Matrix Inequality Tools Research Articles

Enhancing Electric Vehicle Propulsion: PMSM Motor Speed Control via a Fuzzy PI Controller Developed Using a Line-Integral Lyapunov Fuzzy Function

This paper suggests a robust control strategy to enhance the stability and ensure optimal tracking of reference speed for electric vehicles (EVs) equipped with Permanent Magnet Synchronous Motors (PMSM). The strategy involves designing a specific Proportional-Integral (PI) controller using the Takagi-Sugeno (TS) fuzzy model and employing the Linear Integral Lyapunov Function (LILF). Additionally, an H∞ approach is integrated to effectively manage external disturbances such as load torque. The PI controller's gains are determined using the Linear Matrix Inequality (LMI) tool, ensuring efficient and reliable performance under varying operating conditions. Simulation studies confirm the effectiveness of the proposed control strategy and highlighting its capability to achieve robust speed regulation and disturbance rejection in EV propulsion systems

Dynamic Event-triggered Control for Nonlinear PDE System with Actuator Dead-zone

A dynamic event-triggered network control scheme is proposed for a class of distributed parameter systems with time delay and nonlinearity. The security control of the PDE system under DOS attack based on dynamic event-triggered is studied. A dynamic event-triggered scheme is adopted to reduce the communication burden, that is, the sampling data will be sent only when the original trigger condition is violated. At the same time, a new model including denial of service attack (DOS) is established to describe the random network attack. When a hacker launches a DoS attack, it prevents the sampling data from reaching the destination by interfering with the network channel. DOS attacks follow no specific pattern and exhibit non-periodic behavior or irregular probability distribution. A mathematical model of a state-dependent uncertain system with an event-triggered scheme was established to study denial of service attacks. By using the Lyapunov-Krasocskii stability theory and linear matrix inequality tools, sufficient conditions were derived to ensure the index mean square stability of the state-dependent uncertain system. Based on this, sufficient conditions for the asymptotic stability of the closed-loop network control system and the expected performance index of the system were obtained. Numerical examples verified the feasibility of the method, and controller design validated the applicability of the theoretical results.

Active observer-based T-S fuzzy control scheme for maximum power point tracking in PV systems

This paper addresses the problem of maximum power point tracking of photovoltaic (PV) systems in the presence of model uncertainty as well as varying load and atmospheric conditions using techniques based on a Takagi–Sugeno fuzzy model. The proposed approach relies on the linear matrix inequality tool, Lambert W function, and the Newton–Raphson method. First, adopting a quadratic Lyapunov function, an active observer-based fuzzy non-parallel distributed compensation (non-PDC) controller is designed for asymptotic tracking of the desired reference input. Next, to subdue the impact of uncertainty on the PV system, the closed-loop nominal system is regarded as a reference model, and then the main control law is developed using an online lumped uncertainty estimator and keeping the nominal control law within the staple controller. This control law does not require that the bounds on uncertainties be known. The reference voltage is determined by a novel maximum power point-seeking algorithm that is organized based on the one-diode model of PV panel, Lambert W function, and Newton–Raphson method. Finally, simulations are performed for three scenarios to point out the merits and effectiveness of the proposed methodology in the presence of system uncertainties, environmental changes, and load variations.

Minimum‐energy time‐varying formation of distributed multi‐agent systems with interaction constraints

AbstractIn the current paper, minimum‐energy time‐varying formation design and analysis problems of distributed multi‐agent systems (DMASs) subjected to randomly switching topologies and aperiodic interaction pauses are investigated, which can ensure the time‐varying formation achievement with the minimum‐energy consumption in the sense of the linear matrix inequality. Firstly, a formation control protocol is designed with local information of neighboring agents, where the total energy consumption during the formation process is constructed and the impacts of interaction constraints are imposed. Then, minimum‐energy formation design and analysis criteria of DMASs are presented in terms of the linear matrix inequality tool, which can be checked by the generalized eigenvalue method. Finally, a numerical simulation is shown to verify the effectiveness of the main results.

DPWM Applying for Five-Level NPC VSI Powered by PV-Boost Converter Based on Takagi Sugeno Fuzzy Model

Power quality is interesting issue for power conversion PV system. Further there are challenges associated with extract of maximum power and minimize the part losses in commutation. In this paper, a three-phase five-level NPC voltage source inverter (VSI) using discontinuous pulse-width modulation (DPWM) and feeding by a PV/DC-DC boost converter based on a Takagi-Sugeno T-S fuzzy controller is presented. The photovoltaic energy system is described by nonlinear equations. A T-S fuzzy model is used to transform the nonlinear equations into a fuzzy model by modeling the irradiation, temperature and output voltage parameters. The control parameters have been computed based on Linear Matrix Inequalities tools (LMI) and the stability of the system is ensured by Lyapunov approach. In the second stage for power conversion (DC/AC), a discontinuous pulse-width modulation (DPWM) is used and approved; it offers the possibility of reducing switching losses and the THD harmonic rate. The simulation was performed in the MATLAB/Simulink software using an R-L load and the obtained results are confirmed the feasibility and reliability of the proposed method for the PV conversion system.

