Linear Matrix Inequality Tools Research Articles

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.

Finite time stability of linear time varying delay systems using free matrix based integral inequalities

This paper discusses the problem of finite time stability (FTS) for linear delayed systems where the time-varying delay is bounded. First, based on a Lyapunov–Krasovskii Functional (LKF) which contains terms of triple integrals, delay-dependent FTS conditions are provided by introducing some free-weighting matrices. Then, new approximations of the single and multiple quadratic integrals that appear in the LKF derivative are established using integral inequalities, called free-matrix-based integral inequalities. The dimensions of these free matrices integral in our results are less than those obtained in the literature. This reduction in the number of variables does not mean that our method is a particular case but simply that our approach is completely different from the others and therefore more effective. Finally, less conservative design conditions in terms of Linear Matrix Inequalities (LMIs) are proposed and solved by the LMI Tools of MATLAB to show the advantage and effectiveness of the proposed approach.

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.

Observer-based robust actuator fault isolation and identification for microsatellite attitude control systems

Purpose The purpose of this paper is to accomplish robust actuator fault isolation and identification for microsatellite attitude control systems (ACSs) subject to a series of space disturbance torques and gyro drifts. Design/methodology/approach For the satellite attitude dynamics with Lipschitz constraint, a multi-objective nonlinear unknown input observer (NUIO) is explored to accomplish robust actuator fault isolation based on a synthesis of Hinf techniques and regional pole assignment technique. Subsequently, a novel disturbance-decoupling learning observer (D2LO) is proposed to identify the isolated actuator fault accurately. Additionally, the design of the NUIO and the D2LO are reformulated into convex optimization problems involving linear matrix inequalities (LMIs), which can be readily solved using standard LMI tools. Findings The simulation studies on a microsatellite example are performed to prove the effectiveness and applicability of the proposed robust actuator fault isolation and identification methodologies. Practical implications This research includes implications for the enhancement of reliability and safety of on-orbit microsatellites. Originality/value This study proposes novel NUIO-based robust fault isolation and D2LO-based robust fault identification methodologies for spacecraft ACSs subject to a series of space disturbance torques and gyro drifts.

Further results on Mittag-Leffler synchronization of fractional-order coupled neural networks

In this paper, we focus on the synchronization of fractional-order coupled neural networks (FCNNs). First, by taking information on activation functions into account, we construct a convex Lur’e–Postnikov Lyapunov function. Based on the convex Lyapunov function and a general convex quadratic function, we derive a novel Mittag-Leffler synchronization criterion for the FCNNs with symmetrical coupled matrix in the form of linear matrix inequalities (LMIs). Then we present a robust Mittag-Leffler synchronization criterion for the FCNNs with uncertain parameters. These two Mittag-Leffler synchronization criteria can be solved easily by LMI tools in Matlab. Moreover, we present a novel Lyapunov synchronization criterion for the FCNNs with unsymmetrical coupled matrix in the form of LMIs, which can be easily solved by YALMIP tools in Matlab. The feasibilities of the criteria obtained in this paper are shown by four numerical examples.

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.

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.

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.

<i>H</i><SUB align="right">∞ control of asynchronous networked control systems with Markov time delays

In this paper, the solutions to the H∞ synthesis problems of stochastic asynchronous discrete-time (DT) networked control systems (NCSs) with random communication time delays are proposed according to the following steps. Firstly, a new Lyapunov-Krasovskii functional is explicitly constructed to analyse the stochastic stability of the systems. Both sensor-to-controller (S-C) and controller-to-actuator (C-A) random networked-induced delays, which are two Markov chains, are considered in the analysis. Moreover, the stochastic sampling of S-C and holding of C-A are also considered in the analysis. Secondly, based on a specified definition of the state with delay and a more rigorous inequality, sufficient delay-dependent stability conditions can be transformed into the form of linear matrix inequalities (LMIs), the LMIs can be conveniently solved by LMI tools. Finally, the proposed theory is validated by a simulation example.

Event-triggered fault detection filter design for nonlinear networked systems via fuzzy Lyapunov functions

This paper investigates the problem of event-triggered fault detection filter design for nonlinear networked control systems with both sensor faults and process faults. First, Takagi–Sugeno (T–S) fuzzy model is utilized to represent the nonlinear systems with faults and disturbances. Second, a discrete event-triggered communication scheme is proposed to reduce the utilization of limited network bandwidth between filter and original system. At the same time, considering network-induced delays and event-triggered scheme, a novel T–S fuzzy fault detection filter is constructed to generate a residual signal, which has nonsynchronous premise variables with the original T–S fuzzy system. Then, the fuzzy Lyapunov functional based approach and the reciprocally convex approach are developed such that the obtained sufficient conditions ensure that the fuzzy fault detection system is asymptotically stable with H∞ performance and is less conservative. All the conditions are given in terms of linear matrix inequalities (LMIs), which can be solved by LMI tools in MATLAB environment. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed results.

