LMI Approach Research Articles

Reliability-based robust control strategy via LMI approach for TMDs and ATMDs with uncertain parameters

This paper presents an integrated reliability-based H∞ robust control. This method consists of the H∞ control method and the Hasofer-Lind and Rackwitz-Fiessler (HL-RF) strategy. In this respect, the uncertainties in the system should be taken into account by using the random variables, which may arise due to various factors Such as the absence of understanding of the properties of materials, mistakes in design, etc. Also, considering the uncertainties in the system is important because it may cause wide changes in the responses of a system. For this reason, the reliability method must be carefully examined. To reduce the responses of the structure, TMDs and ATMDs are used. The parameters of the dampers (mass, stiffness, damping) are considered with uncertainty. An iterative HL-RF algorithm is used for structure equipped with TMDs to deal with uncertainties. To find the appropriate control force of TAMDs, the combination of the H∞ control strategy based on the linear matrix inequality utilized and the HL-RF method algorithm is expressed. Two types of dampers are vertically distributed on the different floors to increase the reliability of the structure under earthquake excitations. The proposed strategy indicated that the system's responses have been provided greater value by considering the uncertainty that shows the importance of this issue. According to the obtained values, the presented algorithm has performed well. Also, the proper reliability index is acquired by using the HL-RF method.

Extended dissipative performance of fractional-order neural networks via LMI approach

Extended dissipative performance of fractional-order neural networks via LMI approach

Decentralised controller design for robust stabilisation and L 2 gain of nonlinear interconnected systems

In this paper, a decentralised controller is extended for robust stabilisation and L 2 gain analysis of a class of nonlinear interconnected systems via dynamic output feedback control within the LMI framework. This large-scale system is composed of linear subsystems coupled by nonlinear time-varying interconnections satisfying quadratic constraints. An LMI approach is sufficiently proposed as a feasibility problem of a BMI with respect to controller gains via dynamic output feedback structure. An example of inverted pendulums is used to illustrate the applicability of extended approach.

Necessary and sufficient Conditions of Forward Invariance in Hybrid Dnamical Systems: An LMI Approach*

This study focuses on the characterization of the forward invariance property in hybrid dynamical systems, considering state-dependent conditions for both differential and difference inclusions. The first step is to establish necessary and sufficient conditions for (controlled) forward invariance, using cones and set inclusions. For linear hybrid systems, an explicit characterization of the invariance property of polyhedral sets is given in terms of linear matrix inequalities. The result is illustrated by a practical example involving a bouncing ball.

LMI-based Model Predictive Control Design for Supply Manifold Pressure Improvement of Proton Exchange Membrane Fuel Cell realized through Additive Manufacturing

The fuel cell is one of the renewable energy sources and proton exchange membrane (PEM) is the most common and widely used type. With the aim of increasing efficiency, this article first presents a developed PEM fuel cell with additive manufacturing (AM) process. Then, the nonlinear dynamic model describing the behaviour of the AM-based PEM cell is described, and considering the general working class, a new control method for adjusting the pressure of the supply manifold is presented. The planned control method is a combination of model predictive and LMI approaches and in addition to guaranteeing the stability of the closed loop system, it is able to adjust the pressure of the supply manifold and guarantee the optimal operation of the PEM system developed by the additive manufacturing process. The results of simulation and comparison in the MATLAB environment show the efficiency of the proposed control method in meeting the control objectives and improving the transient and permanent response.

New robust state estimation of 2D embedded descriptor systems in Roesser form with bounded disturbance using strict LMI approach

New robust state estimation of 2D embedded descriptor systems in Roesser form with bounded disturbance using strict LMI approach

Online observer of the voltage components of the PEM electrolyzer based on the time-varying linearization of the semi-empirical model

