Linear Matrix Inequality Method Research Articles

The neural network models with delays for solving absolute value equations

An inverse-free neural network model with mixed delays is proposed for solving the absolute value equation (AVE) Ax−|x|−b=0, which includes an inverse-free neural network model with discrete delay as a special case. By using the Lyapunov–Krasovskii theory and the linear matrix inequality (LMI) method, the developed neural network models are proved to be exponentially convergent to the solution of the AVE. Compared with the existing neural network models for solving the AVE, the proposed models feature the ability of solving a class of AVE with ‖A−1‖>1. Numerical simulations are given to show the effectiveness of the proposed delayed neural network models.

Co-design of adaptive event-triggered mechanism and controller for networked control systems with uncertainty and time-varying delay

ABSTRACT This paper investigates the co-design problem of event-triggered mechanisms and state feedback controllers for networked control systems with parameter uncertainty and network-induced delay. Firstly, to overcome the network bandwidth limitation, an adaptive event-triggered mechanism is used to filter the required sampling signals to reduce the network resource occupancy. Second, establish a unified model subject to event triggering mechanisms, parameter uncertainty, and network delay constraints, and derive the stability conditions of the system for the model by combining Lyapunov stability theory and the linear matrix inequality method. Then, the state feedback controller is designed to satisfy the event-triggering condition and certain robust performance requirements, and an optimisation method is proposed to compromise network resource consumption and control performance. Finally, the effectiveness of the proposed method is verified by a numerical example.

Distributed sliding mode control for a class of impulsive uncertain delayed partial differential equations via sliding mode compensator approach

The distributed sliding mode control (SMC) method of delayed partial differential equations (PDEs)with information of periodical impulse and reaction–diffusion terms (RDTs) is discussed in the article. Firstly, by adopting the sliding mode compensator approach, the switching function including impulsive effects is constructed, which is continuous along the system states. The sliding motion equation is then derived, and its parameters depend on that of sliding mode compensator.Via the direct linear matrix inequality method(DLIM), the exponential stability of sliding motion is analyzed. The proposed distributed SMC strategy can eliminate the impulsive effects and drive the closed-loop state onto a specific sliding manifold in limited time. Finally, a numerical simulation is presented to certify the availability of the proposed scheme.

New LMI approach to [formula omitted] control of discrete-time singular systems

This article studies the problem of feedback H∞ control for discrete-time singular system. The objective is to design the controller to make the closed-loop system admissible and satisfy the specified H∞ performance. Firstly, the admissibility of the closed-loop system is analyzed via the Lyapunov function and linear matrix inequality (LMI) method, the admissibility condition of the singular system with H∞ performance is given. Then, applying a useful matrix inequality lemma, the controller design condition for discrete-time singular system is shown by a LMI. Specially, the benefit of the proposed design result is their less conservatism, the validity of the viewpoint is proposed by numeric illustrations.

A Novel Distributed Adaptive Controller for Multi-Agent Systems with Double-Integrator Dynamics: A Hedging-Based Approach

In this paper, we focus on designing a model reference adaptive control-based distributed control law to drive a set of agents with double-integrator dynamics in a leader–follower fashion in the presence of system anomalies such as agent-based uncertainties, unknown control effectiveness, and actuator dynamics. In particular, we introduce a novel hedging-based reference model with second-order dynamics to allow an adaptation in the presence of actuator dynamics. We show the stability of the overall closed-loop multi-agent system by utilizing the Lyapunov Stability Theory, where we analyze the stability condition by using the Linear Matrix Inequalities method to show the boundedness of the reference model and actuator states. Finally, we illustrate the efficacy of the proposed distributed adaptive controller on an undirected and connected line graph in five cases.

Tracking and Disturbance Suppression of the Radio Telescope Servo System Based on the Equivalent-Input-Disturbance Approach

This paper presents a composite control algorithm for the radio telescope servo control system to address the target tracking and matched/mismatched disturbance suppression problems. The algorithm consists of the equivalent-input-disturbance (EID) approach and the optimal control method. An EID estimator is developed using the difference between the estimated output of the state observer and the measurement output and then the estimate of the EID is fed forward into the control input to reject the disturbance. A cost function with clear physical meaning is selected and the weighting parameters are adjusted for the optimal controller to improve tracking performance. Considering the nonminimum phase characteristics of the radio telescope system, the state observer gain is computed using the linear matrix inequality (LMI) method. The system stability is analyzed using the small gain theorem, and the linear quadratic regulator (LQR) control method is utilized to determine the state feedback gain. Finally, the composite controller is designed for an identified telescope model. Simulation results show that for the tracking performance, the settling time of proposed method is 1.13 s and reduces by about 0.32 s and 0.87 s than that of the ADRC controller and PI controller, respectively. For the antidisturbance performance, the RMS value and the maximum error of the proposed method are 0.0039 and 0.0128, which are 42.86% and 40.38% of the ADRC controller and 30.71% and 27.77% of the PI controller, respectively, which indicates that the proposed method has better control performance. In addition, the proposed controller has certain robustness to systematic parameter perturbations.

