Linear Matrix Inequality Approach Research Articles

Global exponential stability results for the host‐parasitoid model of sugarcane borer in stochastic environment with impulsive effects via non‐fragile control: An LMI approach

AbstractIn this article, we evaluate how the random environmental fluctuations affect the interplay between the sugarcane borer (Diatraea saccharalis) and its egg parasitoid (Trichogramma galloi). In order to procure an optimal control input, we considered the uncertainties in the control agent that leads to a non‐fragile control synthesis. Due to the existence of a stochastic environment and uncertainties in the control agent, the impulsive biological control is introduced to stabilize the situation. By means of the classical Lyapunov method, a new sufficient condition for exponential stability of our proposed population model through non‐fragile control and impulsive biological control is established. With the assistance of linear matrix inequality (LMI) solvers, non‐fragile controllers can be obtained effortlessly. In addition, we provide simulation studies that are primarily based on the sugarcane borer system to demonstrate the effectiveness and benefits of our proposed model.

Disturbance observer-based controller for inverted pendulum with uncertainties: Linear matrix inequality approach

<span lang="EN-US">A new approach based on linear matrix inequality (LMI) technique for stabilizing the inverted pendulum is developed in this article. The unknown states are estimated as well as the system is stabilized simultaneously by employing the observer-based controller. In addition, the impacts of the uncertainties are taken into consideration in this paper. Unlike the previous studies, the uncertainties in this study are unnecessary to satisfy the bounded constraints. These uncertainties will be converted into the unknown input disturbances, and then a disturbance observer-based controller will be synthesized to estimate the information of the unknown states, eliminate completely the effects of the uncertainties, and stabilize inverted pendulum system. With the support of lyapunov methodology, the conditions for constructing the observer and controller under the framework of linear matrix inequalities (LMIs) are derived in main theorems. Finally, the simulations for system with and without uncertainties are exhibited to show the merit and effectiveness of the proposed methods.</span>

An LMI approach to Mixed H_∞/H_- fault detection observer design for linear fractional-order systems

This study deals with the problem of robust fault detection for linear time-invariant fractional-order systems (FOSs) assumed to be affected by sensor, actuator and process faults as well as disturbances. The observer-based method was employed to solve the problem, where the detector is an observer. The problem was transformed into the mixed robust optimization problem to make the system disturbance-resistant on one hand and fault-sensitive on the other hand. Then, sufficient conditions were obtained to solve the problem in the linear matrix inequality (LMI) mode. Finally, the effectiveness and superiority of the method were demonstrated by simulating the solutions on a single-input multi-output thermal testing bench.

A new optimal model predictive control scheme for a wind energy conversion system

AbstractThe correct management of power exchange between the doubly‐Fed induction generator (DFIG) and the grid depends on the effective optimal operation of the DFIG based wind energy conversion system (WECS). A modified optimal model predictive controller (MPC) architecture for WECS is proposed in this paper. The proposed scheme is carried out in two stages, as follows: (a) Using the MPC model and the tracking factor, an optimal control law is created, and (b) the aforementioned optimized issue is addressed using the linear matrix inequality (LMI) approach. Some improvements were made to the conventional LMI‐based MPC technique to lower the high computational complexity. To perform active and reactive power control in DFIG, the proposed approach is applied on the rotor‐side converter (RSC) control. The control law is divided into two sections. The first section deals with rotor current, while the second section deals with the RSC switching states. The LMI is used in the second portion of the control law to find the best switching state solution. The proposed method was created using the MATLAB/SIMULINK environment and tested in a 1hP DFIG‐WECS setup. By comparing the obtained results to conventional LMI‐PI, MPC‐based WECS, the effectiveness of the obtained results is verified. Variable wind speed conditions are used to vary all the results. Integral absolute error, integral time absolute error, and Integral square error measurements are used to compare the tracking performance index of all methods.

Optimal gain‐scheduling control of proton exchange membrane fuel cell: An LMI approach

Here, an optimal linear parameter varying (LPV) controller is developed for non-linear proton exchange membrane fuel cell (PEMFC) systems. Two performance criteria are involved in the optimal controller, including the membrane pressure and the power of the PEMFC. The former should be minimized; and, the latter should be maximized. Since the goal is to derive sufficient conditions in terms of linear matrix inequality (LMI) constraints, both performances are re-formulated and augmented in a unique convex optimization problem. Further, the non-linear PEMFC with the equilibrium profile dependent on time-varying parameters, that is, current and temperature, is represented by an LPV model. Using the LMI constraints and the obtained LPV model, the gains of the controller are derived. Comparing with the state-of-the-art methods, the proposed approach offers an optimal control approach with a systematic design method, in which both practical issues are treated, simultaneously. To show the advantages of the developed approach, six typical controllers, including the proposed and existing approaches, are considered and several numerical simulation results are conducted.

