Lyapunov-Krasovskii Functional Method Research Articles

Event-Triggered Predictive Control for Networked Systems Based on a Dual-Rate Sampling Switched Observer

This paper is concerned with predictive control of discrete-time networked control systems (NCSs) based on a dual-rate sampling switched observer, where the multiple output signals of the controlled plant are sampled using a dual-rate sampling mechanism. To reduce the effect of the bilateral network-induced uncertainties on NCSs, a novel predictive control protocol is proposed to compensate for the bilateral network-induced delays and packet dropouts. First, a dual-rate sampled-data-based switched observer with a fixed switching law is designed to estimate the state of the controlled plant, where the switching law is determined by the dual-rate sampled instants. Second, an estimated-state-based predictive controller is designed by synchronizing the control inputs used by the state predictor and the controlled plant, and the networked predictive control system is formulated as a threshold-error-dependent delay system model, where two associated but different event-triggered transmission schemes are introduced to determine whether the estimated states or the control packet should be transmitted or not. Sufficient conditions for co-designing the event-triggered matrix and the predictive controller gain are derived by using the Lyapunov-Krasovskii functional method. Finally, it is shown through a numerical example that the proposed method in this paper is effective for ensuring better system performance.

Finite-Time L2-Gain Asynchronous Control for Continuous-Time Positive Hidden Markov Jump Systems via T-S Fuzzy Model Approach.

This article investigates the finite-time asynchronous control problem for continuous-time positive hidden Markov jump systems (HMJSs) by using the Takagi-Sugeno fuzzy model method. Different from the existing methods, the Markov jump systems under consideration are considered with the hidden Markov model in the continuous-time case, that is, the Markov model consists of the hidden state and the observed state. We aim to derive a suitable controller that depends on the observation mode which makes the closed-loop fuzzy HMJSs be stochastically finite-time bounded and positive, and fulfill the given L2 performance index. Applying the stochastic Lyapunov-Krasovskii functional (SLKF) methods, we establish sufficient conditions to obtain the finite-time state-feedback controller. Finally, a Lotka-Volterra population model is used to show the feasibility and validity of the main results.

Novel Robust Stability Criteria of Uncertain Systems with Interval Time-Varying Delay Based on Time-Delay Segmentation Method and Multiple Integrals Functional

Interval time-varying delay is common in control process, e.g., automatic robot control system, and its stability analysis is of great significance to ensure the reliable control of industrial processes. In order to improve the conservation of the existing robust stability analysis method, this paper considers a class of linear systems with norm-bounded uncertainty and interval time-varying delay as the research object. Less conservative robust stability criterion is put forward based on augmented Lyapunov-Krasovskii (L-K) functional method and reciprocally convex combination. Firstly, the delay interval is partitioned into multiple equidistant subintervals, and a new Lyapunov-Krasovskii functional comprising quadruple-integral term is introduced for each subinterval. Secondly, a novel delay-dependent stability criterion in terms of linear matrix inequalities (LMIs) is given by less conservative Wirtinger-based integral inequality approach. Three numerical comparative examples are given to verify the superiority of the proposed approach in reducing the conservation of conclusion. For the first example about closed-loop control systems with interval time-varying delays, the proposed robust stability criterion could get MADB (Maximum Allowable Delay Bound) about 0.3 more than the best results in the previous literature; and, for two other uncertain systems with interval time-varying delays, the MADB results obtained by the proposed method are better than those in the previous literature by about 0.045 and 0.054, respectively. All the example results obtained in this paper clearly show that our approach is better than other existing methods.

Exponential stability analysis of neural networks with a time‐varying delay via a generalized Lyapunov‐Krasovskii functional method

SummaryAs is known to all that the Lyapunov‐Krasovskii functional (LKF) method plays a significant role in deriving exponential stability criteria of neural networks with a time‐varying delay. However, when the LKF method is adopted, the condition that a functional is required for a neural network with a delay varying in a delay interval is so strong that it may be hard to be satisfied and lead to a conservative criterion. Therefore, a generalized LKF method is proposed by weakening the strong condition in this paper. Then, new exponential stability criteria are derived via applying the proposed method. Finally, the effectiveness of the derived criteria is verified by two numerical examples.

