LMI Technique Research Articles

Adaptive event-triggered secure control for IT2 fuzzy systems vulnerable to hybrid attacks and its application

This work addresses the adaptive event-triggered control issue that interval type-2 (IT2) fuzzy systems are vulnerable to hybrid attacks.They were initially developed for fuzzy systems by thoroughly addressing the characteristics of hybrid attacks, which include deception attacks and replay attacks. Our main goal is to mitigate the effects of hybrid attacks and protect communication resources by developing an event-triggered controller for IT2 fuzzy systems with adjustable thresholds. The proposed hybrid attacks are described by a stochastic random variable that satisfies the Bernoulli distribution. Based on Lyapunov-Krasvoskii stability theory, the resulting closed-loop IT2 fuzzy system clearly satisfies sufficient criteria to ensure mean square stability. Also, the weight matrices of the trigger condition and controller gain matrices are obtained using LMI techniques. Lastly, a numerical example is provided to illustrate the effectiveness and applicability of the proposed control strategy.

Event‐Triggered Secure Control of Positive Networked Control Systems Under Multi‐Channels Attacks

ABSTRACTThis paper focuses on the secure control of positive networked control systems under multi‐channel attacks characterized by a Bernoulli distribution. Specifically, the sensor‐to‐controller channel suffers from false data injection (FDI) attacks, whereas the controller‐to‐actuator channel suffers from denial of service (DoS) attacks. The objective is to design a static output feedback controller that guarantees the positivity and stochastic stability of the closed‐loop system in the presence of DoS and FDI attacks. To conserve communication resources, we employ an event‐triggered scheme to reduce the frequency of information transmission. Due to the positivity of the system, the proposed event‐triggering mechanism employs the 1‐norm form instead of the 2‐norm form, which allows that the controller parameter is determined via linear programming rather than LMI technique. Finally, two simulation examples are provided to verify the effectiveness of our methods.

Novel reachable set estimation results for delayed linear systems with bounded disturbance

Reachable set estimation is a prominent research topic in control theory and systems science. Reachable set estimation for time-delay systems has drawn a lot of interest. Until now, most approaches to the reachable set estimation problem of time-delay systems have involved building intricate Lyapunov functionals and utilizing LMI techniques. This has resulted in complicated LMI conditions and a proof procedure. The reachable set estimation issue for delayed linear systems with bounded disturbance will be reviewed in this paper. A novel reachable set estimation lemma with a time-delay term is proposed, and based on the acquired lemma, a sufficient condition is given to bound the reachable set estimation of the systems under discussion. In addition, an event-based sufficient criterion for reachable set estimation is also provided. The theoretical analysis in this paper is succinct when compared to previous findings, and the obtained conditions are simple to validate. Lastly, two examples are presented to confirm that the theoretical results hold true.

Finite-Time and Fixed-Time Synchronization of Delayed Memristive Neural Networks via Adaptive Aperiodically Intermittent Adjustment Strategy.

This article investigates the finite-time and fixed-time synchronization for memristive neural networks (MNNs) with mixed time-varying delays under the adaptive aperiodically intermittent adjustment strategy. Different from previous works, this article first employs the aperiodically intermittent adjustment feedback control and adaptive control to drive the MNNs to achieve synchronization in finite time and fixed time. First of all, according to the theories of set-valued mappings and differential inclusions, the error MNNs is derived, and its finite-time and fixed-time stability problems are discussed by applying the Lyapunov function method and some LMI techniques. Moreover, by meticulously designing an effective aperiodically intermittent adjustment with adaptive updating law, sufficient conditions that guarantee the finite-time and fixed-time synchronization of the drive-response MNNs are obtained, and the settling time is explicitly estimated. Finally, three numerical examples are provided to illustrate the validity of the obtained theoretical results.

A High-Gain Observer Design for Nonlinear System with Delayed Measurements: Application to a Quadrotor UAV

The paper deals with the design of a high-gain observer for nonlinear system with delayed output measurements and bounded disturbances. The new structure of the proposed observer exhibits good performance in terms of allowing a higher MAVTD (Maximum Allowable Value of the Time-Delay) compared to the existing works, where the MAVTD is limited due to the high value of the high-gain parameter. Based on the LMI technique and using Lyapunov-Krasovskii function, an explicit relation between MAVTD and the LMI tuning parameters is deduced from the stability analysis of the proposed observer. The efficiency of the proposed structure is illustrated through an application to a Quadrotor UAV and a comparison with standard and cascade high-gain observers is performed.

