Linear Matrix Inequality Approach Research Articles

An observer‐based fault tolerance control system with a static filter and its application to high‐rise buildings

AbstractThis article proposes a fault tolerance control (FTC) system that composes of a state observer and a static filter, which can eliminate the adverse effects of sensor failures on the active mass damper control system of high‐rise buildings and realize fault detection and isolation. First, the accurate acceleration responses are obtained through a static filter that is used for minimizing the differences between the estimated and actual feedback signals. The key point is transformed into a gain optimization problem solved by a linear matrix inequality approach. Then, a state observer uses the detected and isolated acceleration responses as the feedback signals to estimate the whole states, which are used to calculate the control forces. Finally, a new observer‐based FTC system is accomplished for high‐rise buildings. To verify its effectiveness, the proposed methodology is applied to a numerical example and an experimental system. The results demonstrate that the fault tolerance controller has a good performance and stable control parameters, which provides good potential for structural vibration control of high‐rise buildings.

Drive-response synchronization of uncertain Markov jump generalized neural networks with interval time varying delays via decentralized event-triggered communication scheme

This paper investigates the synchronization problem of uncertain Markov jump generalized neural networks with interval time varying delays using decentralized event-triggered approach. We present a decentralized event-triggered scheme is utilized to decide if the sensor estimations ought to be sent out or not. Every sensor can choose the transmitted sensor estimations locally as indicated by the related event-triggered condition. By constructing an appropriate Lyapunov–Krasovskii functional (LKF) both continuous and discontinuous LKF, handled by the Jensen’s inequality, peng-park’s inequality (PPI) and a new Wirtinger-based integral inequality (WII) technique respectively. A simple and less conservative synchronization criterion is given to ensure the master systems synchronize with the slave systems by using the linear matrix inequality (LMI) approach. The Lyapunov method is employed to derive a sufficient condition such that the error system is stochastically stable. Moreover, the desired controller gains and event-triggered parameters are derived provided that the sufficient condition is satisfied. Finally, numerical examples are included to show that the results obtained from the proposed method provide less conservative results, which support the superiority of our criteria.

Global dissipativity of fuzzy cellular neural networks with inertial term and proportional delays

ABSTRACTThis paper is concerned with the global dissipativity of fuzzy cellular neural networks with inertial term and proportional delays. Based on Lyapunov functionals and linear matrix inequality approach, new sufficient conditions are derived to ensure the global dissipativity and global exponential dissipativity of the suggested system. Moreover, the globally exponential attractive sets and positive invariant sets are also presented here. Finally, two numerical examples with its simulations are proposed to illustrate the effectiveness of the obtained results.

Global Stability Analysis of Fractional-Order Quaternion-Valued Bidirectional Associative Memory Neural Networks

We study the global asymptotic stability problem with respect to the fractional-order quaternion-valued bidirectional associative memory neural network (FQVBAMNN) models in this paper. Whether the real and imaginary parts of quaternion-valued activation functions are expressed implicitly or explicitly, they are considered to meet the global Lipschitz condition in the quaternion field. New sufficient conditions are derived by applying the principle of homeomorphism, Lyapunov fractional-order method and linear matrix inequality (LMI) approach for the two cases of activation functions. The results confirm the existence, uniqueness and global asymptotic stability of the system’s equilibrium point. Finally, two numerical examples with their simulation results are provided to show the effectiveness of the obtained results.

Regional Stabilization of Input-Delayed Uncertain Nonlinear Polynomial Systems

This paper addresses the problem of local stabilization of nonlinear polynomial control systems subject to time-varying input delay and polytopic parameter uncertainty. A linear matrix inequality approach based on the Lyapunov–Krasovskii theory is proposed for designing a nonlinear polynomial state feedback controller ensuring the robust local uniform asymptotic stability of the system origin along with an estimate of its region of attraction. Two convex optimization procedures are presented to compute a stabilizing controller ensuring either a maximized set of admissible initial states for given upper bounds on the delay and its variation rate or a maximized lower bound on the maximum admissible input delay considering a given set of admissible initial states. Numerical examples demonstrate the potentials of the proposed stabilization approach.

Event-triggered fault detection for T-S fuzzy systems subject to data losses

ABSTRACTThis work focuses on the fault detection for nonlinear networked systems. A fault detection filter is designed to detect the fault signal under the effect of disturbance. The communication channel of the networked system is supposed to be influenced by the limited bandwidth and random data losses. To deal with these, event-triggered scheme and Bernoulli process are employed to describe the problems, respectively. According to the above situation, we employ a formulated random series to describe the input of fuzzy filter. Differential mean value theorem based method is presented to handle the asynchronous membership functions. Synthetically, linear matrix inequality approach is employed to obtain the stability conditions and the filter design process. At last, we verify the performance of this method acting in the simulation example.