Finite-time stability for impulsive stochastic nonlinear system with uncertain parameter

This paper considered the finite-time mean square stability for impulsive stochastic nonlinear system(ISNS) with uncertain parameter. By selecting the modal dependent Lyapunov functional, using average impulsive interval approach and combining Linear Matrix Inequality (LMI) method, the correlation stability criterion of ISNS was obtained. A gain matrix of the feedback controller is obtained on the basis of this sufficient condition. Finally, the LMI toolbox in Matlab was used for data simulation, and the relevant state trajectory demonstrates the availability of the proposed theory.

Linear matrix inequality-based vibration control of three-dimensional Euler–Bernoulli beam with external disturbance

In this paper, we address the LMI-based vibration control problem of a three-dimensional Euler–Bernoulli beam subject to external disturbance. First, the dynamics of the system is characterized by several partial differential equations (PDEs). Second, in order to realize the disturbance rejection, we propose the disturbance observers. Based on these, the boundary control protocols are designed via linear matrix inequality (LMI) method for suppressing elastic vibration. A significant feature of LMI is that the control gains can be efficiently solved by this method. Finally, some simulation examples illustrate the effectiveness of the proposed theoretical results.

Secure memory adaptive event‐triggered filter design of nonlinear network system under hybrid network attacks with application to tunnel diode circuit

AbstractThis article investigates the problem of secure memory adaptive event‐triggered filter design for nonlinear network systems under hybrid network attacks. First, the introduction of memory adaptive event‐triggered mechanism and numerical quantization is employed to enhance system performance, optimize network channel utilization, and prevent network congestion. Second, we consider the impact of deceptive attacks and DoS attacks occurring in the network channel on data transmission, which form the hybrid network attacks studied in this article. Subsequently, based on the established error model, we derive sufficient conditions for the mean‐square exponential stability of the system under a given performance index using Lyapunov–Krasovskii function and linear matrix inequality (LMI) techniques. Furthermore, the filter parameters are determined using the LMI method. Finally, we illustrate the feasibility and generality of the conclusions through numerical simulation examples and a tunnel diode circuit system.

INTELLIGENT CONTROL SYSTEM OF MULTI-MOTION MOBILE ROBOT

Technical devices with irregular motion are described by complex non-linear differential equations, as they have an uncertain environment. Due to interactions and simplifications in these types of control objects, their mathematical models may have certain errors. For this reason, by known methods, for example, the linear matrix inequality method, Lyapunov's quadratic function, etc. The synthesized automatic control systems (ACS) for dynamic objects written by nonlinear mathematical models based on the quadratic matrix determined by The synthesis of regulators for the management of dynamic objects described in nonlinear and uncertain conditions is based on fuzzy logic theory. Since the controllers synthesized by fuzzy logic are based on knowledge, their application to other objects (robots) is limited. In such systems, it is difficult or not at all to determine the dependencies between ACS quality indicators, stability and object parameters. Taking into account the above, a method of analytically parametric synthesis of regulators that ensures the degree of stability and accuracy in ACS’s designed for fuzzy TS-type dynamic objects is proposed. In the article, the solution to the problem of the synthesis of the control system of the mobile robot was considered, and it was successfully applied in the multi-motion mobile robot system. Modeling and experimental results confirm that the operation and stability of the obtained system fully meet the technical requirements. The proposed method has led to an increase in both tracking and control accuracy during high-speed movements. Keywords: multi-motion mobile robot, mathematical model, mechatronic modules, fuzzy TS model, robust controller, fuzzy logic.

Dynamic Event-Triggered H∞ Control for Networked Control Systems With Denial-of-Service Attacks

A dynamic event-triggered H∞ control for networked control systems (NCSs) subject to denial-of-service (DoS) attacks is investigated in this paper. Firstly, the DoS attacks model in communication channel are established based on stochastic variables that obey the Bernoulli distribution, and the attacks rate over network along with switching rules are described. Secondly, the dynamic event-triggered mechanism (DETM) is applied to weaken the influence of DoS attacks and avoid excessive transmission. The threshold parameters under the event-trigger condition can be adjusted by the dynamic characteristics of the systems. Thirdly, by using Lyapunov-Krasovskii functional (LKF) and Linear matrix inequality (LMI) methods, a sufficient condition for NCSs to satisfy the asymptotic stability of given H∞ is obtained. In addition, a cooperative design scheme of DETM parameters and controller gain is proposed. Finally, a RLC series circuit systems is used as an example to show the effectiveness of the method.