Stabilisation in distribution by delay feedback controls for hybrid stochastic delay differential equations

This article aims to design a linear delay feedback control to stabilise an unstable hybrid stochastic delay differential equation in distribution. Under the global Lipschitz condition, sufficient criteria are established to guarantee the stability of the controlled system. Then LMI techniques are employed to design the control law in two structure forms: state feedback and output injection.

Distributed nonstationary control system synthesis on a basis of spectral representation in space-time domain

It is proposed, based on the spectral representation of the system, to solve the problem of synthesis of a distributed control plant described by PDE, using LMI technique. The system is described by a spectral characteristic vector with the amplitudes of the space-time modes of the Fourier series as components. The spectral characteristic vector is satisfied to an infinite SLAE composed for an initial PDE using the spectral method. For the spectral plant representation in space-time domain the stability, controllability, and observability criterions are formulated. The procedure of control synthesis on the basis of solving of stabilization problem with full information and observation problem is proposed. The expression for time-dependent matrix regulator gain is received.

Event-triggered annular finite-time [formula omitted] filtering for stochastic network systems

The event-triggered annular finite-time H∞ filtering problem is addressed for stochastic network systems in this paper. The influence of stochastic disturbance is considered in the whole framework of filter design. A zero-order-holder (ZOH) is introduced to maintain and send the delayed output signals for filter updating. By resorting to a novel delay-dependent Lyapunov-Krasovskii functional (LKF) and LMI technique, the stochastic annular finite-time boundedness of the filtering error system is analyzed. Furthermore, the H∞ filter design under the event-triggered mechanism is established in the sense of a prescribed H∞ performance level. Finally, two numerical examples are realized to illustrate the validity of the proposed results.

Robust Fuzzy Feedback Control for Nonlinear Systems With Input Quantization

In this article, we study the robust quantized feedback control problem for nonlinear discrete-time systems that are described by Takagi–Sugeno (T–S) fuzzy model with norm-bounded uncertainties. The dynamic quantizer composed of a dynamic parameter and a static quantizer is considered to quantize the control input signal. An improved two-step approach to design controller and dynamic quantizer for T–S fuzzy system is proposed based on the LMI technique. In the first step, a robust controller is designed to guarantee that the quantized fuzzy closed-loop system with norm-bounded uncertainties is asymptotically stable with prescribed <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathcal {H}_{\infty }$</tex-math></inline-formula> performance. Then, the parameter-dependent (membership function) scalar variable is obtained to determine the dynamic quantizer’s parameter in the second step. Finally, the simulation result of truck–trailer system is presented to validate the effectiveness and feasibility of the proposed two-step design approach.

Sparse Filtering Under Norm-Bounded Exogenous Disturbances Using Observers

The paper considers the sparse filtering problem under arbitrary norm-bounded exogenous disturbances. We propose a simple and universal observer-based approach to its solution, based on the LMI technique and the method of invariant ellipsoids; it allows the use of a reduced number of system outputs. From a technical point of view of application, we reduce the original problem to semi-definite programming, which is easily solved numerically. The proposed simple approach is easy to implement and can be equally extended to systems in continuous and discrete time.

Global Practical Conformable Stabilization by Output Feedback for a Class of Nonlinear Fractional‐Order Systems

Researchers have explored the concept of “practical stability” in the literature, pointing out that stability investigations always guarantee “practical stability” and the inverse is not true. The concept “practical stability” means that the origin is not an equilibrium point and the convergence of the system state is towards a ball centered at the origin. The primary purpose of this work is to investigate the notation of practical stability for a new class of fractional-order systems using the general conformable derivative. As a second objective, the nonlinear condition chosen is novel in that it is not Lipschitz as is customary, which is original in and of itself. In addition, some new analysis related to the LMI techniques was used to prove the main results. To begin, a method of stabilization is provided. Following that, the proposed system’s observer design is presented. Also, the principle of separation is described. Finally, a numerical example is offered to demonstrate the proposed methodology’s validity.