Output Tracking and Feedback Controller Design for Nonlinear Stochastic Time-Delay System

This paper considers the design of output tracking and feedback controllers for nonlinear stochastic systems. The system status cannot be measured. The studied system contains nonlinear state functions, noise disturbances and time delays. We use the free weight matrix method to avoid the conservatism caused by the use of model transformation or cross-term bounded techniques. Based on the Lyapunov-Krasovskii functional method, we propose an output tracking and feedback controller design method based on linear matrix inequality (LMI). Numerical examples show the validity of the obtained results.

Observer-based adaptive neural control of nonlinear time-delay systems with unknown output function and unknown control directions

This paper is concerned with the problem of output feedback adaptive tracking control for a class of uncertain nonlinear time-delay systems (NTDS) with both uncertain output function and unknown control directions. By introducing a linear state transformation, the original system is transformed into a new system for which output feedback control design becomes feasible. Without the precise information on output function, an input-driven high-gain state observer is presented to estimate the unavailable states of the new system. Moreover, some radial basis function neural networks (RBFNNs) are employed to approximate the lumped unknown nonlinear functions during the procedure of control design. Then, by combining the Lyapunov–Krasovskii functional method, the Nussbaum gain function approach and the backstepping technique, a novel adaptive output feedback control scheme including only one parameter to be updated is developed for such systems. As a result, all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB) while the tracking error can remain in a small neighbourhood of zero. Finally, two simulation examples are given to validate the effectiveness and applicability of the proposed design method.

Leader-following consensus control for semi-Markov jump multi-agent systems: An adaptive event-triggered scheme

The problem of event-triggered leader-following consensus control for semi-Markov multi-agent systems is investigated in this paper. A semi-Markov process is used to describe the sudden parameter changes between every agent. An adaptive event-triggered control strategy is proposed to make a balance between reducing unnecessary communication and meeting the required performance. A control protocol which can resist actuator faults is used to ensure the reliable leader-following consensus. By employing the Lyapunov–Krasovskii functional method, some sufficient conditions are provided to guarantee that the leader-following consensus can be achieved in mean-square sense. The consensus controller and the event-triggered parameter can be co-designed. Finally, the effectiveness of the proposed method is verified by a F-404 aircraft engine system.

Stabilization of Linear Systems With Input Saturation and Large Delay

This paper investigates a stabilization problem for linear systems subject to saturation and time-varying delays in the control input, where the delay takes both large and small values in an alternating manner. Based on the delay values, the considered system is described by a switched system including a stabilizable subsystem and an unstabilizable subsystem. By using Lyapunov-Krasovskii functional method, a time-dependent switching rule orchestrating the proposed controllers is established to guarantee the regional stabilization of the closed-loop system. To obtain a domain of attraction as large as possible, an optimization problem is formulated in the form of linear matrix inequalities. Numerical examples and simulations are provided to demonstrate the effectiveness of the proposed method.

An improved -gain analysis method of nonlinear delay systems and its application to delayed neural networks

The Lyapunov–Krasovskii functional (LKF) method is widely used to derive -gain analysis criteria of delay systems. Nevertheless, how to improve the method for obtaining less conservative -gain analysis criteria is still an open problem. In this paper, an improved -gain analysis method called a delay-mode-based Lyapunov–Krasovskii functional (DMBLKF) method is proposed to replace the LKF method. This is achieved by weakening the condition that a LKF is required for a system with a delay varying in a delay interval. With the help of the DMBLKF method, new -gain analysis criteria of delayed neural networks are obtained and a numerical example is given to show that the DMBLKF method is more effective than the LKF method.

Exponential Synchronization of Inertial Cohen–Grossberg Neural Networks with Time-Varying Delays via Periodically Intermittent Control

This paper deals with the exponential synchronization problem of inertial Cohen–Grossberg neural networks with time-varying delays under periodically intermittent control. In light of Lyapunov–Krasovskii functional method and inequality techniques, some sufficient conditions are attained to ensure the exponential synchronization of the master-slave system on the basis of p-norm. Meanwhile, the periodically intermittent control schemes are designed. Finally, in order to verify the effectiveness of theoretical results, some numerical simulations are provided.

Event-Triggered Output Feedback Synchronization of Master-Slave Neural Networks Under Deception Attacks.