Dependable Sensor Fault Reconstruction in Air-Path System of Heavy-Duty Diesel Engines.

This paper addresses the problem of robust sensor faults detection and isolation in the air-path system of heavy-duty diesel engines, which has not been completely considered in the literature. Calibration or the total failure of a sensor can cause sensor faults. In the worst-case scenario, the engines can be totally damaged by the sensor faults. For this purpose, a second-order sliding mode observer is proposed to reconstruct the sensor faults in the presence of unknown external disturbances. To this aim, the concept of the equivalent output error injection method and the linear matrix inequality (LMI) tool are utilized to minimize the effects of uncertainties and disturbances on the reconstructed fault signals. The simulation results verify the performance and robustness of the proposed method. By reconstructing the sensor faults, the whole system can be prevented from failing before the corrupted sensor measurements are used by the controller.

T-S fuzzy tracking control of nonlinear constrained time-delay systems using a reference-management approach

A new control design approach is proposed for a class of nonlinear systems expressed by Takagi–Sugeno (T-S) fuzzy model, considering several objectives including robustness against input time-varying delay, input constraint satisfaction, and reference tracking. The proposed controller is designed on the basis of an augmented model, Lyapunov–Krasovskii functional, linear matrix inequality (LMI) tools, and parallel distributed compensation (PDC) approach. Proof of the input-to-state stability (ISS) criterion is provided for the error dynamics. Input constraint satisfaction is performed using a reference-management algorithm based on the linearized closed-loop system from the reference input to the constrained variables. In order to illustrate the effectiveness of the proposed control approach, simulations are performed on three practical examples, including a flexible-joint robot and a continuous stirred tank reactor (CSTR).

Augmented robust T-S fuzzy control based PMSG wind turbine improved with H∞ performance

<p>In this paper, an improved augmented Takagi-Sugeno fuzzy control design applied to the system of converting wind turbine energy was proposed. The wind generator used is based on a permanent magnet synchronous wind power generator (PMSG) under varying operation of the wind speed. The proposed T-S fuzzy control strategy aims to maximize wind energy in low wind speed. A part of our contribution lies in the limitation of the power output of the wind generator in high wind speed. Through the concept of the virtual desired variables, the design of the output tracking controller is achieved. In light of this concept, the developed T-S fuzzy control was designed via parallel-distributed compensation (PDC) approach with H<sub>∞</sub> performance.</p><p>Sufficient conditions for the stability of the closed-loop system affected by external disturbances are proved from Lyapunov’s direct method and the feedback gains of the controller strategy are determined by linear matrix inequalities (LMIs) tools. Another contribution is in showing the robustness of the Takagi-Sugeno based control strategy, with a focus on a set of system parameters with model uncertainties. The simulation results show the high performance of the proposed controller strategy for a 5MW (PMSG) obtained through simulation.</p>

Robust stabilization and tracking control schemes for disturbed multi-input multi-output Hammerstein model in presence of approximate polynomial nonlinearities

This article presents robust stabilization and tracking control problems for multi-input multi-output Hammerstein model with external disturbances. This model is characterized by static nonlinear elements followed by a linear dynamic block. Moreover, the unknown parameters of the identified mathematical model are estimated using the multivariable output error state space subspace algorithm. Unlike the general control strategy that used the nonlinearity inversion method, the nonlinearities are supposed not bijective. In this context, inverse nonlinear functions of polynomial structure are suggested in this article. Furthermore, the composition of the static nonlinear elements and their approximate inverses in series with the linear dynamic block are then decomposed into a set of linear parts using the Takagi–Sugeno fuzzy representation. Consequently, new sufficient stability conditions with decay rate and disturbance attenuation using the [Formula: see text] criterion and linear matrix inequality tools are discussed. Finally, simulation studies are provided to illustrate the merit of our purpose.

