Linear Matrix Inequality Technique Research Articles

Switching adaptive dynamic event-triggered consensus of nonlinear multi-agent systems under DoS attacks and communication delay

This article addresses the issue of achieving security consensus in multi-agent systems (MASs) that are susceptible to denial-of-service attacks (DoS-As) and time-varying communication delays (TCD). We have developed a novel unified model to describe DoS-As and TCD. Firstly, a new switching adaptive dynamic event-triggered mechanism (SADETM) is proposed to conserve communication resources during DoS-As and TCD. The mechanism transforms into three event-triggered strategies adapted to highly dynamic MASs. Then, a consensus control protocol is designed through consensus errors based on SADETM. Finally, the sufficient conditions for ensuring the stability of MASs are solved by combining the Lyapunov-Krasovskii functional (LKF) method and the linear matrix inequality (LMI) technique. The effectiveness of this method is verified through simulation examples.

Distributed observer for fault estimation in Load-Frequency Control of multi-area power systems with communication delays

This paper proposes an innovative approach to designing a distributed observer for fault and state estimations in Load Frequency Control (LFC) of time-delayed multi-area interconnected power systems. To reach this goal, the paper first provides exhaustive information and analysis on the structure, disturbances, and faults in multi-area power systems. Then, an L1 observer with the capability to simultaneously estimate the system’s states, process/actuator faults, and sensor faults is proposed. This observer exhibits robustness against various types of disturbances as well as time delays present within both the system and the communication network. The sufficient conditions for designing the proposed observer, guaranteeing the system stability, and minimizing the L1 performance index, are expressed as optimization problems employing Linear Matrix Inequality (LMI) techniques. Additionally, the effectiveness and credibility of the proposed distributed observer in estimating all states and faults in all areas are validated through simulation results.

Mittag-Leffler function based security control for fractional-order complex network system subject to deception attacks via Observer-based AETS and its applications

The goal of this paper is to investigate the security control for uncertain fractional-order delayed complex network systems under deception attacks using the Mittag-Leffler function and observer-based adaptive event-triggered scheme (AETS) with the fractional commensurate order in q ∈ (0, 1). The adaptive event-triggering scheme is used during the data transmission process from the sensors to the observer, where the triggering threshold can be dynamically modified to reduce resource waste. We make a novel model for the estimation error system that takes into account both the effects of the adaptive event-triggered scheme and the effects of deception attacks. A sufficient condition is obtained to guarantee the stochastic mean-square stability of the augmented error system using the Mittag-Leffler (M-L) functions and the Lyapunov functional method and by using the singular value decomposition (SVD) and linear matrix inequality (LMI) techniques, the co-design problem of desired observer and controller gains is found, and it is shown that the solution ensures the stability of a closed-loop uncertain fractional-order complex networked system. At the end of this study, two numerical examples and diesel engine system model are given to show that the above findings are correct.

Observer-based adaptive memory event-triggered consensus tracking control for high-speed train under DoS attacks

AbstractThis paper focuses on the event-triggered consensus tracking of high-speed trains under denial-of-service (DoS) attacks. A novel anti-disturbance control strategy is proposed, based on an adaptive memory state observer and a disturbance observer. A memory is introduced to buffer system output information which enhancing the precision of the state observer, and the gust disturbance during the high-speed train operation is estimated by the disturbance observer. The Linear Matrix inequality technique is used to obtain the observer feedback coefficient and the controller gain, and the Lyapunov theory is employed to demonstrate the controller’s consistency tracking performance. Applying the memory to the event-triggered mechanism, a new adaptive memory event-triggered scheme is designed to better ensure system performance and effectively prevent the occurrence of Zeno behavior. To achieve precise identification of DoS attacks in the event-triggered environment, a new detection algorithm is proposed. Finally, simulation examples are used to validate the effectiveness and practicality of the proposed scheme.