Optimal linear quadratic Gaussian control based frequency regulation with communication delays in power system

&lt;p&gt;In this paper, load frequency regulator based on linear quadratic Gaussian (LQG) is designed for the MAPS with communication delays. The communication delay is considered to denote the small time delay in a local control area of a wide-area power system. The system is modeled in the state space with inclusion of the delay state matrix parameters. Since some state variables are difficult to measure in a real modern multi-area power system, Kalman filter is used to estimate the unmeasured variables. In addition, the controller with the optimal feedback gain reduces the frequency spikes to zero and keeps the system stable. Lyapunov function based on the LMI technique is used to re-assure the asymptotically stability and the convergence of the estimator error. The designed LQG is simulated in a two area connected power network with considerable time delay. The result from the simulations indicates that the controller performed with expectation in terms of damping the frequency fluctuations and area control errors. It also solved the limitation of other controllers which need to measure all the system state variables.&lt;/p&gt;

Adaptive Event‐Triggered Control for Complex Dynamical Network with Random Coupling Delay under Stochastic Deception Attacks

This study concentrates on adaptive event‐triggered control of complex dynamical networks with unpredictable coupling delays and stochastic deception attacks. The adaptive event‐triggered mechanism is used to avoid the wasting of limited bandwidth. The probability of data communicated by the network is established by statistical properties and Bernoulli stochastic variables with an uncertain occurrence probability. Stability analysis based on Lyapunov–Krasovskii functional (LKF) and the stability of the closed‐loop system is guaranteed. Using the LMI technique, we obtain triggered parameters. To demonstrate the feasibility and usefulness of the suggested methodology, two examples are shown.

Development of MADB of P‐I controller using LMI technique in a renewable energy based AGC system and study its application in a deregulated environment including energy storage device

AbstractIn recent decades, inclusion of renewable resources is considered as one of the most promising options for the long run uninterrupted power supply without depending on conventional resources. Thus, the renewable energy generation will get more attention and massive growing, so that the goal of 40% share of electricity in the worldwide energy portfolio in 2050 would be realized. But during replacement of renewable energy by conventional energy, engineers are facing a lot of problem due to solar generation, wind generation change their characteristic rapidly with weather condition, which may cause large synchronizing imbalance between different units and generate large system delay or communication delay in large interconnected grid. In this article, the authors propose linear matrix inequalities techniques to developed margin of allowable delay for delay dependent stable hybrid system. Initially, to judge the efficacy of proposed chaotic atomic search optimization (CASO) algorithm over other evolutionary algorithms with PID controller, a thermal‐hydro gas system is considered. The second part of this article is motivated by the fact that proposed CASO algorithm with P‐I controller is superior in contrast to bacterial foraging algorithm technique. In addition to this, some energy storage devices such as fuel cell, aqua electrolyzer, and ultra‐capacitor are used to achieve a better dynamic response within specified delay margin. Moreover, to study the impact of communication delays (delay margin) due to the loss of synchronism between solar‐wind (for their unpredicted environmental features) and thermal unit (nonlinearities like generation rate constraints, boiler dynamics, and governor with the dead band) are considered in thermal unit and the simulation results verify with the effectiveness of the proposed approach on providing a balance between the delay margin and the damping performances is evaluated under deregulated environment. The simulation results help to make an inter‐relation between the delay margin and the controller gain (P‐I) which help the system operator in designing controllers gain for stable operation of the proposed hybrid system.

LPV approach for collision avoidance: Controller design and experiments

This paper presents a robust approach for the lateral controller design and analysis. This controller is an important part of the Advanced Evasive Steering system for improving driving safety in emergency situations. First, the path-following problem is formulated in a generic LPV framework taking into account the actuator’s rate constraint and the avoidance trajectory disturbance. Then, a simple static state-feedback is optimized using LMI technique. It is shown that a good compromise between performance and robustness of the controller can be achieved with this method. Moreover, the simplicity and the low tuning effort is beneficial for implementation of the proposed controller on conventional automotive ECUs. Experimental results obtained with different driving scenarios confirm the effectiveness of this method.

