a unified framework for the first time. The time-delay terms of the controlled systems are compensated by novel Lyapunov–Krasovskii functionals. The asymmetric barrier Lyapunov function (BLF) is adopted to guarantee that the full states are always restricted within prescribed constraints. RBF neural networks are utilised to approximate the lumped unknown functions in the design process. Furthermore, the dynamic surface control (DSC) technique is employed to simplify the process of control design significantly. Stability analysis shows all closed-loop signals are SGUUB, and full-state constraints are not violated. Finally, simulation results confirm the effectiveness of the proposed control scheme.

Robust H∞ output consensus of heterogeneous nonlinear multi-agent systems with external disturbance and unknown time-delay based on distributed Lyapunov-based MPC

This paper investigates a Lyapunov-based Model Predictive Control (LMPC) for solving the output consensus problem of nonlinear heterogeneous Multi-Agent Systems (MASs) subject to external disturbances and unknown time delay. Considering an appropriate Lyapunov–Krasovskii Functional (LKF), the optimization problem of the cost function is stated based on the given LKF which is effective in reducing the computational load. Additionally, sufficient conditions are derived to achieve the output consensus based on the H ∞ performance index by solving the Linear Matrix Inequalities. To eliminate the effects of the unknown time delay in the MASs, the distributed controllers include both state feedback and time-delay state feedback terms. At last, numerical and practical examples are provided to show the applicability and effective performance of the proposed method.

Delay-dependent stability of load frequency control with adjustable computation accuracy and complexity

Cyber–physical power systems (CPPS) utilize wide-area measurement system, where communication networks employed in the control loop introduce time delays inevitably. The existing studies focus on either computation accuracy or efficiency for investigating the delay-dependent stability of large-scale delayed CPPS. Whereas, the requirements for calculation accuracy and efficiency vary from the demand for online stability analysis and offline controller design. This paper investigates the demand-oriented stability of the delayed CPPS and takes load frequency control (LFC) systems as typical examples. Novel regulation schemes have been proposed with adjustable conservatism and computation complexity. Different from existing studies, this paper establishes regulated stability criteria by constructing variable Lyapunov–Krasovskii functionals and using compatible integral inequalities for estimations. Then, an algorithm is designed by introducing a threshold parameter to calculate accurate delay margins or to realize high computation efficiency flexibly. Case studies are complemented on the two-area LFC scheme and IEEE 39-bus system. It is illustrated that the proposed method can realize on-demand adjustments for real power systems, i.e., setting the threshold parameter to zero achieves almost accurate delay margins like the frequency-domain method, which guides the offline controller design with desired performance; less computation complexity is achieved with a relatively large threshold parameter, and thus, the proposed method is applicable for online stability analysis.

Performance Error Estimation and Elastic Integral Event Triggering Mechanism Design for T–S Fuzzy Networked Control System Under DoS Attacks

This article analyzes the mechanism of denial-of-service (DoS) attacks initiated by hackers from the perspective of computer networks. In order to effectively estimate the performance error generated by the T–S fuzzy networked control systems under DoS attacks, we transform the performance error estimation problem into the one of finding ellipsoid constraints <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathfrak {J}(P_{i})$</tex-math></inline-formula> . First, improved Lyapunov–Krasovskii functions (LKFs) based on fuzzy membership functions are constructed, which combine the characteristics of nonlinear problems in the system to reduce the initial constraints. Then, a second-order weight method (SOWM) is introduced to divide the time interval of sampling meticulously. Besides, the information stored in the LKFs is enhanced. Furthermore, we construct the novel looped functions by relying on the SOWM. Next, a suitable integral elastic event trigger mechanism is established to ensure that the performance errors caused by the attacks are estimated. Finally, the feasibility of the proposed method is verified by a two-degree-of-freedom helicopter system.

Nonlinear Algorithms for Controlling a Group of Mobile Agents on a Segment

A group of mobile agents on a straight line is considered. Agents are understood as numbered points that can change their position. It is assumed that the dynamics of agents is modeled by second-order integrators, with each agent receiving information from one of its left and one of its right neighbors (not necessarily nearest neighbors). It is required to provide a given nonlinear-uniform (uniform with respect to a prescribed nonlinear function) deployment of agents on a straight line segment. It is worth mentioning that, in numerous applications such as optic, acoustics, physiology, information theory, thermodynamics, etc., instead of linear scale, nonlinear ones (for instance, logarithmic) are used. In addition, it should be noted that an important class of formation control problems is synchronization of processes with respect to certain functions of phase coordinates. To solve the stated problem, nonlinear decentralized protocols are proposed. The conditions on the control parameters are determined, under which the agents converge to the required positions. The robustness of the constructed control protocols with respect to communication delay and network topology switching (replacing chosen neighbors by the other ones) is investigated. In this case, it is assumed that information about the magnitude of the delay and about the switching law may be absent. It is shown that for any constant non-negative delay and any admissible law for switching connections, a given deployment of agents is guaranteed. The proofs of the stated statements are based on the application of the Lyapunov direct method and a special form of the decomposition method. Original constructions of Lyapunov functions and Lyapunov—Krasovskii functionals are used. The results of numerical simulation are presented, confirming the obtained theoretical conclusions.