A Novel Robust H∞ Control Approach Based on Vehicle Lateral Dynamics for Practical Path Tracking Applications

This paper proposes a robust lateral control scheme for the path tracking of autonomous vehicles. Considering the discrepancies between the model parameters and the actual values of the vehicle and the fluctuation of parameters during driving, the norm-bounded uncertainty is utilized to deal with the uncertainty of model parameters. Because some state variables in the model are difficult to measure, an H∞ observer is designed to estimate state variables and provide accurate state information to improve the robustness of path tracking. An H∞ state feedback controller is proposed to suppress system nonlinearity and uncertainty and produce the desired steering wheel angle to solve the path tracking problem. A feedforward control is designed to deal with road curvature and further reduce tracking errors. In summary, a path tracking method with H∞ performance is established based on the linear matrix inequality (LMI) technique, and the gains in observer and controller can be obtained directly. The hardware-in-the-loop (HIL) test is built to validate the real-time processing performance of the proposed method to ensure excellent practical application potential, and the effectiveness of the proposed control method is validated through the utilization of urban road and highway scenes. The experimental results indicate that the suggested control approach can track the desired trajectory more precisely compared with the model predictive control (MPC) method and make tracking errors within a small range in both urban and highway scenarios.

Observer-based security control for state-dependent fractional-order system with multiple attacks via polytope-type approach and application to tunnel diode model

This work examines a polytope-type approach for observer-based security control of a fractional-order system that is under multiple attacks via an event-triggered scheme. A novel multiple-attack model is first proposed for fractional-order systems such as denial-of-service attacks and reply attacks, which can destroy the system's security during the signal process. In contrast to previous studies, the design of the controller is developed using an observer-based event-triggered scheme in the presence of multiple attacks. An event-triggering strategy is proposed to reduce the communication burden of the output measurement signals. An observer-based control is designed to keep the fractional-order system stable in all scenarios where one or more simultaneous attacks may occur. These findings can ensure the absence of Zeno behaviour and considerably reduce data transmissions. By employing the suitable Lyapunov–Krasovskii functional, sufficient conditions are derived to ensure fractional-order system stability. Controller and observer-gain matrices are obtained by using the linear matrix inequality technique. Finally, two examples are provided to demonstrate the feasibility and usefulness of the suggested methodology.

A fractional-order multiple-model type-2 fuzzy control for interconnected power systems incorporating renewable energies and demand response

Frequency regulation in Multi-region Interconnected Power Systems (MIPS), incorporating wind turbine systems, energy storage units, and demand response, is a challenging control problem. The problem involves maintaining grid stability, integrating variable renewable energy sources, enhancing grid resilience, optimizing energy storage and demand response capabilities, and ensuring regulatory compliance. Effective frequency regulation is a key problem for reliable and sustainable power system operation. In this paper, complex and uncertain dynamics in various components of a MIPS are modeled using multiple first-order dynamic fractional-order Type-2 Fuzzy Logic Systems (T2-FLSs). The models are evaluated, and the best possible dynamic model is chosen. With the best possible model, an optimal controller is designed. The stability and optimality analysis are presented through a Linear Matrix Inequality (LMI) approach. The adaptive laws of T2-FLSs are derived such that some LMI-based conditions are satisfied. The designed controller does not depend on the dynamics of MIPS. The uncertainties of time-varying load, wind energy, and solar power are modeled using T2-FLSs. The suggested LMI technique presents adaptation laws for T2-FLSs to ensure stability in the presage of natural disturbances and errors. The designed scheme is validated by applying to a practical 39-bus IEEE test system that includes the wind farms, demand response, and energy storage systems. The simulation results under various conditions verify the usefulness of the suggested controller. The comparisons with conventional controllers demonstrate that the suggested approach is more effective under uncertainties and natural perturbations.

Dissipativity-based robust filter design for singular fuzzy systems with dynamic quantization and event-triggered mechanism

This paper focus on the design issue of event-based dissipative filter for quantized nonlinear singular systems. To save the communication resource, we employ a dynamic quantizer to quantized the measurement output signal prior to transmitting it to the filter via digital communication. Furthermore, the paper also presents an event-triggered mechanism for determining the transmission of the quantized signal. The intention of this paper is to try to propose an event-triggered filter to ensure that the filtering error system (FES) is admissible and satisfies strictly dissipativity performance, in the presence of dynamic quantization and occurring uncertainties. The Lyapunov function is utilized to establish a sufficient condition for the FES to meet the strictly dissipative performance. Depending on the obtained conditions, the required filter parameters are proposed using the standard linear matrix inequality (LMI) technique. Ultimately, the effectiveness of the developed method is verified by an actual circuit simulation.

