Linear Matrix Equalities Research Articles

Secure estimation for cyber‐physical systems under adversarial actuator attacks

Almost all of the available literature on secure state estimation focus on sensor attacks. Unlike the existing results, this study investigates the attack-resilient state estimation problem for continuous-time linear systems with sparse actuator attacks and process noises. It is assumed that, the attacker has limited resources and can only manipulate a certain number of actuators. Specifically, a novel switched observer is proposed with milder design conditions which are derived in terms of linear matrix (in)equalities. It is shown that, the observer not only provides an attack-resilient state estimation, but also guarantees that the resulting observer error system is with noise attenuation level which can be optimised. Finally, a simulation example of a linearised reduced-order aircraft system is provided to show the effectiveness of the proposed approach.

Static output feedback design for a class of constrained Takagi–Sugeno fuzzy systems

This paper addresses the static output feedback (SOF) control problem of Takagi–Sugeno fuzzy systems subject to both control input and state constraints. A new parameter-dependent sector condition is proposed to deal with the input saturation in SOF control context. Based on a judicious use of Finsler’s lemma in fuzzy Lyapunov control framework, new design conditions guaranteeing the existence of a stabilizing controller are recast as an LMI-based optimization with additional slack variables. These extra variables offer more flexibility to reduce the design conservatism. In particular, the proposed method requires neither special constraints on the state-space system matrices nor linear matrix equalities, which are hard to be satisfied. Several numerical examples are given to demonstrate the interests of the new control method.

Stability of hybrid stochastic differential systems with switching and time delay

ABSTRACTThis article introduces a hybrid stochastic differential system with impulsive, switching and time-delay. Some stability criteria of p-moment global asymptotical stability, p-moment global exponential stability and mean square stability of this system are derived by using switching Lyapunov function approach, Itô formula, impulsive differential inequality method, and linear matrix equality techniques. Three examples are presented to demonstrate the efficiency of the obtained results.

Receding-Horizon <inline-formula> <tex-math notation="LaTeX">$l_{2}{-}l_{\infty}$</tex-math> </inline-formula> FIR Filter With Embedded Deadbeat Property

This brief proposes a new finite-impulse response (FIR) receding-horizon filter for discrete-time linear systems in state space. A solution has l 2 -l ∞ performance with the embedded deadbeat property and is called the FIR l 2 -l ∞ filter (FIRllF). Based on the linear matrix inequality (LMI) and linear matrix equality (LME) formulations, a sufficient condition is found such that the FIRllF ascertains the guaranteed l 2 -l ∞ performance with the deadbeat property. Using this result, we further obtain a new LMI condition for the existence of the FIRllF without using the LME. Through a numerical example, the proposed FIRllF is shown to be more robust against unexpected uncertainties than the existing l 2 -l ∞ filter.

Robust unknown input observer design for state estimation and fault detection using linear parameter varying model

This paper proposes a robust unknown input observer for state estimation and fault detection using linear parameter varying model. Since the disturbance and actuator fault is mixed together in the physical system, it is difficult to isolate the fault from the disturbance. Using the state transforation, the estimation of the original state becomes to associate with the transform state. By solving the linear matrix inequalities (LMIs)and linear matrix equalities (LMEs), the parameters of the UIO can be obtained. The convergence of the UIO is also analysed by the Layapunov theory. Finally, a wind turbine system with disturbance and actuator fault is tested for the proposed method. From the simulations, it demonstrates the effectiveness and performances of the proposed method.

Finite-Time Stability of Neural Networks with Impulse Effects and Time-Varying Delay

In this paper, the impulsive effects on the finite-time stability of neural networks with time-varying delay are considered. Several novel criteria which govern the systems considered are finite-time stable are obtained by the idea of Lyapunov–Krasovskii functional and the average impulsive interval method. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities which can be easily checked by Matlab LMI toolbox. The results proposed show that the model can achieve stable in finite time with stabilizing impulsive effects on one hand, and it can preserve the finite-time stability property in presence of destabilizing impulses on the other hand. Numerical examples are presented to demonstrate the effectiveness of the obtained results.

Admissibility analysis for Takagi–Sugeno fuzzy singular systems with time delay

The issue of admissibility analysis for Takagi–Sugeno (T–S) fuzzy singular system with time delay is investigated in this paper. By adopting a novel tighter integral inequality, a sufficient delay-dependent criterion is built on the basis of strict linear matrix equalities (LMIs), which guarantees the admissibility of the considered system. A numerical example shows that the proposed method is efficient and less conservative.

Robust Repetitive Control and Disturbance Rejection Based on Two‐Dimensional Model and Equivalent‐Input‐Disturbance Approach

AbstractA new configuration of a modified repetitive‐control system has been devised for a class of strictly proper plants that suppresses exogenous disturbances and uncertainties in the dynamics of the plant. It extends the applicability of the control system. The system consists of four parts: a two‐dimensional augmented model of the plant, which takes into account the difference in characteristics between continuous control and discrete learning in repetitive control; an equivalent‐input‐disturbance estimator; a state observer; and a state‐feedback controller. A robust‐stability condition expressed in terms of a linear matrix equality is used to determine the gains of the observer and the controller. Finally, a comparison of our method with repetitive control based on linear active disturbance rejection control (LADRC) shows how effective our method is and that it is superior to LADRC‐based repetitive control.