Dissipativity-based iterative learning control for singular systems

In this paper, the framework of dissipativity-based iterative learning control for singular systems (SSs) is established for the first time. Firstly, under the P-type learning algorithm, it has been demonstrated that the dissipative SSs can achieve the accurate tracking for the desired trajectory in a finite time interval. Secondly, a sufficient condition for the SSs to satisfy dissipativity is given by using the linear matrix inequality (LMI) method, and the solvability criterion of the LMI is further presented. Moreover, the relationship between dissipativity and positive realness is revealed. Finally, two examples are given to verify the effectiveness of the proposed method.

Observer‐based residual‐driven dynamic compensation strategy for performance improvement of grid‐forming inverter

SummaryGrid‐forming (GFM) inverters offer stable frequency support for microgrid systems, even in the absence of synchronous generators. However, the GFM inverters have low inertia and vulnerability to system uncertainties and external disturbances. The conventional dual‐loop proportional integral (PI) control strategy, while widely used for its simplicity and robustness, suffers from poor dynamic performance. Motivated by this, this paper presents an observer‐based residual‐driven dynamic compensation (RDDC) strategy based on the coprime factorization technic and the Youla parameterization theory to achieve the primary control of the GFM inverter. The observer‐based RDDC strategy comprises four components: a PI controller for tracking control, a linear quadratic regulator (LQR) controller for dynamic adjustment, a residual generator based on the Kalman filter for state estimation and residual generation, and a residual compensation controller designed using model matching theory and solved through linear matrix inequality (LMI) methods for disturbance suppression. Simulation and experiment results consistently demonstrate that the observer‐based RDDC strategy ensures system robustness, enhances the dynamic and steady‐state performance of the GFM inverter system, and strengthens the ability of the GFM inverter to suppress disturbances.

Robust Cooperative Control for Heterogeneous Uncertain Nonlinear High-Order Fully Actuated Multiagent Systems.

This research is intended to address a robust cooperative control problem of heterogeneous uncertain nonlinear high-order fully actuated multiagent systems (HUN-HOFAMASs). A nonlinear HOFA system model is used to describe the multiagent systems (MASs) with heterogeneous uncertain nonlinear dynamics, which is called the HUN-HOFAMASs. A predictive terminal sliding-mode control-based robust cooperative control scheme is presented to address this problem. In this scheme, heterogeneous nonlinear dynamics of original system are offset to establish a linear constant HOFA system with the help of full actuation feature. Then, a terminal sliding-mode variable for enhancing the system robustness is introduced to handle the uncertainties. Furthermore, a linear incremental prediction model is developed in a HOFA form by means of a Diophantine equation. According to this model, the multistep terminal sliding-mode predictions are yielded to optimize the robust cooperative control performance and compensate for the network-induced communication constraints in the feedback and forward channels. Based on a linear matrix inequality (LMI) method, a necessary and sufficient criterion is derived to discuss the simultaneous consensus and stability of closed-loop HUN-HOFAMASs. The simulation and comparison results of cooperative flying around of multiple spacecraft system are shown to illustrate the capability and advantage of the presented predictive terminal sliding-mode control for robust cooperative control.

Delayed Impulsive Control for Lag Synchronization of Delayed Neural Networks Involving Partial Unmeasurable States.

In the framework of impulsive control, this article deals with the lag synchronization problem of neural networks involving partially unmeasurable states, where the time delay in impulses is fully addressed. Since the complexity of external environment and uncertainty of networks, which may lead to a result that the information of partial states is unmeasurable, the key problem for lag synchronization control is how to utilize the information of measurable states to design suitable impulsive control. By using linear matrix inequality (LMI) and transition matrix method coupled with dimension expansion technique, some sufficient conditions are derived to guarantee lag synchronization, where the requirement for information of all states is needless. Moreover, our proposed conditions not only allow the existence of unmeasurable states but also reduce the restrictions on the number of measurable states, which shows the generality of our results and wide-application in practice. Finally, two illustrative examples and their numerical simulations are presented to demonstrate the effectiveness of main results.