$H_2$ 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.

Laser-range-finder localization based fuzzy control for mobile robots

PurposeBased on laser-range-finder (LRF) sensing, the control design of location and orientation stabilization for the mobile robot is investigated. However, the practical limitation of the LRF sensing is usually ignored in the control design, which leads to incorrect localization and unexpected control results. The purpose of this study is to design the fuzzy controller subject to the practical limitation on the LRF-based localization for a differentially driven wheeled mobile robot.Design/methodology/approachFirst, the Takagi–Sugeno (T-S) fuzzy model is derived from the polar kinematic model of a differentially driven mobile robot. Then, the fuzzy controller is designed to the derived T-S fuzzy kinematic model in accordance with the Lyapunov stabilization theorem. The derived Lyapunov stabilization conditions for the fuzzy control design are expressed as the linear matrix inequality (LMI) form and effectively solved by LMI tools. The practical limitation on the LRF-based localization is also expressed as the LMI form and simultaneously solved with the control design.FindingThe location and posture stabilization experiments are carried out on a mobile robot with LRF-based localization to prove the effectiveness of the proposed T-S fuzzy model-based control design. Furthermore, the ground truth experiment evaluates the accuracy of LRF-based localization.Originality/valueThe contribution of this study is to develop the fuzzy control law for a differentially driven wheeled mobile robot under the practical limitation on LRF-based localization. The proposed control design can be applied to other robots with practical limitations on the sensors.

H∞Controller Design for Asynchronous Hybrid Systems with Multiple Delays

Solutions for theH∞synthesis problems of asynchronous hybrid systems with input-output delays are proposed. The continuous-time lifting approach of sampled-data systems is extended to a hybrid system with multiple delays, and some feasible formulas to calculate the operators of the equivalent discrete-time (DT) system are given. Different from the existing methods derived from symplectic pair theory or by state augmentation, a Lyapunov-Krasovskii functional to solve the synthesis problem is explicitly constructed. The delay-dependent stability conditions we obtained can be described in terms of nonstrict linear matrix inequalities (LMIs), which are much more convenient to be solved by LMI tools.

Angle Stability Analysis of Power System with Multiple Operating Conditions Considering Cascading Failure

A method to analyze the angle stability of power system with multiple operating conditions considering cascading failure is proposed in this paper. First, considering stochastic events such as uncertain operation of protection/breaker and system hardware failure, the system operating condition set is determined based on the flow transfer theory and the matrix of transfer probability between different operating conditions is calculated. On this basis, the discrete Markov power system model with multiple operating conditions considering cascading failure is established. And then, construct the Lyapunov functional containing the Markov model, and derive the robust stochastic stability criterion which satisfies the disturbance attenuation degree γ by iteration and the angle stability of power system could be identified according to the criterion using linear matrix inequality tools. Finally, stability index μ is defined to establish the relationship between transfer probability and system stability. Time-domain simulation tests on the IEEE 16-machine 68-bus system verify that, the proposed method could identify the stability of power system with multiple operating conditions effectively, with no need to obtain the operating trajectory of the system. Compared with traditional time-domain simulation method, the computation amount is reduced. Besides, it is simple and easy to implement.

Delay-range-dependent control of nonlinear time-delay systems under input saturation

Summary This paper describes a delay-range-dependent local state feedback controller synthesis approach providing estimation of the region of stability for nonlinear time-delay systems under input saturation. By employing a Lyapunov–Krasovskii functional, properties of nonlinear functions, local sector condition and Jensen's inequality, a sufficient condition is derived for stabilization of nonlinear systems with interval delays varying within a range. Novel solutions to the delay-range-dependent and delay-dependent stabilization problems for linear and nonlinear time-delay systems, respectively, subject to input saturation are derived as specific scenarios of the proposed control strategy. Also, a delay-rate-independent condition for control of nonlinear systems in the presence of input saturation with unknown delay-derivative bound information is established. And further, a robust state feedback controller synthesis scheme ensuring L2 gain reduction from disturbance to output is devised to address the problem of the stabilization of input-constrained nonlinear time-delay systems with varying interval lags. The proposed design conditions can be solved using linear matrix inequality tools in connection with conventional cone complementary linearization algorithms. Simulation results for an unstable nonlinear time-delay network and a large-scale chemical reactor under input saturation and varying interval time-delays are analyzed to demonstrate the effectiveness of the proposed methodology. Copyright © 2015 John Wiley & Sons, Ltd.