Frequency Regulation System: A Deep Learning Identification, Type-3 Fuzzy Control and LMI Stability Analysis

In this paper, the problem of frequency regulation in the multi-area power systems with demand response, energy storage system (ESS) and renewable energy generators is studied. Dissimilarly to most studies in this field, the dynamics of all units in all areas are considered to be unknown. Furthermore time-varying solar radiation, wind speed dynamics, multiple load changes, demand response (DR), and ESS are considered. A novel dynamic fractional-order model based on restricted Boltzmann machine (RBM) and deep learning contrastive divergence (CD) algorithm is presented for online identification. The controller is designed by the dynamic estimated model, error feedback controller and interval type-3 fuzzy logic compensator (IT3-FLC). The gains of error feedback controller and tuning rules of the estimated dynamic model are extracted through the fractional-order stability analysis by the linear matrix inequality (LMI) approach. The superiority of a schemed controller in contrast to the type-1 and type-2 FLCs is demonstrated in various conditions, such as time-varying wind speed, solar radiation, multiple load changes, and perturbed dynamics.

Observer-Based Control for Nonlinear Time-Delayed Asynchronously Switching Systems: A New LMI Approach

This paper designs an observer-based controller for switched systems (SSs) with nonlinear dynamics, exogenous disturbances, parametric uncertainties, and time-delay. Based on the multiple Lyapunov–Krasovskii and average dwell time (DT) approaches, some conditions are presented to ensure the robustness and investigate the effect of time-delay, uncertainties, and lag issues between switching times. The control parameters are determined through solving the established linear matrix inequalities (LMIs) under asynchronous switching. A novel LMI-based conditions are suggested to guarantee the H∞ performance. Finally, the accuracy of the designed observer-based controller is examined by simulations on practical case-study plants.

Event-based master–slave synchronization of complex-valued neural networks via pinning impulsive control

This paper investigates the synchronization problem of complex-valued neural networks via event-triggered pinning impulsive control (ETPIC). A time-delayed pinning impulsive controller is proposed based on three levels of event-triggered conditions. By employing the Lyapunov functional method and differential inequality technique, sufficient delay-dependent synchronization criteria are derived under the proposed ETPIC scheme. The obtained result shows that synchronization of master and slave complex-valued neural networks can be achieved even if the sizes of delays exceed the length of intervals between any two consecutive impulsive instants determined by Lyapunov-based event-triggered conditions in the proposed control strategy. Moreover, the linear matrix inequality approach is utilized to exclude Zeno behavior. Numerical examples are provided to illustrate the effectiveness of the theoretical results.

Leader-follower non-fragile consensus of delayed fractional-order nonlinear multi-agent systems

This paper addresses the leader-follower non-fragile consensus of nonlinear fractional-order (FO) multi-agent systems (FOMAS) with state time delay. The structured uncertainties occurring in both the plant and the controller are considered for the first time. Using the linear matrix inequality approach and the FO Razumikhin theorem, a delay- and order-dependent protocol is obtained to guarantee the leader-follower non-fragile consensus of the FOMAS with uncertain parameters. New sufficient conditions for the leader-follower non-fragile consensus of FO linear multi-agent systems are presented. The feasibility and effectiveness of the protocol proposed is verified with three numerical examples. Compared with the existing schemes, the approach reveals good robustness and can be extended to different kinds of consensus problems.

Guaranteed Cost Leaderless Consensus Protocol Design for Fractional-Order Uncertain Multi-Agent Systems with State and Input Delays

This paper addresses the guaranteed cost leaderless consensus of delayed fractional-order (FO) multi-agent systems (FOMASs) with nonlinearities and uncertainties. A guaranteed cost function for FOMAS is proposed to simultaneously consider consensus performance and energy consumption. By employing the linear matrix inequality approach and the FO Razumikhin theorem, a delay-dependent and order-dependent consensus protocol is formulated for FOMASs with input delay. The proposed protocol not only guarantees the robust stability of the closed-loop system error but also ensures that the performance degradation caused by the system uncertainty is lesser than that obtained with other approaches. Two numerical examples are provided in order to verify the effectiveness and accuracy of the proposed protocol.