This paper presents a method to estimate the components of the PEM electrolyzer voltage with the dynamic input current. The total voltage can be divided into reversible voltage and irreversible voltage that the former always can be described as a function of temperature and pressure. For the irreversible voltage, a dynamic semi-empirical model is linearized by a dynamic expansion point varying with the input power. A Luenberger observer is established from the linearized model to estimate the anode overvoltage, cathode overvoltage and ohmic overvoltage effectively and rapidly, for which the stability is proved by LMI approach. Considering the deviation caused by local linearization, a switching scheme of the expansion point is also analyzed to provide an appropriate solution for fluctuating current when accessed to renewable energy power. Simulations have been carried out to testify and verify the method with varying input current, different switching expansion points, and uncertain parameters. The results show that the online Luenberger observer can achieve fine accuracy. And for the varying input current, updating the expansion point with a certain scale can further improve the observation accuracy, which enhances the performance of the observer to adapt the hydrogen production with renewable energy to evaluate the behavior of the PEM electrolyzer.

Synchronization of fractional-order reaction-diffusion neural networks via mixed boundary control

This article studies the synchronization issue of fractional reaction-diffusion neural networks (FRDNNs) with time delay and mixed boundary condition. First, a novel boundary controller with constant-valued gain is designed, which only relies on the boundary state information. Subsequently, by virtue of Lyapunov direct technique and LMI approach, the Mittag–Leffler synchronization conditions are established. Besides, to effectively regulate the control gain, a fractional-order adaptive boundary controller is developed and the adaptive synchronization of FRDNNs is rigorously analyzed. Note that, the above control strategies are also workable for traditional integer-order reaction-diffusion neural networks. The developed theoretical analysis is supported eventually via a numerical example.

Non-fragile sampled-data control for synchronization of chaotic fractional-order delayed neural networks via LMI approach

This study addresses the master and slave synchronization problem of chaotic fractional-order delayed neural networks using a non-fragile sampled-data control (NFSDC) scheme which includes uncertainty information in the control gain matrix. An appropriate Lyapunov functional is constructed with information about sampling instants. A new, improved fractional-order inequality is developed to estimate the integral term. Then, based on the new integral inequality, the delay-dependent stability criteria are derived in the form of linear matrix inequality, which guarantees the asymptotic stability of the fractional-order error systems. This implies that the proposed NFSDC can synchronize the fractional-order master and slave systems. Moreover, numerical simulation results illustrate the synchronization nature and the influence of fractional derivatives in the system dynamics. Finally, it can be concluded that the proposed method and control scheme are effective.

Reset control and ℒ2-gain analysis of piecewise-affine systems

This paper is concerned with reset controller design and L 2 -gain stability of piecewise-affine systems under the framework of hybrid systems. Firstly, stability conditions of piecewise-affine systems under dynamic state-feedback control are established through bilinear matrix inequality conditions. Secondly, a reset controller with reset rules under the hybrid systems framework is proposed in the sense of Lyapunov and sufficient conditions for exponential and L 2 -gain stability of the closed-loop systems are provided. Different from the piecewise-affine systems with the dynamic state-feedback controller, the reset controller is designed such that the L 2 -gain performance of piecewise-affine systems can be enhanced. Thirdly, an LMI approach is proposed to avoid the difficulty of solving the bilinear matrix inequalities. Furthermore, robustness to inflations of the flow and jump sets is established, and robustness to the norm-bounded uncertainties is proposed. Finally, numerical simulations including a robot arm system, an inverted pendulum system and the Chua's circuit system are provided to illustrate the results.

Controller Design for Game Theoretic Steady-State Control: An LMI Approach

We consider a set of LTI agents subject to constant external disturbances seeking to minimize coupled cost functions in steady-state, modelled as a game-theoretic problem. Using a novel framework, the Nash equilibrium seeking problem has been shown to reduce to the design of a set of decentralized stabilizing controllers. Herein, we consider two such controller designs, based off LMI approaches. The first employs a diagonal stability argument, and the second relies on H∞ design coupled with the small gain theorem. Applications to sensor networks are provided and the trade-offs between the two methods are discussed.