A Novel Adaptive Finite-Time Position Tracking Control Strategy for Teleoperation System with Varying Communication Delays

Based on the traditional control approach, the position-tracking performance of the teleoperation system with communication delay is generally asymptotically stable. In practical applications, the closed-loop system is expected to achieve stable and finite-time convergence performance. A novel finite-time bilateral control scheme for a telerobotics system with communication delay is presented in this paper. On the basis of the traditional proportional damping injection control, this paper proposes and designs a new finite-time control method by introducing the non-integer power to the position error, velocity, and the combined error with position error and velocity. In comparison to existing proportional damping injection and finite-time control structures, the proposed method not only achieves the finite-time convergence performance of position tracking, but it also has the advantages of a simple structure and fewer gain coefficients. The controller also incorporates the radial basis function (RBF) neural network and adaptive approach to compensate unknown dynamics and external forces, thus also avoiding the measurement of force signals. The Lyapunov–Krasovskii function is then defined, and it is demonstrated that the position tracking of closed-loop teleoperation system has bounded stability and finite-time control performance. The simulation experiment is also performed, and the results further illustrated the bounded stability of the system. Moreover, compared to the position tracking errors of other non-finite-time control methods, it is demonstrated that the proposed finite-time control scheme has a faster convergence rate and higher convergence precision.

State estimation for delayed genetic regulatory networks with reaction diffusion terms and Markovian jump

Robust state estimation for delayed genetic regulatory networks with reaction–diffusion terms and uncertainties terms under Dirichlet boundary conditions is addressed in this article. The main purpose of the problem investigation is to design a novel state observer for estimate the true concentrations of mRNA and protein by available measurement outputs. Based on Lyapunov–Krasovskii functions and linear matrix inequalities (LMI), sufficient conditions are given to ensure the robust stability of the estimation error networks. Two examples are presented to illustrate the effectiveness of the proposed approach.

Bounded real lemmas and exponential [formula omitted] control for memristor-based neural networks with unbounded time-varying delays

This paper focuses on developing a bounded real lemma (BRL) and designing a state-feedback controller which guarantees a prescribed H∞ performance level for a class of memristor-based neural networks (MNNs) with unbounded time-varying delays. Firstly, a BRL for MNNs is presented by taking a new approach based on system solutions. This approach requires neither transformation of the model nor construction of Lyapunov–Krasovskii functionals, thereby reducing computational effort and complexity. In addition, the obtained BRL contains only a few simple inequalities, which can be easily solved by using MATLAB. Secondly, the condition for the existence of exponential H∞ controller is given based on the obtained BRL. Finally, two simulation examples demonstrate the validity of the theoretical results.

Exponential stability of linear discrete systems with multiple delays by degenerated Lyapunov–Krasovskii functionals

The problem of exponential stability of delayed discrete systems with multiple delays x(n+1)=(I+A)x(n)+∑i=1sBix(n−i),n=0,1,…is studied, where x=(x1x2…xm)T is an unknown vector, m and s are fixed positive integers, A, Bi are square constant matrices and I is a unit matrix. A new degenerated Lyapunov–Krasovskii functional is used to derive sufficient conditions for exponential stability and to derive an exponential estimate of the norm of solutions. Though often used in the study of stability, the assumption that the spectral radius of the matrix of linear terms is less than 1 is not applied here. The criterion derived is illustrated by an example and compared with previously known results.

A new stability criterion and its application to robust stability analysis for linear systems with distributed delays

Recently, the possibility to verify positive definiteness of Lyapunov–Krasovskii functionals only on a specific Razumikhin-type set of functions to conclude on the stability of linear time delay systems was shown. In this paper, for a class of systems with multiple concentrated and distributed delays, we extend the result and prove that this specific set may be applied while verifying the negative definiteness of the functionals derivatives along the solutions as well. The result is applied in the robustness analysis with respect to uncertainties both in the system matrices and in the delays. It provides a simple way to prove the robust stability conditions due to obviating the need to work with indefinite derivatives of functionals along the solutions of a perturbed system. As a by-product, the estimates for an unstable eigenvalue of the system are derived, and the functionals defined on complex-valued initial functions are presented.