Limited-Budget Formation Control for High-Order Linear Swarm Systems with Fix Topologies

This paper discusses limited-budget time-varying formation design and analysis problems for a high-order linear swarm system with a fixed communication topology. Firstly, the communication topology among agents is modeled as an undirected and connected graph, and a new formation control protocol with an energy integral term is proposed to realize formation control and to guarantee the practical energy assumption is less than the limited energy budget. Then, by the matrix inequality tool, sufficient conditions for limited-budget formation design and analysis are proposed, respectively, which are scalable and checkable since they are independent of the number of agents of a swarm system and can be transformed into linear matrix inequality constraints. Moreover, an explicit expression of the formation center function is given, which contains the formation function part and the cooperative state part and is not associated with the derivatives of the formation functions. Finally, a numerical simulation is shown to demonstrate the effectiveness of theoretical results.

Energy-Constraint Formation for Multiagent Systems With Switching Interaction Topologies

The current paper investigates energy-constraint formation design and analysis problems for multiagent systems with two types of switching interaction topologies; that is, leaderless ones and leader-following ones. Firstly, a new formation control protocol with switching interaction topologies is shown, where the whole energy supply is limited previously. Then, by constructing the relationship of the whole energy supply and the matrix variable, sufficient conditions for leaderless energy-constraint formation design and analysis are respectively presented by the linear matrix inequality tool. Furthermore, an approach is proposed to determine an explicit expression of the formation center function, which determines the macroscopic motion of a multiagent system as a whole and consists of two parts: the initial state term and the formation function term. Moreover, main conclusions of leaderless energy-constraint formation are extended into leader-following multiagent systems by a new two-step transformation approach, where the asymmetric structure feature of leader-following switching interaction topologies is well dealt with. Finally, two numerical examples are provided to demonstrate the effectiveness of main conclusions.

Synthesis of Cooperative Adaptive Cruise Control With Feedforward Strategies

Cooperative adaptive cruise control (CACC) technique enhances the coordination of vehicles on road. Through CACC controllers, the platoon can exhibit promising traffic performance. In this paper, we study the control synthesis for two types of CACC systems, one of which uses acceleration feedforward while the other uses control feedforward. Under the predecessor-following topology, a general state-space model of vehicle platoon is established and the CACC characteristics including stabilization and string stability are realized by a set of constraints. To relax computation, complete quadratic Lyapunov-Krasovskii functionals are adopted and the CACC controllers are solved by linear matrix inequality tools. The proposed method provides a computationally efficient way to realize CACC design, and comparative experiments with existing work demonstrate the advantages.

Proportional PDC Design-Based Robust Stabilization and Tracking Control Strategies for Uncertain and Disturbed T-S Model

This paper presents a proportional parallel distributed compensation (PPDC) design to the robust stabilization and tracking control of the nonlinear dynamic system, which is described by the uncertain and perturbed Takagi–Sugeno (T-S) fuzzy model. The proposed PPDC control design can greatly reduce the number of adjustable parameters involved in the original PDC and separate them from the feedback gain. Furthermore, the process of finding the common quadratic Lyapunov matrix is simplified. Then, the global asymptotic stability with decay rate and disturbance attenuation of the closed-loop T-S model affected by uncertainties and external disturbances are discussed using the H∞ synthesis and linear matrix inequality (LMI) tools. Finally, to illustrate the merit of our purpose, numerical simulation studies of stabilizing and tracking an inverted pendulum system are presented.

Steering and Lateral Motorcycle Dynamics Estimation: Validation of Luenberger LPV Observer Approach

In this paper, we proposed a realistic validation of the nonlinear Luenberger observer initially introduced in one of our recent work. The validation is performed by means of a commercial motorcycle simulator. The previous paper has introduced the design of a nonlinear Luenberger observer to simultaneously estimate both the motorcycle lateral dynamics and the rider action. The vehicle lateral motion is described with a two-body linear model which takes into account the time-varying longitudinal velocity. Then, the Takagi–Sugeno approach combined with the Lyapunov theory, linear matrix inequalities tools and $L_2$ -gain property are used to demonstrate the observer's convergence through an input-to-error stability. Finally, the effectiveness and the robustness of the observer are illustrated on three different realistic riding scenarios by means of co-simulation of Matlab/Simulink and the well-known multibody simulator BikeSim. Finally, the estimation performances are compared to previous works.

Proportional integral observer-based decentralized stabilization design scheme for nonlinear complex interconnected systems

For a class of complex interconnected nonlinear disturbed systems, a proportional integral (PI) decentralized observer-based feedback robust decentralized controller technique is proposed, relying on H∞ synthesis for disturbance mitigation and linear matrix inequality (LMI) tools to achieve asymptotic stabilization and stability analysis within the Lyapunov framework. The proposed design method draws on a prominent optimization problem that can be tackled in terms of LMI constraints to evaluate the decentralized controller and PI observer gain matrices jointly, to maximize the nonlinearity coverage tolerated by the system without destabilization and to improve the robustness of the proposed control strategy by minimizing an H∞ criterion despite exogenous disturbances and strong nonlinear interconnections affecting the subsystems. The efficacy and high performance of the proposed control approach, compared with a renowned decentralized guaranteed cost control strategy from the literature, are validated by numerical simulations on a greatly interconnected three-machine power system.

