Krasovskii Method Research Articles

A Lyapunov--Krasovskii Method for Semiglobal Stabilization of a Class of Time-Delay Nonlinear Systems With Uncontrollable Linearization by Linear Feedback

A Lyapunov--Krasovskii Method for Semiglobal Stabilization of a Class of Time-Delay Nonlinear Systems With Uncontrollable Linearization by Linear Feedback

Event‐triggered adaptive secure lateral stabilization for autonomous vehicles under actuator attacks

SummaryFalse data injection attacks can disrupt the steering control actions and make a real threat to both the security and safety of autonomous vehicles. In this paper, a secure event‐triggered lateral control approach of autonomous vehicles subject to actuator attacks is investigated. Firstly, an arbitrary unknown actuator attacks is considered in the secure lateral steering control of autonomous vehicles. Thus, to save communication resources for the limited bandwidth CAN bus, the periodic event‐triggered transmission scheme is utilized, transforming the established lateral steering control into a time‐delay system through the consideration of periodic event‐triggered sampling. Then, an adaptive control compensation scheme is developed to mitigate the malicious effects caused by actuator attacks. The proposed secure control approach is skilled in compensating the unknown attacked steering control actions in an adaptive way. The stabilization criteria under the adaptive secure control law is well derived by Lyapunov–Krasovskii method and some linear inequality matrices operations. At last, the effectiveness of the proposed secure control scheme is verified by some numerical experiments borrowed from a practical vehicle.

High-Gain-Observer-Based Predictive Output Feedback for Nonlinear Systems With Large Input-Delays

Abstract The predictor feedback has been demonstrated to be quite effective in large delay compensation. However, few researches in the field of predictor feedback for large delays focused on output feedback control (OFC). This paper develops the previous work to design high-gain-observer-based predictive output feedback for nonlinear systems with large delays. Two methods are employed for large delay compensation: the backstepping-based partial differential equation (PDE) method and the reduction-based ordinary differential equation (ODE) method. It appears that, for continuous-time control, the first method leads to simpler linear matrix inequality (LMI) conditions and deal with larger delays, whereas the second method is easily exploited for sampled-data implementation under continuous-time measurement. Lyapunov–Krasovskii method is presented to guarantee the exponential stability of the nonlinear systems under predictor-based controllers. Through a simulation example of pendulum, the proposed methods are demonstrated to be efficient when the input delays are too large for the system to be stabilized without a predictor.

Razumikhin and Krasovskii stability of impulsive stochastic delay systems via uniformly stable function method

This paper generalizes Razumikhin-type theorem and Krasovskii stability theorem of impulsive stochastic delay systems. By proposing uniformly stable function (USF) in the form of impulse as a new tool, some properties about USF and some novel pth moment decay theorems are derived. Based on these new theorems, the stability theorems of impulsive stochastic linear delay system are acquired via the Razumikhin method and the Krasovskii method. The obtained results enhance the elasticity of the impulsive gain by comparing the previous results. Finally, numerical examples are given to demonstrate the effectiveness of theoretical results.

Lie-brackets-based averaging of affine systems via a time-delay approach

In this paper, we study input-to-state stability (ISS) of affine systems with a small parameter ɛ>0 and additive disturbances in the presence of state-delays. We present a time-delay approach to Lie-brackets-based averaging, where we transform the system to a time-delay (neutral type) one. The latter has a form of perturbed Lie brackets system. The ISS of the time-delay system guarantees the same for the original one. We present a direct Lyapunov–Krasovskii (L–K) method for the time-delay system and provide sufficient conditions for regional ISS. Further we apply the results to stabilization of linear uncertain systems under unknown control directions using the bounded extremum seeking controller with measurement delay. In contrast to the existing results that are all qualitative, we derive constructive linear matrix inequalities for finding quantitative upper bounds on ɛ and the time-delay that ensure regional ISS of the original system and on the resulting ultimate bound. Numerical examples illustrate the efficiency of our method.