Adaptive control for memristive system via compensatory controller and Chebyshev neural network

In this paper, based on linear matrix inequality technique, a simple controller and a compensatory controller are designed. It can track arbitrary fixed points and any periodic orbits. In addition, a synchronization control method via Chebyshev neural network with external disturbances is proposed. An adaptive controller is given. The Chebyshev neural network is used to approximate the uncertain nonlinear function and the adaptive law is used to adjust the corresponding parameters in the system. Taking a 4D memristive chaotic system as examples, the results are in consistent with the simulations. From a framework and control theoretical point of view, the proposed synchronization approach via compensation controller and Chebyshev neural network is firstly presented. From an application point of view, the proposed scheme can simplify the complexity of controller design. It is promising in many applications for mem-systems as secure communications and neural networks.

Robust security‐based model predictive control for nonlinear cyber‐physical system under random occurring deception attacks and actuator saturation

AbstractThis article presents a robust security‐based model predictive control (MPC) framework for a class of discrete‐time nonlinear cyber‐physical systems (CPSs) suffering random deception attacks and persistent actuator saturation. In CPSs, the attacks can significantly degrade the control performance. Naturally, a larger degree of control is required, prompting the consideration of actuator saturation in CPS's structure. In our work, the cyberattacks on the controller‐actuator (C‐A) channel are described as a stochastic process with specific probability and bounded energy. The security‐related constraint is introduced to improve the resistance and robustness against attacks. Mean‐square quadratic boundedness is derived to estimate the robustly invariant set. By placing the saturated input into a convex hull, a robust security‐based MPC optimization problem is addressed less conservatively with linear matrix inequality technique. Furthermore, the feasibility of the proposed method is proved recursively, and the stability and security of the closed‐loop system are established in mean‐square sense. In the end, the laboratory tank and reactor‐separator process are applied to validate the effectiveness of the proposed algorithm.

Fault-tolerant control for Markov jump nonlinear systems based on an observer and finite-time fast integral terminal sliding mode control

This paper develops a novel fault-tolerant control based on an observer for underactuated robot manipulators with unknown external disturbances, uncertainties, and actuator faults. First, unlike the traditional approach of treating the robot system as a parameter time-varying system, the underactuated robot manipulator with different drive modes can be considered as one of the classical Markov jump nonlinear systems (MJNSs). Second, an adaptive disturbance observer is designed to estimate the state and disturbances of the system. Finally, based on the observation results, a nonsingular fast integral terminal sliding mode controller (NFITSMC) is utilized to implement fault-tolerant control of the system. Compared with traditional observer and terminal sliding mode controller, the adoption of the novel controller and observer can improve response time and reduce chattering. Especially, in order to eliminate chattering, the integral term is introduced into the nonsingular fast terminal sliding mode controller. Structuring Lyapunov–Krasovskii functional (LKF) and based on linear matrix inequalities (LMIs) techniques, the convergence of control strategy and tracking errors is proved. The simulation results show that the actuator faults can be observed successfully and the error system is finite-time stable.

Asynchronous output feedback quantized sliding mode dissipative control for Markovian jump time-delay systems with generally bounded transition rates

This article figures out the asynchronous output feedback sliding mode dissipative control issue for Markovian jump delay systems (MJDSs) with uncertain parameters and external disturbances. Different from the massive methods of constructing sliding mode surfaces (SMS), a new dynamic output feedback (DOF) integral SMS is developed, where the SMS is composed of a virtual controller with quantized output and the controller is asynchronous with the system mode. Meanwhile, the reachability of the SMS is guaranteed. In addition, the transition rates (TRs) considered in this paper are generally bounded, which means that the designed method applies to the more general case of TRs, such as fully known and partially unknown TRs. The sufficient criteria of stochastic stability and strict dissipation for the MJDSs are deduced. The design scheme of the controller gain matrix is proposed by the linear matrix inequality (LMI) technique. Finally, two examples are shown to demonstrate the effectiveness and feasibility of the designed technique.