The problem of event-triggered synchronization of master-slave neural networks is investigated in this article. It is assumed that both communication channels from the sensor to controller and from controller to actuator are subject to stochastic deception attacks modeled by two independent Markov processes. Two discrete event-triggered mechanisms are introduced for both channels to reduce the number of data transmission through the communication channels. To comply with practical point of view, static output feedback is utilized. By employing the Lyapunov-Krasovskii functional method, some sufficient conditions on the synchronization of master-slave neural networks are derived in terms of linear matrix inequalities, which make it easy to design suitable output feedback controllers. Finally, a numerical example is presented to show the effectiveness of the proposed method.

Adaptive asymptotic tracking control of uncertain nonlinear time-delay systems depended on delay estimation information

This paper investigates the issue of adaptive asymptotic tracking control for high-order strict-feedback systems with mismatched unstructured nonlinearities and unknown time delays. Under the proposed control strategy, unknown time delays are estimated with the help of adaptation mechanism and projection operator, which abandons the use of the conventional Lyapunov-Krasovskii functional method and avoids the discussion of controller singularity problem. It is mentioned that most of current reported results on adaptive control of nonlinear delay systems under fuzzy approximation are semi-globally bounded. To achieve the asymptotic control objective, the upper bounds of approximation errors and other residual errors are properly estimated by establishing appropriate adaptive laws. Based on the estimation information of time delays and errors bounds, a novel adaptive sliding tracking control scheme is developed such that the tracking error will be forced to keep sliding along the origin once the upper bounds are reached. Therefore, the asymptotic tracking control objective is achieved. Simulation example verifies the effectiveness of the proposed scheme.

Quantitative Control of Nonlinear Systems Based on an Event Trigger Mechanism

In this study, we use an event-based mechanism for the quantitative control of nonlinear systems to obtain an optimized stable controller. We define a nonlinear system model based on an event trigger mechanism and a quantization mechanism. The layout of the model includes a sampler, which is continuously monitored, and the sampled signal. The latter is detected by the event trigger mechanism when a given threshold is fulfilled. The quantizer is used to discretize the incoming control signal, the controller output, the feedback, and the nonlinear system. As the second step, we define a neural network controller that is optimized using a suitable genetic algorithm. To reduce the conservativeness of the system, we use a piecewise Lyapunov–Krasovskii functional method. By analyzing the inherent transmission time delay, the synchronous controller is converted into the equivalent stability problem for the corresponding time-delayed system. The effectiveness and advantages of the proposed method are shown by numerical simulations based on an inverted pendulum.

Optimal Consensus-Based Event-Triggered Control Strategy for Resilient DC Microgrids

In this paper, an optimal consensus-based event-triggered control strategy is proposed to coordinate multiple distributed energy resources (DERs) in a dc microgrid. In the proposed control strategy, the average bus voltage restoration and the proportional current sharing are integrated by transforming the coordinated control problem into an optimization problem. The proposed solution enhances the resilience of the controller strategy in extreme events with uncertain initial states. Accordingly, the proposed control strategy provides a sampled-data-based event-triggered mechanism considering the limited availability of communication resources, which reduces communication burdens and avoids Zeno behaviors. The sufficient conditions are demonstrated using the Lyapunov-Krasovskii functional method for maintaining the stability of the proposed control strategy. Several case studies are presented using the PSCAD/EMTDC platform and the results are discussed to validate the effectiveness of the proposed control strategy for enhancing the dc microgrid resilience.

Finite‐time H∞ control of distributed parameter switched systems with event‐triggered scheme

AbstractThis manuscript addresses the finite‐time (FT) H∞ control issue for distributed parameter switched systems (DPSSs). First, finite‐time boundedness for DPSSs is studied. By applying piecewise Lyapunov–Krasovskii functional method incorporated with average dwell time approach, sufficient conditions of the FT boundedness for the DPSSs are derived in terms of linear matrix inequalities. Then, an event‐triggered scheme is constructed to design output feedback controller, which guarantees the closed‐loop system to be FT bounded. Based on the conditions in FT boundedness and event‐triggered FT stabilization, FT H∞ control problem for DPSSs is developed. Finally, two numerical examples are given to verify the effectiveness of the proposed results.