Neural event-triggered optimal filtering co-design of Markovian jump systems with hidden mode detections

The modified H∞ filtering problem for a class of Markovian jump systems with unknown nonlinear dynamics is investigated in the work by developing the neural event-triggered filter co-design method. Moreover, the true system modes are assumed to be inaccessible such that the estimated jumping modes are utilized for the mode-dependent filters. In particular, a novel event-triggered mechanism is introduced to improve filtering communication efficiency, where the unknown nonlinearity approximation is conducted by a neural network. By virtue of employing Lyapunov–Krasovskii method, sufficient filtering conditions are constructed to ensure the optimal H∞ performance under the mean-square framework, based on which desired mode-dependent filter gains, event-triggering, and neural network parameters are co-designed with an aid of matrix techniques. Illustrative simulations with two practical examples are finally carried out to validate the usefulness and advantages of our developed approach.

Sampled-Data Extremum Seeking With Constant Delay: A Time-Delay Approach

This article proposes a constructive method for sampled-data extremum seeking (ES) with square wave dithers and constant delays, by using two time-delay approaches: one to averaging and the other to sampled-data control. We consider gradient-based ES for static maps which are of quadratic forms. By transforming the ES system to the time-delay system, we have developed a stability analysis via a Lyapunov–Krasovskii method. We derive the practical stability conditions in terms of linear matrix inequalities for the resulting time-delay system. The time-delay approach offers a quantitative calculation on the upper bound of the dither and sampling periods, constant delays that the ES system is able to tolerate, as well as the ultimate bound of the extremum seeking error. This is in the presence of uncertainties of extremum value and extremum point.

Two categories of new criteria of [formula omitted]th moment stability for switching and impulsive stochastic delayed functional differential equation with markovian switching

This note focuses on the pth moment stability for switching and impulsive stochastic delayed functional differential equation with Markovian switching. Under delay and Markovian switching, several novel stability criteria of pth moment input-to-state stability and pth moment integral input-to-state stability are enumerated by wielding Razumikhin/Krasovskii stability theory. Meanwhile, we show the correlation and differences for Razumikhin and Krasovskii method. The characteristic of the criteria requires that the time derivatives of the Razumikhin or Krasovskii functionals are enabled to be a function of time various, which can slacken guard in requirement. It is shown that, if the subsystems are stable in some interval but the discrete dynamics are not, the stochastic delayed hybrid system is stable. On the contrary, when the jump maps are stable with uncertain subsystems, the delayed-dependent impulses may overcome the destabilizing effects to achieve the stability. Finally, an example is given to show the effectiveness and practicability of the results.

Design of Synchronization Tracking Adaptive Control for Bilateral Teleoperation System with Time-Varying Delays.

The performances of position synchronization and force interaction of the teleoperation system provide a safe and efficient way for operators to perform tasks in remote, hazardous environments. In practice, however, communication delays and dynamic uncertainties can impair the performance of position synchronization controls. Under the above factors, it is necessary to study and design appropriate bilateral control methods to achieve stable and effective position synchronization control. In this paper, a new adaptive control architecture based on velocity feedback filter and radial basis function neural network is proposed. In the proposed control scheme, only the position signal is transmitted during the communication process, and the speed feedback filter and compensation method are designed and adopted to avoid the use of acceleration signals. In addition, a new auxiliary variable with a tracking error integral term is used to reduce the steady-state error of position tracking under nonzero external environmental forces. Using the Lyapunov–Krasovskii method, the stability of closed-loop remote operating systems is demonstrated. In the simulation and experiment sections, the algorithm was verified separately and compared with other algorithms. The results of a master–slave robot system verify the tracking performance of our proposed control scheme.

Event-Based Distributed Fuzzy Load Frequency Control for Multiarea Nonlinear Power Systems With Switching Topology

This article investigates the event-based distributed fuzzy load frequency control approach for nonlinear interconnected power systems under a switching topology. Specifically, nonlinear factors and uncertain parameters existing in turbine and governor dynamics are modeled and analyzed under the interval type-2 fuzzy method. New memory-based adaptive event-triggered mechanisms, whose directions and threshold parameters are dynamically updated based on the output change trend and relative output error of multiple memories, are proposed to further save network energy. Aiming at communication topology changes in multiarea power systems, a novel switched control system is established by introducing a time-varying communication matrix. Then, the system’s asymptotic stability is ensured by the piecewise Lyapunov–Krasovskii method. Furthermore, to further relax stability conditions, slack matrices are considered with the boundary information of membership functions. Finally, three-area power systems are shown to demonstrate the effectiveness of proposed distributed load frequency control strategies.