Finite-time extended dissipative filtering for nonlinear Markovian jump systems with unknown transition rates and time-varying delays

The problem of finite-time filtering for nonlinear Markovian jump systems subject to extended dissipativity with unknown transition rates and time-varying delays is investigated in this paper. Firstly, by constructing novel Lyapunov-Krasovskii functionals and utilizing delay partitioning method, the error system is proved to be stochastically finite-time bounded and extended dissipative. Secondly, in virtue of linear matrix inequalities approach, the desired mode-dependent filter is obtained. Finally, two simulations are illustrated for the purpose of demonstrating the less conservativeness and effectiveness of the proposed method.

Noninteracting Control Design for 6-DoF Active Vibration Isolation Table with LMI Approach

This paper proposes a novel control strategy for six degrees-of-freedom active vibration isolation tables. In these systems, the most challenging issue is to suppress the external vibrations and isolate the internal interactions while still preserving the system’s robustness when facing uncertainties. A noninteracting controller is designed to tackle these problems. The resulting control system is completely decoupled in the sense that each system output is independently controlled to follow the corresponding reference signal. In this paper, the model of an active vibration isolation table is firstly derived. Conditions for system stability and decoupled performance are then discussed. The control law is formulated using the linear matrix inequality approach, which results in optimal control gains for the control objectives. With the proposed controller, complex system characteristics can be handled more efficiently such that an effective system is designed to obtain good control performance. Finally, simulations and comparison studies were conducted, and the results validate the efficiency of the proposed scheme.

A direct parameterized approach to global exponential stability of neutral-type Cohen–Grossberg neural networks with multiple discrete and neutral delays

For a class of neutral-type Cohen–Grossberg neural networks with multiple discrete and neutral delays, the existence and uniqueness of equilibrium point are derived by the homeomorphism mapping theory between topology spaces. By proposing a direct parameterized approach that is based on a parameterized estimation of solutions, it is the first time to investigate a sufficient condition guaranteeing that the unique equilibrium point is globally exponentially stable. The stability condition contains only some very simple inequalities, which is easily solved by applying the toolbox YALMIP of MATLAB.Three numerical examples in literature are employed to demonstrate the effectiveness of the obtained criterion over the previously achieved ones. In addition, the proposed approach is different from the popular linear matrix inequality approach, since no Lyapunov–Krasovskii functional is required. Therefore, the obtained criterion can be evaluated as an important contribution to the stability issue of the considered neural networks. It is potential that the proposed approach is applied to stability issues of various types of neural networks.

Sensor and actuator fault-tolerant control based on fuzzy unknown input observer: A polynomial fuzzy approach

This paper studies sensor and actuator Fault-Tolerant Control (FTC) of nonlinear systems. The fault tolerance is necessary to have desired performance and prevent the system from instability. A Polynomial Fuzzy Unknown Input Observer (PFUIO) with immeasurable premise variable is proposed to estimate the states of the system, and sensor and actuator faults; and to use them in the controller to compensate the faults. The essence of the sensor fault necessitates considering the third class of Polynomial Fuzzy Model (PFM) with immeasurable premise variables. This makes the design procedure more complicated. Application of PFM reduces the conservatism and increases modeling accuracy. Moreover, the disturbance and model uncertainties are considered to realize more practical conditions. The polynomiality leads to Sum Of Squares (SOS), which can be solved using existing software. The proposed approach is evaluated by applying it to the inverted pendulum system. Simulating results show better performance of the proposed method as compared with the Linear Matrix Inequality (LMI) approach

Asymptotical stability of fractional neutral-type delayed neural networks with reaction-diffusion terms

This article investigates the asymptotical stability of the equilibrium point for a class of fractional neutral-type delayed neural networks with reaction-diffusion terms in sense of Riemann–Liouville. In terms of linear matrix inequalities approach, inequality scaling techniques and Green’s theorem, by constructing a suitable Lyapunov functional, some less conservative criterion of asymptotical stability for the neural networks system are given. Inspired by some achievements, the results obtained in this paper are more general and can easily test the stability of practical neural networks systems. Finally, two numerical examples are elaborated to substantiate the validity and conciseness of theoretical results.