Resilient dynamic event‐triggered control for multi‐area power systems with renewable energy penetration under DoS attacks

Resilient dynamic event-triggered control design problem is concerned for frequency stabilisation of multi-area power systems with renewable energy penetration under transmission delay and denial-of-service (DoS) attacks. The main works are presented as followings: (1) A novel state-space model is established to describe multi-area power systems with solar and wind generation disturbance under load frequency control and virtual inertia control (LFC-VIC). (2) The influence of DoS attacks is considered and first modelled by model-based average dwell time (MDADT). A criterion of preserving desired exponential performance is obtained about the required lower bound of average dwell time (ADT) of sleep intervals, namely and the tolerable upper bound of ADT of attack intervals, namely . (3) To reduce communication load, a dynamic event-triggered mechanism (DETM) is proposed and designed jointly with resilient LFC-VIC scheme by using piecewise Lyapunov–Krasovskii functional method and LMIs technique. (4) To defence DoS attacks actively, based on the resulting MDADT criterion, a dynamic prediction strategy is proposed to compensate the packet drops with unknown bound subjected to attack strategy. Finally, a numerical example for a two-area power system is carried out to verify the designed resilient LFC-VIC scheme and the DETM.

Producing Stable Periodic Solutions of Switched Impulsive Delayed Neural Networks Using a Matrix-Based Cubic Convex Combination Approach.

This article is dedicated to designing a novel periodic impulsive control strategy for producing globally exponentially stable periodic solutions for switched neural networks with discrete and finite distributed time-varying delays. First, tunable parameters and cubic convex combination approach are proposed to study the globally exponential convergence of switched neural networks. Second, a sufficient criterion for the existence, uniqueness, and globally exponential stability of a periodic solution is demonstrated by using contraction mapping theorem and the impulse-delay-dependent Lyapunov-Krasovskii functional method. It is worth emphasizing that the addressed Lyapunov-Krasovskii functional covers both triple integral terms and novel quadruple integral terms, which makes the conservatism of the above criteria decrease. Even if the original neural network models are unstable or the impulsive effects are strong, the addressed neural network model can produce a globally exponentially stable periodic solution. These results here, which include boundedness, globally uniformly exponential convergence, and globally exponentially stability of the periodic solution, generalize and improve the earlier publications. Finally, two numerical examples and their computer simulations are given to show the effectiveness of theoretical results.

Stability of high-order delayed Markovian jumping reaction-diffusion HNNs with uncertain transition rates

This paper focuses on mean square exponential stability of high-order Markovian jump reaction-diffusion HNNs (RHNNs) with uncertain transition rates (GUTRs) and time-varying delays by Lyapunov-Krasovskii functional method and linear matrix inequality (LMI). In this GUTR model, only part of the transition rates can be known, namely, its estimate error and estimate value are known, but the others have no useful information. Our models are more comprehensive and some existing results are special cases of ours. Finally, a numerical example illustrates the validity of our findings.

Projective synchronization of fuzzy memristive neural networks with pinning impulsive control

This paper is concerned with the problems of projective synchronization for fuzzy memristive neural networks (FMNNs) with pinning impulsive control. At first, the mathematical model of FMNNs is formulated on the basis of Takagi-Sugeno (T-S) fuzzy rules. According to the physical properties of memristor, the fact of parameters mismatch is also considered between the master and slave systems. Then, through introducing a novel type of pinning impulsive controllers and applying the Lyapunov-Krasovskii functional (LKF) method, some corresponding weak projective synchronization criteria are constructed. In order to handle the difficulties of error system discontinuous, the extended comparison principle based on the formula for variation of parameters and Cauchy matrix of linear impulsive system are introduced. Furthermore, complete projective synchronization criteria are also discussed under some given conditions. Finally, two simulation examples are given to show the effectiveness and validity of the obtained results.

Formula omitted] and [formula omitted]-[formula omitted] state estimation for delayed memristive neural networks on finite horizon: The Round-Robin protocol

In this paper, a protocol-based finite-horizon H∞ and l2-l∞ estimation approach is put forward to solve the state estimation problem for discrete-time memristive neural networks (MNNs) subject to time-varying delays and energy-bounded disturbances. The Round-Robin protocol is utilized to mitigate unnecessary network congestion occurring in the sensor-to-estimator communication channel. For the delayed MNNs, our aim is to devise an estimator that not only ensures a prescribed disturbance attenuation level over a finite time-horizon, but also keeps the peak value of the estimation error within a given range. By resorting to the Lyapunov–Krasovskii functional method, the delay-dependent criteria are formulated that guarantee the existence of the desired estimator. Subsequently, the estimator gains are obtained via figuring out a bank of convex optimization problems. The validity of our estimator is finally shown via a numerical example.