A Car-Following Model for Connected and Automated Vehicles With Heterogeneous Time Delays Under Fixed and Switching Communication Topologies

This paper proposes a new car-following (CF) model to capture the realistic behaviors of connected and automated vehicles (CAVs), whose communication topology (CT) among vehicles is characterized by graph theory in the V2V communication environment. By considering the heterogeneous time delays under the fixed and switching CTs, a generalized CF model is proposed. Based on the Lyapunov–Krasovskii method, a convergence analysis has been implemented for this new CF model with multiple time delays to obtain the convergence condition. Meanwhile, provides an estimate of the time delay bound. Finally, numerical experiments are performed under three typical fixed CTs (i.e., PF topology, BDLF topology, and TPLF topology) and the corresponding switching topology. Results support that the proposed CF model is capable of accurately reproducing the velocity, acceleration, position, and space headway profiles of CAVs traffic flow.

Observer-based robust control for a class of sampled-data systems with model uncertainty and external disturbance

This paper studies the issue of observer-based feedback stabilisation for a class of linear sampled-data systems with model uncertainty and external disturbance. First, for a sampled-data system with external disturbance, a sampled-data observer is designed to estimate the system state. Subsequently, a robust controller based on the observer is developed. For a continuous sampling interval, the gain matrices of both observer and controller change exponentially. Second, using the state coordinate transformations with an exponential rate, a unified dynamics is constructed by augmenting the state estimation error and the closed-loop system state as a new state. Next, the sufficient conditions ensuring the asymptotical stability of the closed-loop system are given by the Lyapunov–Krasovskii method and linear matrix inequality (LMI) technique. Finally, the effectiveness of the proposed method is verified by a helicopter model.

Finite-Time Asynchronous Event-Triggered Formation of UAVs with Semi-Markov-Type Topologies.

In this paper, the finite-time formation problem of UAVs is investigated with consideration of semi-Markov-type switching topologies. More precisely, finite-time passivity performance is adopted to overcome the dynamical effect of disturbances. Furthermore, an asynchronous event-triggered communication scheme is proposed for more efficient information exchanges. The mode-dependent formation controllers are designed in terms of the Lyapunov–Krasovskii method, such that the configuration formation can be accomplished. Finally, simulation results are given to demonstrate the validity of the proposed formation approach.

Dynamic event-triggered resilient state estimation for time-varying complex networks with Markovian switching topologies

This paper addresses a resilient state estimation problem for an array of nonlinear complex networks with switching topologies under the dynamic event-triggered mechanism (ETM). To reduce the unnecessary data delivery, the dynamic ETM is introduced to schedule the data delivery from sensors to estimators. The model of the switched complex networks is established by adopting a Markov chain which is better to reflect the characteristics of practical complex networks. A set of novel estimators is obtained by using the properties of Kronecker product combining with the Lyapunov–Krasovskii method, and some easy-to-check conditions are derived such that the dynamics of state estimation error satisfies the prescribed H∞ performance index. In addition, the parameters of the designed resilient state estimators can be acquired by solving a series of convex optimization problems. In the end, a simulation example is given to demonstrate the validity of the proposed theoretical results in this paper.

Hierarchical Optimization-Based Model Predictive Control for a Class of Discrete Fuzzy Large-Scale Systems Considering Time-Varying Delays and Disturbances

In this manuscript, model predictive control for class of discrete fuzzy large-scale systems subjected to bounded time-varying delay and disturbances is studied. The considered method is Razumikhin for time-varying delay large-scale systems, in which it includes a Lyapunov function associated with the original non-augmented state space of system dynamics in comparison with the Krasovskii method. As a rule, the Razumikhin method has a perfect potential to avoid the inherent complexity of the Krasovskii method especially in the presence of large delays and disturbances. The considered large-scale system in this manuscript is decomposed into several subsystems, each of which is represented by a fuzzy Takagi–Sugeno (T-S) model and the interconnection between any two subsystems is considered. Because the main section of the model predictive control is optimization, the hierarchical scheme is performed for the optimization problem. Furthermore, persistent disturbances are considered that robust positive invariance and input-to-state stability under such circumstances are studied. The linear matrix inequalities (LMIs) method is performed for our computations. So the closed-loop large-scale system is asymptotically stable. Ultimately, by two examples, the effectiveness of the proposed method is illustrated, and a comparison with other papers is made by remarks.