Variance‐constrained resilient H∞ filtering for mobile robot localization under dynamic event‐triggered communication mechanism

AbstractThis paper is concerned with the mobile robot localization problem subject to filter gain uncertainty under dynamic event‐triggered communication mechanism, and meanwhile, the H∞ filtering performance and the error variance constraint are guaranteed. For saving the sensor energy, a dynamic event‐triggered communication mechanism is introduced to manage the transmission of the measurement data from the sensor to the filter. To characterize the possible fluctuations of the desired filter gain, a resilient filter is constructed for the mobile robot localization. The aim of this paper is to find a solution to the mobile robot localization problem by designing a nonlinear resilient filter such that the filtering error dynamics satisfies both the H∞ performance requirement and the error variance constraint over a finite time horizon simultaneously. By resorting to the Lyapunov theory and the stochastic analysis technique, the sufficient conditions are established to guarantee that the error dynamic system satisfies both the H∞ performance requirement and the error variance constraint. Then, a recursive linear matrix inequality (RLMI) approach is employed to design the desired filter. Based on the proposed filter design scheme, the corresponding localization algorithm is presented. Finally, an experiment is conducted in the simulation environment to verify the effectiveness of the proposed localization algorithm.

Passivity based on synchronization of T-S fuzzy energy resources system

This paper investigates the use of Takagi-Sugeno fuzzy and passive control techniques to synchronize a four-dimensional energy resource system. A passivity-based fuzzy controller is designed to synchronize the two identical four-dimensional energy resource systems using an effective Lyapunov function and linear matrix inequality approach. Finally, computational and simulation results are presented to show the benefits of the proposed findings.

비간섭화 제어이론기반 정밀작업용 테이블의 진동억제시스템 구축에 관한 연구

This paper presents a novel method for designing a active vibration isolation system (AVIS) by noninteracting control theory. In the result, the designed system can effectively reject the impact of disturbances on high precision fabrication table. In particular, the authors provide a noninteracting control scheme to decrease and delete the interactions appeared in the controlled system dynamics such that the control performance can be improved. For designing an optimal servo system, the LMI (linear matrix inequality) approach is introduced. To verify the effectiveness of the proposed method, a simulation is performed. In the result, the vibration suppression performance is significantly improved, thereby enabling higher precision works.

A robust delay-dependent guaranteed cost PID multivariable output feedback controller design for time-varying delayed systems: An LMI optimization approach

This paper deals with the new formulated problem of designing a robust delay-dependent guaranteed optimal cost proportional-integral-derivative (PID) multivariable output feedback controller for linear uncertain time delay systems with nonlinear parameter perturbations using a linear matrix inequalities (LMI) approach. Several less conservative delay-dependent stability conditions are formulated for the time-delay system under consideration in terms of LMIs. Based on an augmented form of Lyapunov-Krasovskii functionals, the free weighting matrices and Wirtinger inequality techniques are employed to obtain improved performance. An optimal guaranteed cost PID controller which minimizes the upper bound of cost function is provided. The main advantage of the proposed approach is to decouple the input and the output gain matrices allowing to synthesize the controller gain matrices through a strict LMI technique. The synthesis conditions are thus formulated in LMI form which avoids the use of any iterative approach to resolve the feasibility problem. Two numerical examples selected from the literature are presented to illustrate the effectiveness of the developed methodology. The numerical results indicate that the proposed method performs efficiently in comparison to the approaches from the existing literature.

Stable fuzzy controllers via LMI approach for non-linear systems described by type-2 T–S fuzzy model

PurposeThe purpose of this paper is to stabilize the type-2 Takagi–Sugeno (T–S) fuzzy systems with the sufficient and guaranteed stability conditions. The given conditions efficaciously handle parameter uncertainties by the upper and lower membership functions of the type-2 fuzzy sets (FSs).Design/methodology/approachThis paper reports on a relevant study of stable fuzzy controllers and type-2 T–S fuzzy systems and reported that the synthesis of controller for nonlinear systems described by the type-2 T–S fuzzy model is a key problem and it can be resolve to convex problems via linear matrix inequalities (LMIs).FindingsThe multigain fuzzy controllers are established to improve the solvability of the stability conditions, and the authors design multigain fuzzy controllers which have extensive information of upper and lower membership grades. Consequently, the authors derive the traditional stability condition in terms of LMIs. One simulation examples illustrate the effectiveness and robustness of the derived stabilization conditions.Originality/valueThe uncertain MIMO nonlinear system described by Type-2 Takagi-Sugeno (T-S) fuzzy model, and successively LMI approach used to determine the system stability conditions. The proposed control approach will give superior fault-tolerant control permanence under the actuator fault [partial loss of effectiveness (LOE)]. Also the controller robust against the unmeasurable process disturbances. Additionally, the statistical z-test are carried out to validate the proposed control approach against the control approach proposed by Himanshukumar and Vipul (2019a).