Health-aware control design based on remaining useful life estimation for autonomous racing vehicle

The accurate estimation of the State of Charge (SOC) and an acceptable prediction of the Remaining Useful Life (RUL) of batteries in autonomous vehicles are essential for safe and lifetime optimized operation. The estimation of the expected RUL is quite helpful to reduce maintenance cost, safety hazards, and operational downtime. This paper proposes an innovative health-aware control approach for autonomous racing vehicles to simultaneously control it to the driving limits and to follow the desired path based on maximization of the battery RUL. To deal with the non-linear behavior of the vehicle, a Linear Parameter Varying (LPV) model is developed. Based on this model, a robust controller is designed and synthesized by means of the Linear Matrix Inequality (LMI) approach, where the general objective is to maximize progress on the track subject to win racing and saving energy. The main contribution of the paper consists in preserving the lifetime of battery and optimizing a lap time to achieve the best path of a racing vehicle. The control design is divided into two layers with different time scale, path planner and controller. The first optimization problem is related to the path planner where the objective is to optimize the lap time and to maximize the battery RUL to obtain the best trajectory under the constraints of the circuit. The proposed approach is formulated as an optimal on-line robust LMI based Model Predictive Control (MPC) that steered from Lyapunov stability. The second part is focused on a controller gain synthesis solved by LPV based on Linear Quadratic Regulator (LPV-LQR) problem in LMI formulation with integral action for tracking the trajectory. The proposed approach is evaluated in simulation and results show the effectiveness of the proposed planner for optimizing the lap time and especially for maximizing the battery RUL.

Robust model reference tracking control for interval type‐2 fuzzy stochastic systems

This study considers the uncertainty and disturbance estimator-based control problem for interval type-2 fuzzy stochastic systems with disturbances. The proposed control approach accurately estimates system unknown delays, uncertainties, non-linearities and external disturbances by introducing an appropriate filter. Precisely, the filter's bandwidth is one of the most important parameters in designing and tuning the controller to deal with unknown delays, uncertainties, non-linearities and disturbances. By using the Lyapunov–Krasovskii stability theorem and the linear matrix inequality approach, the required stability conditions and the control gain matrices for the system under consideration are obtained. Further, the effectiveness of the proposed control law is verified using two numerical examples.

Observer‐based robust preview tracking control for a class of non‐linear systems

This study provides an observer-based robust preview tracking controller for Lipschitz non-linear systems. Firstly, the non-linear system dynamics is studied and the non-linear observer is designed. By introducing the Lyapunov function, the observer gain matrix is obtained through linear matrix inequalities (LMIs). To obtain an effective tracking control law, an augment error system which consists of difference of estimation error, tracking error, difference of estimated status and reference preview information is constructed. The sufficient solutions for observer-based robust preview controller are analysed using the LMI approach. Two numerical examples are provided to show the flexibility and effectiveness of the proposed robust preview tracking controller.

Parameter-dependent linear matrix inequality approach to robust state estimation of noisy genetic networks

Genetic networks play an important role in systems biology as they explain the interactions between genes and proteins. However, the genetic networks are described by dynamical systems with nonlinear uncertainties and usually affected by stochastic internal fluctuations, and stochastic external disturbances. The design addressed in this paper is concerned with robust state estimator of stochastic genetic networks in the presence of nonlinear uncertainties. The objective is to estimate the true concentrations of mRNAs and proteins of the noisy nonlinear genetic networks. Based on the notion of Lyapunov functions, we improve the design condition for the robust estimator to ensure that the estimation error satisfies H∞ performance criterion. The sufficient condition is derived in terms of parameter-dependent linear matrix inequalities, which are convex constraints, and can be efficiently solved via the sum-of-squares technique. We provide two numerical examples of real genetic networks to illustrate the effectiveness of the proposed method.