Adaptive Optimal Terminal Sliding Mode Control for T-S Fuzzy-Based Nonlinear Systems

This study utilizes the Takagi–Sugeno fuzzy model to represent a subset of nonlinear systems and presents an innovative adaptive approach for optimal dynamic terminal sliding mode control (TSMC). The systems under consideration encompass bounded uncertainties in parameters and actuators, as well as susceptibility to external disturbances. Performance evaluation entails the design of an adaptive terminal sliding surface through a two-step process. Initially, a state feedback gain and controller are developed using Linear Matrix Inequality (LMI) techniques, grounded on H2-performance and partial eigenstructure assignment. Dynamic sliding gain is subsequently attained via convex optimization, leveraging the derived state feedback gain and the designed terminal sliding mode (TSM) controller. This approach diverges from conventional methods by incorporating control effort and estimating actuator uncertainty bounds, while also addressing sliding surface and TSM controller design intricacies. The TSM controller is redefined into a strict feedback form, rendering it suitable for addressing output-tracking challenges in nonlinear systems. Comparative simulations validate the effectiveness of the proposed TSM controller, emphasizing its practical applicability.

Combined Observer-Based State Feedback and Optimized P/PI Control for a Robust Operation of Quadrotors

This paper deals with a discrete-time observer-based state feedback control design by taking into consideration bounded parameter uncertainty, actuator faults, and stochastic noise in an inner control loop which is extended in a cascaded manner by outer PI- and P-control loops for velocity and position regulation. The aim of the corresponding subdivision of the quadrotor model is the treatment of the control design in a systematic manner. In the inner loop, linear matrix inequality techniques are employed for the placement of poles into a desired area within the complex z-plane. A robustification of the design towards noise is achieved by optimizing both control and observer gains simultaneously guaranteeing stability in a predefined bounded state domain. This procedure helps to reduce the sensitivity of the inner control loop towards changes induced by the outer one. Finally, a model-based optimization process is employed to tune the parameters of the outer P/PI controllers. To allow for the validation of accurate trajectory tracking, a comparison of the novel approach with the use of a standard extended Kalman filter-based linear-quadratic regulator synthesis is presented to demonstrate the superiority of the new design.

A New Observer Design for the Joint Estimation of States and Unknown Inputs for a Class of Nonlinear Fractional-Order Systems

This article designs an observer for the joint estimation of the state and the unknown input for a class of nonlinear fractional-order systems (FOSs) such that one portion satisfies the Lipschitz condition and the other does not necessarily satisfy such a condition. Firstly, by reconstructing system dynamics, the observer design is transformed equivalently into the tracking problem between the original nonlinear FOSs and the designed observer. Secondly, the parameterized matrices of the desired observer are derived by use of the property of the generalized inverse matrices and the linear matrix inequality (LMI) technique combined with the Schur complement lemma. Moreover, an algorithm is presented to determine the desired observer for the nonlinear FOSs effectively. Finally, a numerical example is reported to verify the correctness and efficiency of the proposed algorithm.

Finite-time interval stabilization for time-varying stochastic delayed systems via interval matrix method by piecewise controllers

This paper presents a comprehensive study addressing the problem of finite-time interval stabilization (FTIS) for two distinct types of systems: linear time-invariant stochastic delayed systems (LTISDSs) and linear time-varying stochastic delayed systems (LTVSDSs). To begin, the definition of FTIS is established, which is based on employing piecewise state feedback controllers. Subsequently, a time-varying Lyapunov-Krasovskii functional (LKF) is proposed and a novel optimization algorithm is designed to address the challenge of FTIS for LTISDSs. Additionally, this paper investigates the equivalence of LTVSDSs to uncertain stochastic delayed systems with interval parameters, represented as a series of convex combinations. Notably, both the optimization algorithm and the linear matrix inequalities (LMIs) technique are employed to establish sufficient conditions for achieving FTIS in LTVSDSs. Furthermore, when compared to traditional state feedback controllers, the piecewise controllers not only enhance the precision of system control but also lead to reduced control gains and fewer control effort requirements. Finally, the findings are substantiated through the presentation of two numerical examples, providing practical validation for the proposed methodologies and their effectiveness.