Non-fragile ${H_\infty }$ filter design for uncertain neutral Markovian jump systems with time-varying delays

<abstract> <p>This paper deals with the problem of non-fragile ${H_\infty }$ filter design for a class of neutral Markovian jump systems with parameter uncertainties and time-varying delays. The parameter uncertainties are norm-bounded, and time-varying delays include state and neutral time-varying delays. First, by selecting the appropriate stochastic Lyapunov-Krasovskii functional and using the integral inequality technique, sufficient conditions are obtained to make the filtering error system not only stochastically stabilized, but also mode and delay dependent. Second, by the utilizing linear matrix inequality method, sufficient conditions are obtained for the filtering error system to be stochastically stable and to have a prescribed ${H_\infty }$ performance level $\gamma $. Based on this result, by processing the uncertainty terms, sufficient conditions for the existence of the filter are obtained, and mode-dependent filter parameters are given. Finally, by numerical simulation, the feasibility and validity of the theoretical results are verified.</p> </abstract>

Asynchronous finite‐time dynamic output feedback control for discrete‐time switched linear systems with admissible edge‐dependent average dwell time

AbstractThis paper is concerned with the problem of asynchronous finite‐time dynamic output feedback (DOF) control for a class of discrete‐time switched linear systems under the admissible edge‐dependent average dwell time (AED‐ADT) switching scheme. The main goal of the paper is to design a DOF controller to ensure that the resulting closed‐loop system is finite‐time bounded with AED‐ADT switching and has a specific performance. Firstly, some new sufficient conditions for stability criterion and performance analysis are established based on the multiple Lyapunov functionals technique and the linear matrix inequalities method. Secondly, a type of DOF controllers that guarantee that the closed‐loop system has desired performance is designed. Finally, the effectiveness of the proposed approaches is elaborated with a numerical example.

Optimal Control of Hybrid Photovoltaic/Thermal Water System in Solar Panels Using the Linear Parameter Varying Approach

During photovoltaic (PV) conversion in solar panels, a part of the solar radiation is not converted to electricity by the cells, producing heat that could increase their temperature. This increase in temperature deteriorates the performance of the PV panel. In this paper, a hybrid PV/thermal (PV/T) water system is proposed to mitigate this problem. This system combines a PV panel and a thermal collector. In this paper, we focused on the modeling and control of this hybrid system in the linear parameter varying (LPV) framework. An optimal linear quadratic regulator (LQR) is proposed to control the PV cell temperature around an optimal value that maximises electricity generation. Since the system model is nonlinear, an optimal LQR gain-scheduling state-feedback control approach based on an LPV representation of the nonlinear model is designed using the Linear Matrix Inequality (LMI) method. The goal is to obtain the maximum electrical power for each solar panel. Since a reduced number of sensors is available, an LPV Kalman filter is also proposed to estimate the system states required by the state-feedback controller. The obtained results in a laboratory setup in simulation are used to assess the proposed approach, showing promise in terms of control performance of the PV/T system.

Novel adaptive filter design for complex‐valued network systems under hybrid cyber attacks

AbstractThis paper is concerned with the problem of designing adaptive event‐triggered filter for complex‐valued network system under complex‐valued hybrid cyber attack. Firstly, the main contribution of the article is to propose a complex‐valued adaptive event triggered strategy to improve the resource utilisation in the network channel. Secondly, during the modeling process of the filtering error model, we introduce complex‐valued stochastic deception attacks and replay attacks that follow the Bernoulli distribution, thereby forming the complex‐valued hybrid network attacks investigated in this paper. Sufficient conditions for the asymptotic stability of the designed complex‐valued filtered error system are derived using Lyapunov stability theory. In addition, the parameters of the filter are derived using the linear matrix inequality (LMI) method. Finally, a numerical simulation example is given to verify the feasibility of the proposed method.

Optimal oxygen excess ratio tracking of proton exchange membrane fuel cell with uncertainty based on robust model predictive control strategy

AbstractTo address the challenge of tracking the optimal oxygen excess ratio (OER) in the cell stack cathode of the proton exchange membrane fuel cell (PEMFC), which is subject to norm‐bounded parameter uncertainty and frequent external perturbations, this manuscript provides a novel robust model predictive control strategy with a state feedback control structure and hard constraints. We aim to minimize the tracking error of OER while maximizing the net power under varying operational conditions of the PEMFC. Initially, a control‐oriented model for the air supply system is built and its accuracy is validated by comparing it with experimental results. Next, we construct the discrete state‐space equations for optimal control and employ the linear matrix inequality (LMI) method to transform the problem of difficult min‐max optimization solutions into a convex optimization problem with LMI constraints. Finally, the effectiveness of the proposed control algorithm is validated through simulation. The results demonstrate the strong robustness and superiority of the proposed controller against uncertainties in plant parameters for robust OER trajectory tracking. It improves the transient performance through robust precision tracking applications, which will eventually accelerate PEMFC commercialization.