Design of Interval Type-2 Fuzzy Controllers for Active Magnetic Bearing Systems

This article proposes an active levitation control system composed of an active magnetic bearing (AMB) rotor and an interval type-2 (IT2) model-based fuzzy logic controller (FLC). The controller aims to achieve fast and stable levitation by compensating for system uncertainties via proper design of IT2 membership functions. In particular, the complex nonlinear dynamics of the AMB are modeled as a set of local linear systems around multiple operating points, which can be stabilized by a parallel distributed compensation scheme. Sufficient conditions are derived to guarantee the asymptotical stability of the closed-loop system based on the linear matrix inequality approach and the Lyapunov stability theory. Moreover, input constraints are applied in an enhanced version of the controller. Experiments on a real AMB platform were conducted to demonstrate the effectiveness and superiority of the proposed IT2 FLC.

Asynchronous H∞ control for nonhomogeneous higher-level Markov jump systems

This paper investigates about asynchronous H∞ control for nonhomogeneous higher-level Markov jump systems, where a higher-level transition probability matrix is considered. The asynchronous H∞ controller designed is subject to an independent Markov chain. Using a linear matrix inequality approach, sufficient conditions are established such that system with controller is stochastically stable. A numerical example is presented to demonstrate the effectiveness of our method developed.

The H∞ Model Following Control: An LMI Approach

The aim of this paper is to develop a new approach for a solution of the model following control (MFC) problem with a dynamic compensator by using linear matrix inequalities (LMIs). TheH1 model following control problem is derived following LMI formulation. First, the H1 optimal control problem is revisited by referring to Lemmas assuring all admissible controllers minimizing the H1 norm of the transfer function between the exogenous inputs and the outputs. Then, the solvability condition and a design procedure for a two degrees of freedom (2 DOF) dynamic feedback control law is introduced. The existence of a 2 DOF dynamic output feedback controller for the model following control is proven and the stability of the closed-loop system is satisfied by assuring the Hurwitz condition. The benchmark thermal process (PT-326) as the first order process with timedelay is regulated by the presented 2 DOF dynamic output feedback controller. The simulation results illustrate that the presented controller regulates a system with dead-time as a large set of generic industrial systems and the H1 norm of the closed-loop system is assured less than the H1 norm of the desired model system.

Robust state estimation for fractional-order delayed BAM neural networks via LMI approach

This paper is concerned with the robust state estimation problem for a class of delayed fractional-order bidirectional associative memory (FOBAM) neural networks (NNs) with norm-bounded uncertainties. The objective of the study is to construct an efficient estimator in such a way that the behavior of the corresponding error state is stable in the Mittag-Leffler sense. Distinct to the previous studies, the state estimation problem of FOBAM NNs is investigated through fractional-order Lyapunov direct method. The sufficient conditions that ensure the global Mittag-Leffler stability of the error system are derived as a set of solvable linear matrix inequalities (LMIs) without uncertainties. The proposed stability conditions are further extended to the FOBAM NNs by considering the effect of uncertainties. In order to validate the effectiveness of the proposed theoretical results, two numerical examples have been illustrated.

Distributed set-membership filtering for time-varying systems under constrained measurements and replay attacks

In this paper, the distributed set-membership filtering problem is investigated for a class of time-varying system subject to constrained measurements and replay attacks over sensor network. The constrained measurements refer to the saturation of sensors and the quantization effect of measured signals. Because of the openness and sharing of the network, the transmitted measurement signals can be attacked by malicious adversary. In our study, we assume that the adversary adopts replay attack strategy. The aim of this paper is to design the secure distributed set-membership filter for a class of time-varying systems over unsafe and bandwidth-limited sensor network. By employing linear matrix inequality approach, sufficient conditions guaranteeing the desired distributed filter are obtained, which are in the form of recursive linear matrix inequality. Moreover, an optimization algorithm is proposed to make sure the local optimal filtering performance. Finally, the effectiveness of the proposed secure distributed filtering algorithm is demonstrated by a simulation example.

Fault-Tolerant Synchronization of Chaotic Systems with Fuzzy Sampled Data Controller Based on Adaptive Event-Triggered Scheme

This paper deals with the problem of the fault-tolerant fuzzy master–slave systems synchronization through an adaptive event-triggered scheme (AETS). First, a Takagi–Sugeno (T–S) fuzzy model is employed to represent the master–slave system dynamics. Second, an AETS is introduced to judge whether the newly sampled controller’s signals should be released to the slave system or not. Consequently, the less computation resources and network bandwidth are utilized under the AETS. Meanwhile, a novel adaptive law is designed to achieve the threshold of event-triggering condition on-line. Third, a novel fuzzy controller is designed, containing a state feedback controller and a fault compensator to achieve the fault-tolerant synchronization, which is formulated to study the global asymptotical stability of the error system. As a results, applying Lyapunov theory and inequality technique, new sufficient condition is obtained to guarantee the stability of the error system. Further, the controller gain and the weight of event-triggering condition are designed through linear matrix inequalities (LMIs) approach. Finally, a numerical simulation example is employed to demonstrate the practical utility of this method.