Event-Triggered Guaranteed Cost Leader-Following Consensus Control of Second-Order Nonlinear Multiagent Systems

This article deals with the event-triggered leader-following guaranteed cost consensus control problem for second-order nonlinear multiagent systems, in which the guaranteed cost function is proposed to facilitate to enhance the consensus tracking regulation performance. To reduce the frequency of information transmission, a distributed event-triggered mechanism, which broadcasts the triggered states to its neighbours for each agent, is designed, and the triggering condition is then constructed for leader-following second-order nonlinear multiagent systems. By employing Lyapunov–Krasovskii method and Barbalat’s lemma, some sufficient conditions are derived to ensure the leader-following consensus and guaranteed cost performance for second-order nonlinear multiagent systems. It is also exhibited that the constructed triggering condition can efficaciously exclude the Zeno behavior. To testify the efficacy of the proposed theoretical methodology, a simulation example is offered.

Consensus Analysis in Multi-agent Systems with Non-uniform Time-varying Delays and Uncertain Topologies

This paper analyzes the consensus problem in a group of networked agents with nonuniform time-varying delays communicating over an uncertain communication network. Time-varying delays are assumed to be associated with each link in a directed communication graph topology. The network topology for information exchange is modeled with communication links subject to bounded multiplicative uncertainties. By using the the Lyapunov–Krasovskii method, delay-dependent consensus conditions are derived in terms of linear matrix inequalities. A numerical simulation is presented to illustrate the accuracy of the proposed theoretical approach.

Memory‐based dynamic event‐triggered control for networked interval type‐2 fuzzy systems subject to DoS attacks

SummaryIn this article, the memory‐based dynamic event‐triggered controller design issue is investigated for networked interval type‐2 (IT2) fuzzy systems under non‐periodic denial‐of‐service (DoS) attacks. For saving limited network bandwidth, a novel memory‐based dynamic event‐triggered mechanism (DETM) is proposed to schedule data communication. Unlike existing event‐triggered generators, the developed memory‐based DETM can utilize a series of newly released signals and further save network resources by introducing interval dynamic variables. Moreover, to improve design flexibility, an IT2 fuzzy controller with freely selectable fuzzy rule number and premise membership functions (MFs) is synthesized. Then, a new switched time‐delay system with imperfectly matched MFs is established under the consideration of memory‐based DETM and DoS attacks simultaneously. Besides, based on the property of MFs, the boundary information of membership grades and slack matrices are introduced in the stability analysis. Furthermore, by using a piecewise Lyapunov–Krasovskii method, membership‐functions‐dependent criteria are deduced to ensure the asymptotic stability of built fuzzy switched systems. Finally, the effectiveness of proposed control strategies is demonstrated by simulation examples.

Self-discipline predictive control against large-scale packet dropouts using input delay approach

This paper develops a novel self-discipline predictive control (SPC) scheme to compensate the missing control inputs of networked control systems (NCS) under arbitrary bounded packet dropouts. Since no feedback measurements are available when there are packet dropouts, the key idea of SPC scheme is that one can adjust its controller gains only based on the latest received state measurement rather than waiting the next available measurement. Then, the future controller gains are predicted by using input delay approach while input to state stability (ISS) is arrived under Lypunov–Krasovskii method and switched system framework. In what follows, the SPC scheme based on the predicted controller gains are used to update the control inputs during packet dropout intervals. A main advantage of this work lies in that the proposed SPC scheme realises a self-stabilisation with only limited feedback measurements under large-scale packet dropouts. At last, simulations on path following control of autonomous vehicles are carried out to show the validity of the proposed SPC scheme.

Sampled‐data implementation of extended PID control using delays

AbstractWe study the sampled‐data implementation of extended PID control using delays for the nth‐order stochastic nonlinear systems. The derivatives are approximated by finite differences giving rise to a delayed sampled‐data controller. An appropriate Lyapunov–Krasovskii (L‐K) method is presented to derive linear matrix inequalities (LMIs) for the exponential stability of the resulting closed‐loop system. We show that with appropriately chosen gains, the LMIs are always feasible for small enough sampling period and stochastic perturbation. We further employ an event‐triggering condition that allows to reduce the number of sampled control signals used for stabilization and provide ‐gain analysis. Finally, three numerical examples illustrate the efficiency of the presented approach.