Exponential synchronization for spatio-temporal directed networks via intermittent pinning control

In this paper, the exponential synchronization of directed spatio-temporal complex networks is concerned via intermittent pinning control, where the underlying topology is very generic and is not necessarily node balanced or strongly connected. Firstly, based on the decomposition of the topological graph into several maximal strongly connected subgraphs, two intermittent pinning controllers are developed. Subsequently, by adding the synchronized state as a virtual node to the original network, the exponential pinning synchronization of the underlying network is discussed, and several sufficient criteria are derived by utilizing M-matrix and LMI technique. Finally, the feasibility of theoretical results is substantiated by an illustrative example.

Design and Implementation of Novel LMI-Based Iterative Learning Robust Nonlinear Controller

An iterative learning robust fault-tolerant control algorithm is proposed for a class of uncertain discrete systems with repeated action with nonlinear and actuator faults. First, by defining an actuator fault coefficient matrix, we convert the iterative learning control system into an equivalent unknown nonlinear repetitive process model. Then, based on the mixed Lyapunov function approach, we describe the stability of the nonlinear repetitive mechanism on time and trial indices and have appropriate conditions for the repeated control system’s stability in terms of linear matrix inequality theory. Through LMI techniques, we have obtained satisfactory results and controller stability, and robustness against fault tolerance is also discussed in detail. Finally, the simulation results of the output tracking control of the two exemplary models verify the effectiveness of the proposed algorithm.

Fuzzy Intermittent Extended Dissipative Control for Delayed Distributed Parameter Systems With Stochastic Disturbance: A Spatial Point Sampling Approach

In this article, the extended dissipative performance of distributed parameter systems (DPSs) with stochastic disturbances and multiple time-varying delays is studied by using a new fuzzy aperiodic intermittent sampled-data control strategy. Different from the previous fuzzy sampled-data control results, the state sampling of the proposed sampled-data controller occurs only in space and is intermittent rather than continuous in the time domain. By introducing a novel multitime-delay-dependent switched Lyapunov functional to explore the dynamic characteristics of the controlled system, and by means of the famous Jensen’s inequality with reciprocally convex approach, Wirtinger’s inequality, the criterion of the system’s mean square stabilization is established based on the LMI technique, which quantitatively reveals the relationship between the control period, the control length, and the upper bound of the control sampling interval. Especially, the optimal control gain is given by designing an optimized algorithm in the article, which greatly reduces the cost. Finally, two numerical examples are presented to demonstrate the effectiveness and superiority of the proposed approach.

Observer‐based preview repetitive control for uncertain discrete‐time systems

AbstractIn this paper, the preview repetitive control (PRC) problem is considered for uncertain discrete‐time systems subject to a previewable periodic reference signal. First, an augmented system including future information on the previewable reference signal is constructed. Second, considering the state unmeasured and periodic tracking reference signal, state observer and preview repetitive controller (PRCr) are designed in both state feedback and output feedback settings. To achieve signal tracking performance, a two‐dimensional (2D) model approach and some LMI technique are presented to describe the control and learning actions of the PRC system by using the lifting technique. Then, by Lyapunov–Krasovskii functions, sufficient conditions for asymptotic stability of the 2D system are derived in the form of a set of LMIs, and meanwhile, the design of a repetitive controller with preview actions is proposed through the LMI approach. Finally, two examples illustrate the effectiveness of the results.

Stability and Hopf bifurcation of a delayed giving up smoking model with harmonic mean type incidence rate and relapse

Tobacco epidemic which is the primary risk factor for noncommunicable diseases such as cardiovascular, cancers, diabetes and hear diseases, has been one of the most serious public health problems in the globe. It is of vital significance to control tobacco epidemic and reduce smoking rate in order to protect our health and life. For this purpose, a delayed giving up smoking model considering relapse is proposed in this research work. Local stability and existence of Hopf bifurcation are performed through taking different combinations of the two delays as bifurcation parameters. Specially, global exponential stability is proved with aid of LMI techniques. Finally, the theoretical results are verified numerically and graphically.