Asynchronous event-triggered guaranteed cost control of uncertain 2-D Markov jump Roesser systems with actuator saturation

This paper investigates the asynchronous event-triggered guaranteed cost control problem for two-dimensional Markov jump Roesser systems with parameter uncertainties and actuator saturation. The hidden Markov model is constructed to characterize the asynchronous phenomenon induced by the mode mismatch between the system and the controller, and a hidden Markov model-based event-triggered mechanism is adopted in controller design to save communication resources. The convex hull representation is employed to process saturated inputs. By using the quadratic Lyapunov function methods and linear matrix inequality techniques, some sufficient criteria are developed to guarantee the asymptotic stability of the addressed system with a guaranteed cost under three different boundary conditions. Finally, a convex optimization algorithm with linear matrix inequality constraints is proposed to design the optimal asynchronous event-triggered guaranteed cost controller, and a numerical example is considered to demonstrate its validity.

Switching-like event-triggered control of uncertain NCSs under delay distribution and DoS attacks

The paper addresses the switching-like event-triggered control for uncertain networked control systems with time-varying delay under DoS attacks. First of all, to reduce the communication burden, a switching-like event-triggered mechanism is designed to automatically select the trigger condition according to whether the system is under DoS attacks, which have the advantage of reducing the number of data packets transmitted. Secondly, unlike the traditional assumption of time-varying delay, here it satisfies the condition that the probability is known, and combines the networked control systems to propose a novel time-delay system model, which can obtain a larger upper bound on the delay. Then, by using both the Lyapunov functional method and linear matrix inequality technique, we obtain sufficient conditions of uncertain networked control systems to achieve exponentially stable in the mean square sense. Furthermore, under the common limitations of the maximum continuous packet losses caused by the DoS attacks and delay, the stability criterion is derived, which can be used to estimate the communication parameters and security controller gain. Finally, through two simulation examples, the larger upper bound of time delay, less trigger times, faster convergence rate are obtained, which verify the validity of our theoretical analysis.

Resilient coordination of multi-agent systems in the presence of unknown heterogeneous actuation efficiency and coupled dynamics: distributed approaches

To guarantee the stability and performance of an overall heterogeneous multi-agent system, feedback control structures must be capable of addressing the presence of heterogeneous agent-based nonlinear uncertainties, unknown actuation performance, and coupling effects. Additionally, some tasks require agents to track the leader's state and reach different states in a distributed way. Therefore, this paper proposes a distributed adaptive controller that drives a set of agents to user-assigned positions in the presence of the mentioned heterogeneous system anomalies. To address actuator dynamics, a hedging-based reference model is used to decouple adaptive updating from the actuator dynamics. To deal with the coupled dynamics, an observer-based estimation algorithm is proposed. Finally, the low-frequency learning method is used to deal with the high-frequency control response and, therefore, to obtain a better transient performance. The overall closed-loop system's stability is investigated using the Lyapunov Stability Theory, and the Linear Matrix Inequalities (LMI) technique is employed to identify stability limits regarding the actuator bandwidths of each agent. Illustrative numerical examples are presented to demonstrate the designed controller's performance in a heterogeneous uncertain multi-agent system's dynamics with unknown actuation capabilities and coupled dynamics.

Finite-Time Synchronization of Fractional-Order Nonlinear Systems with State-Dependent Delayed Impulse Control

This paper delves into the topics of Finite-Time Stabilization (FTS) and Finite-Time Contractive Stabilization (FTCS) for Fractional-Order Nonlinear Systems (FONSs). To address these issues, we employ a State-Dependent Delayed Impulsive Controller (SDDIC). By leveraging both Lyapunov theory and impulsive control theory, we establish sufficient conditions for achieving stability criteria for fractional-order systems. Initially, we employ the aforementioned sufficient conditions to derive stability criteria for general FONSs within the SDDIC framework, employing Linear Matrix Inequality (LMI) techniques. Furthermore, we apply these theoretical findings to tackle the challenge of finite-time synchronization in fractional-order chaotic systems using the proposed SDDIC. We substantiate the efficacy of these theoretical advancements through numerical simulations that vividly demonstrate their capability to achieve finite-time synchronization in fractional-order cellular neural networks and fractional-order Chua’s circuits. Moreover, we introduce an innovative chaos-based multi-image encryption algorithm, thereby contributing significantly to the field. To ensure the algorithm’s robustness, we subject it to rigorous statistical tests, which confidently affirm its capacity to provide the requisite level of security.