Leader-following consensus conditions for fractional-order descriptor uncertain multi-agent systems with 0 < α < 2 via output feedback control

The leader-following consensus problem for fractional-order uncertain multi-agent systems with descriptor linear dynamics is investigated in this paper. Firstly, a consensus protocol is proposed based on output feedback when fractional-order α satisfies 0 < α < 2. Secondly, an appropriate transformation is conducted to transform consensus problem into stability problem. Based on stability theory of fractional-order systems, sufficient conditions are presented to guarantee the leader-following consensus of fractional-order descriptor uncertain multi-agent systems with 0 < α < 2. In addition, output feedback controller is designed by using linear matrix inequality approach and matrix’s singular value decomposition. Finally, numerical examples are given to illustrate the effectiveness of our conclusions.

LMI-Based Robust Stabilization of a Class of Input-Constrained Uncertain Nonlinear Systems with Application to a Helicopter Model

This paper is concerned with the robust stabilization of a class of continuous-time nonlinear systems, with an application to the pitch dynamics of a simple helicopter model, via an affine state-feedback control law using the linear matrix inequality (LMI) approach. The nonlinear dynamics is subject to norm-bounded parametric uncertainties and disturbances. In addition, the problem of actuator nonlinearity is addressed by considering the saturation effect of the control law. We demonstrate first that the synthesis problem of the saturated controller is expressed in terms of bilinear matrix inequalities (BMIs). Thanks to the Schur complement lemma and the matrix inversion lemma, we convert these BMIs into LMIs allowing the simultaneous computation of the two gains of the affine controller. Furthermore, we address in this work the estimation problem of the domain of attraction using the invariant set concept. This is solved by computing the largest attractive invariant ellipsoid. Compared with previous works, the research procedure of such ellipsoidal set is achieved in a single step with a reduced number of LMI constraints and then with less conservative conditions. A portfolio of numerical results is presented. The effectiveness and robustness of the proposed saturated controller in the stabilization of the adopted helicopter pitch model toward parametric uncertainties and disturbances are illustrated through simulation results.

Synchronisation of uncertain chaotic systems via fuzzy-regulated adaptive optimal control approach

ABSTRACTThis study investigates the adaptive synchronisation of uncertain chaotic systems with unmodelled nonlinearities, dynamic mismatch, parametric perturbations, and external disturbances. A fuzzy-regulated adaptive optimal control (FRAOC) scheme is derived to realise chaotic synchronisation under both structure and parameter uncertainties. In the proposed scheme, the uncertain chaotic dynamics is firstly captured and estimated using a self-organising learning algorithm in an online fuzzy rule database. Based on the complicated and uncertain chaotic information, control strategy is adaptively regulated and configured in the form of weighting matrix for the subsequent optimal controller by the use of fuzzy logic inference. An adaptive optimal controller is then developed, so that its control behaviour and performance are adaptively adjusted for the chaotic synchronisation and compound uncertainty compensation. A supervisory compensator with recursive adaptation law is also designed to attenuate the residual compensation error and guarantee the synchronisation stability. Chaotic synchronisation convergence using the proposed approach can be mathematically ensured and speeded up with satisfactory robustness. Simulation results also demonstrate the effectiveness of the proposed control method in comparison with robust quadratic optimal control based on linear matrix inequality approach.

Dissipative-based non-fragile filtering for fuzzy networked control systems with switching communication channels

The problem of finite-time dissipative-based non-fragile filter design for a class of discrete-time nonlinear networked control systems subject to randomly occurring parameter uncertainties, external disturbances as well as packet dropouts due to unreliable communication channels and networked induced time-varying delay is discussed. The randomly occurring uncertainties are assumed to satisfy Bernoulli distribution and the considered stochastic variables are mutually independent. Multiple communication channel scenario is taken into account to enhance the data transmission performance and the channel switching phenomena is governed by a Markov chain. The intention here is to design a dissipative-based non-fragile filter for the filtering error system such that it is stochastically finite-time bounded and attains a prescribed dissipative performance attenuation level. Lyapunov stability theory and linear matrix inequality approach are exploited to develop a set of sufficient criterion for the existence of the desired filter. Finally, the filter design framework is applied to the truck-trailer model to demonstrate its effectiveness.