Extended dissipative output‐feedback control for discrete‐time bidirectional associative memory neural networks via delay‐partitioning approach

AbstractThis paper is concerned with the analysis of an extended dissipativity performance for a class of bidirectional associative memory (BAM) neural networks (NNs) having time‐varying delays. To achieve this, the idea of the delay‐partitioning approach is used, where the range of time‐varying delay factors is partitioned into a finite number of equidistant subintervals. A delay‐partitioning based Lyapunov–Krasovskii function is introduced on these intervals, and some new delay‐dependent extended dissipativity results are established in terms of linear matrix inequalities, which also depend on the partition size of the delay factor. Further, numerical examples are performed to acknowledge the extended dissipativity performance of delayed discrete‐time BAM NN; further, four case studies were explored with their simulations to validate the impact of the delay‐partitioning approach.

Dissipativity analysis for Lur'e systems with two additive time‐varying delays via some novel Lyapunov–Krasovskii functionals

AbstractThe problem of dissipativity analysis is discussed for Lur'e systems with two additive time‐varying delays (ATDs) in this paper. Based on the dynamic delay interval (DDI) method, some novel Lyapunov‐Krasovskii functionals (LKFs) are constructed, in which part of Lyapunov matrices are requested to be positive definite. Then strictly dissipativity criteria of Lur'e systems with ATDs are presented in terms of linear matrix inequalities (LMIs). As by‐products, the stability criteria of Lur'e systems with ATDs and the systems with ATDs are derived. Finally, several numerical examples are used to illustrate the effectiveness and superiority of these criteria.

Sequential Predictors for Uncertain Euler–Lagrange Systems with Large Transmission Delays

This paper investigates the state prediction problems for uncertain Euler–Lagrange systems with large time delays during data transmissions. A set of sequential predictors is proposed to estimate the actual real-time states of the systems by using the delayed information of measurements. The arbitrarily large delays are handled by applying adequate numbers of serial sub-predictors. Meanwhile, the novel prediction structure of each subsystem is designed to deal with nonlinearities and unknown dynamics in the systems. Then, the predictor design is extended to the case without using delayed velocity measurements by updating the structure of the first sub-predictor. Sufficient conditions for the design of predictor gains, ensuring the boundness of prediction errors, are obtained through Lyapunov–Krasovskii functionals. The effectiveness and robustness of the uncertainties of the proposed method are verified by comparative results in simulations.

Input-to-State Stability for Time-Delay Systems With Large Delays

In this article, we consider the input-to-state stability (ISS) problem for a class of time-delay systems with intermittent large delays, which may cause the invalidation of traditional delay-dependent stability criteria. The topic of this article features that it proposes a novel kind of stability criterion for time-delay systems, which is delay dependent if the time delay is smaller than a prescribed allowable size. While if the time delay is larger than the allowable size, the ISS can be preserved as well provided that the large-delay periods satisfy the kind of duration condition. Different from existing results on similar topics, we present the main result based on a unified Lyapunov-Krasovskii function (LKF). In this way, the frequency restriction can be removed and the analysis complexity can be simplified. A numerical example is provided to verify the proposed results.

A prescribed-performance-based adaptive finite-time tracking control scheme circumventing the dependence on the system initial condition

This paper is concerned with the prescribed finite-time tracking control problem for a class of nonlinear systems with unknown initial condition, state time-varying delays and external disturbances. A new adaptive prescribed finite-time tracking control scheme bypassing system initial condition is proposed via the prescribed performance method. Several nonlinear mapping functions (NMFs) and a new prescribed finite-time performance function (PFTPF) combining finite-time control with prescribed performance control are constructed to obtain the scheme. In this paper, the assumptions on the time-delay terms are removed by means of the designed Lyapunov–Krasovskii functions. In addition, to avoid step impact effect arisen by an overlarge initial control input, a control input with zero initial value is obtained. Aiming at the design of zero initial control input, a new Lyapunov stability criterion form is put forward. Two practical examples are presented to confirm the effectiveness and superiority of the proposed scheme.

Stability analysis of T–S fuzzy systems with time-varying delay via parameter-dependent reciprocally convex inequality

The stability problem of T–S fuzzy systems with time-varying delay is investigated in this article. The purpose is to establish the less conservative stability conditions for T–S fuzzy systems with time-varying delays. Firstly, a parameter-dependent reciprocally convex inequality is proposed to improve the estimation accuracy of reciprocal convex terms. Secondly, based on the line-integral Lyapunov–Krasovskii (L–K) function and the developed parameter-dependent reciprocally convex inequality, a less conservative stability condition is established. Finally, two examples are used to verify the feasibility and superiority of the proposed method.