Observer-Based Stabilization of Lipschitz Nonlinear Systems by Using a New Matrix-Multiplier-Based LMI Approach

Observer-Based Stabilization of Lipschitz Nonlinear Systems by Using a New Matrix-Multiplier-Based LMI Approach

Communication security of autonomous ground vehicles based on networked control systems: The optimized LMI approach

The paper presents a study of networked control systems (NCSs) that are subjected to periodic denial-of-service (DoS) attacks of varying intensity. The use of appropriate Lyapunov–Krasovskii functionals (LKFs) help to reduce the constraints of the basic conditions and lower the conservatism of the criteria. An optimization problem with constraints is formulated to select the trigger threshold, which is solved using the gradient descent algorithm (GDA) to improve resource utilization. An intelligent secure event-triggered controller (ISETC) is designed to ensure the safe operation of the system under DoS attacks. The approach is validated through experiments with an autonomous ground vehicle (AGV) system based on the Simulink platform. The proposed method offers the potential for developing effective defense mechanisms against DoS attacks in NCSs.

Robust LQG Controller Design by LMI Approach of a Doubly-Fed Induction Generator for Aero-Generator

Robust LQG Controller Design by LMI Approach of a Doubly-Fed Induction Generator for Aero-Generator

Adaptive event-trigger-based sampled-data stabilization of complex-valued neural networks: a real and complex LMI approach

Adaptive event-trigger-based sampled-data stabilization of complex-valued neural networks: a real and complex LMI approach

Delay-dependent and order-dependent LMI-based sliding mode [formula omitted] control for variable fractional order uncertain differential systems with time-varying delay and external disturbance

This paper concentrates on the sliding mode H∞ control for variable fractional order uncertain differential systems with time-varying delay and external disturbance by using the delay-dependent and order-dependent LMI approach. Firstly, by designing a suitable variable fractional order sliding mode surface, an equivalent control law has been given and the new state-space model has been introduced. Secondly, by using a Lyapunov–Krasovskii function and constructing an appropriate variable fractional order inequality, a novel delay-dependent and order-dependent stability theorem of the nominal systems without external disturbance is proposed. Then, based on the above stability conditions and the H∞ performance, the delay-dependent and order-dependent stability conditions for the systems with external disturbance are discussed. Moreover, the reachability of the sliding mode surface has been presented. In order to stabilize the systems with uncertainties, the controller gain matrices are also derived with the help of the proposed stability criteria. All the results are in the form of linear matrix inequalities. Finally, two numerical examples are provided to verify the effectiveness of the introduced theoretical formulation.

Multi-objective T-S fuzzy control of Covid-19 spread model: An LMI approach

Due to the importance of control actions in spreading coronavirus disease, this paper is devoted to first modeling and then proposing an appropriate controller for this model. In the modeling procedure, we used a nonlinear mathematical model for the covid-19 outbreak to form a T-S fuzzy model. Then, for proposing the suitable controller, multiple optimization techniques including Linear Quadratic Regulator (LQR) and mixed H2-H∞ are taken into account. The mentioned controller is chosen because the model of corona-virus spread is not only full of disturbances like a sudden increase in infected people, but also noises such as unavailability of the exact number of each compartment. The controller is simulated accordingly to validate the results of mathematical calculations, and a comparative analysis is presented to investigate the different situations of the problem. Comparing the results of controlled and uncontrolled situations, it can be observed that we can tackle the devastating hazards of the covid-19 outbreak effectively if the suggested approaches and policies of controlling interventions are executed, appropriately.

An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

An LMI Approach to Robust Iterative Learning Control for Linear Discrete-time Systems

Robust model predictive anti-slip controller and speed profile tracking of an electric train based on LMI approach

Robust model predictive anti-slip controller and speed profile tracking of an electric train based on LMI approach

A Takagi-Sugeno model approach for robust fuzzy control design for trajectory tracking of non-linear systems

This article investigates the robust fuzzy tracking control design for a class of uncertain nonlinear systems using the Takagi–Sugeno (TS) fuzzy models. The main purpose of this study is to design state feedback and observer-based controllers such that the closed-loop system is asymptotically stable. Based on the Lyapunov theory, sufficient conditions are derived such that the closed-loop system is robustly stable. The linear matrix inequality LMI approach is used to obtain the state-feedback and observer gains. The effectiveness of the proposed design approach is provided via numerical simulations for a pendulum system.