$H_2$ Output-Feedback Control With Finite Multiple Measurement Information

This paper proposes a new $H_2$ output-feedback control with finite multiple measurement information for discrete-time systems with disturbances. This control is called an $H_2$ finite multiple measurement output-feedback control (H2FMMOFC). The new control ascertains the $H_2$ performance for disturbances and the equivalence to the $H_2$ state-feedback control without disturbances on a finite measurement horizon. The boundedness and exponential stability of the proposed H2FMMOFC are also investigated. The gain matrices of the H2FMMOFC are obtained by solving a convex problem utilizing the linear matrix inequality tool. Via a numerical example, the H2FMMOFC is shown to ensure the $H_2$ performance as well as the excellent robustness property against unexpected temporary model uncertainty although the uncertainty is not considered in its design.

Intelligent control of grid‐connected AC–DC–AC converters for a WECS based on T–S fuzzy interconnected systems modelling

Control of power converters is undoubtedly an essential issue in wind-energy systems. This study focuses on the development of a control scheme dedicated to a wind-energy conversion system (WECS) based on Takagi-Sugeno (T-S) fuzzy model. The treated system includes a wind turbine followed by a permanent magnet synchronous generator and power electronic converters. After describing the elements constituting the WECS, the main objectives of control are to extract the maximum amount of available power and to control the DC-bus voltage. The proposed approach is based on the concept of decentralised stabilisation. First, as to reduce the complexity of the system, the WECS is divided into two interconnected non-linear subsystems. Then, each subsystem is represented by a T-S fuzzy model. Using the parallel distributed compensation concept, a decentralised fuzzy controller is synthesised for each subsystem. Sufficient conditions are derived from Lyapunov theory and the local feedback gains for each controller are calculated by using linear matrix inequalities tools. Therefore, the whole closed-loop fuzzy system is stable using the elaborated fuzzy control scheme. Simulation results are included to show the performance of the proposed algorithm.

Control Strategies for the Grid Side Converter in a Wind Generation System Based on a Fuzzy Approach

Abstract Two techniques for the control of a grid side converter in a wind energy conversion system. The system is composed of a fixed pitch angle wind turbine followed by a permanent magnet synchronous generator and power electronic converters AC-DC-AC. The main interest is in how to control the inverter in order to ensure the stability of the DC link voltage. Two control methods based on the fuzzy approach are applied and compared. First, a direct Mamdani fuzzy logic controller is presented. Then, a T-S fuzzy controller is elaborated based on a T-S fuzzy model. The Lyapunov theorem and H-infinity performance are exploited for stability analysis. Besides, the feedback controller gains are determined using linear matrix inequality tools. Simulation results are derived in order to prove the robustness of the proposed control algorithms and to compare their performances.

Chaos Synchronization via Linear Matrix Inequalities: A Comparative Analysis

abstract In this paper, three chaos synchronization approaches using Linear Matrix Inequality (LMI) tools are evaluated and compared. The comparative analysis is supported by four examples of Piecewise affine (PWA) chaotic systems: The Chua’s original circuit, the Chua’s modified system, the Lur’e like circuit and the five-scroll attractor system. To evaluate the performances of each synchronization approach, we examine first, the practical implementation of the LMIs. We analyze then, by simulation results, the feasibility of each approach for each PWA chaotic system. The elapsed time for solving the predefined LMIs and the influence of their tuning parameters’ domain belonging on the feasibility and the performances of each approach are finally the considered comparative criteria.

Fault estimation and observer-based fault-tolerant controller in finite frequency domain

In this paper, the problems of finite-frequency fault estimation (FE) and fault tolerant controller design are investigated for a class of systems subjected to both sensor and actuator faults. To begin with, by introducing an expanded state vector, the original system is transformed into a descriptor system, and then an unknown input proportional-integral observer (PI) is developed to provide state and FE, which avoids the overdesign problems occurring in the entire frequency domain. After this, based on reconstructed information, an observer-based fault-tolerant controller is designed to stabilize the closed-loop system even if it suffers from faults and disturbances. In addition, the sufficient conditions of the existence of the PI and fault tolerant controller are derived by linear matrix inequality (LMI) tools. Finally, a simulation example is presented to demonstrate the effectiveness of the proposed techniques.