Delay-dependent LMI-based robust stability criterion for discrete and distributed time-delays Markovian jumping reaction–diffusion CGNNs under Neumann boundary value

In this paper, variational methods, Lyapunov stability theory, Homomorphic mapping theory, M-matrix, H-matrix and linear matrix equality (LMI) technique are synthetically employed to obtain the LMI-based stochastically exponential robust stability criterion for a discrete and distributed time-delays Markovian jumping reaction–diffusion Cohen–Grossberg neural networks (CGNNs) with uncertain parameters. It is worth mentioning that the methods employed in this paper improve those of previous related literature to some extent, and the obtained stability criterion can be easily and efficiently computed by computer LMI toolbox. Moreover, a numerical example is presented to illustrate the effectiveness of the proposed methods thanks to the large allowable variation range of time-delays.

Finite-time boundedness and stabilization of uncertain switched neural networks with time-varying delay

This paper deals with the finite-time boundedness and stabilization problem for a class of switched neural networks with time-varying delay and parametric uncertainties. Based on Lyapunov-like function method and average dwell time technique, some sufficient conditions are derived to guarantee the finite-time boundedness of considered uncertain switched neural networks. Furthermore, the state feedback controller is designed to solve the finite-time stabilization problem. Moreover, the proposed sufficient conditions can be simplified into the form of linear matrix equalities for conveniently using Matlab LMI toolbox. Finally, two numerical examples are given to show the effectiveness of the main results.

New preceding vehicle tracking algorithm based on optimal unbiased finite memory filter

In recent years, visual object tracking technologies have been used to track preceding vehicles in advanced driver assistance systems (ADASs). The accurate positioning of preceding vehicles in camera images allows drivers to avoid collisions with the preceding vehicle. Tracking systems typically take advantage of state estimators, such as the Kalman filter (KF) and the particle filter (PF), in order to suppress noises in measurements. In particular, the KF is popular in visual object tracking, because of its computational efficiency. However, the visual tracker based on the KF, referred to as the Kalman tracker (KT), has the drawback that its performance can decrease due to modeling and computational errors. To overcome this drawback, we propose a novel visual tracker based on the optimal unbiased finite memory filter (OUFMF) in the formulation of a linear matrix inequality (LMI) and a linear matrix equality (LME). We call the proposed visual tracker the finite memory tracker (FMT), and it is applied to the preceding vehicle tracking. Through extensive experiments, we demonstrate the FMT’s performance that is superior to that of the KT and other filter-based tracker.

Design of IIR Digital Filters with Arbitrary Flatness Using Iterative Quadratic Programming

This paper presents a design method of Chebyshev-type and inverse-Chebyshev-type infinite impulse response (IIR) filters with an approximately linear phase response. In the design of Chebyshev-type filters, the flatness condition in the stopband is preincorporated into a transfer function, and an equiripple characteristic in the passband is achieved by iteratively solving the QP problem using the transfer function. In the design of inverse-Chebyshev-type filters, the flatness condition in the passband is added to the constraint of the QP problem as the linear matrix equality, and an equiripple characteristic in the stopband is realized by iteratively solving the QP problem. To guarantee the stability of the obtained filters, we apply the extended positive realness to the QP problem. As a result, the proposed method can design the filters with more high precision than the conventional methods. The effectiveness of the proposed design method is illustrated with some examples.

Stabilization of Networked Distributed Systems with Partial and Event-Based Couplings

The stabilization problem of networked distributed systems with partial and event-based couplings is investigated. The channels, which are used to transmit different levels of information of agents, are considered. The channel matrix is introduced to indicate the work state of the channels. An event condition is designed for each channel to govern the sampling instants of the channel. Since the event conditions are separately given for different channels, the sampling instants of channels are mutually independent. To stabilize the system, the state feedback controllers are implemented in the system. The control signals also suffer from the two communication constraints. The sufficient conditions in terms of linear matrix equalities are proposed to ensure the stabilization of the controlled system. Finally, a numerical example is given to demonstrate the advantage of our results.

Sampled-data state estimation for delayed neural networks with discontinuous activations

This paper firstly treats of the sampled-data state estimation issue for the dynamic neural networks with mixed time-delays and discontinuous activation. Based on the theory of differential inclusion and non-smooth analysis, several criteria are presented to guarantee the existence of the desired state sampled-data estimator for the discontinuous neural networks by solving some linear matrix equalities. The obtained results are also applicable to neural networks with continuous activations since they are a special cases of neural networks with discontinuous activations. Results of this paper improve a few previous known results. Finally, two numerical simulations are given to illustrate the effectiveness of the proposed methods.

Robust exponential [formula omitted] control for uncertain time-varying delay systems with input saturation: A Markov jump model approach

This paper is concerned with the state feedback stabilization problem for uncertain time-varying delay systems with input saturation. Based on the stochastic property of time-varying delay, the considered system can be transformed into a continuous Markov jump system with stochastic delays, where the growth trend and the maximum value of the time-varying delay are limited. The problem we address is to design a robust state feedback controller which can switch with time-varying delay in terms of Markov process, such that the system is exponentially mean-square stable with disturbance attenuation γ. Conditions for the existence of solutions to this problem are obtained in terms of linear matrix equalities (LMIs). When these LMIs are feasible, the desired robust controller is given. Finally, two examples are provided to demonstrate the effectiveness of the proposed approach.

Combined feedback–feedforward tracking control for networked control systems with probabilistic delays

In this paper, we investigate the combined feedback–feedforward tracking control problem for networked control systems (NCSs) under the discrete-time framework. Network-induced delays, both on the network links from the sensor to the controller (S–C) and from the controller to the actuator (C–A), are considered. It is assumed that the probability for the occurrence of each delay is known within a set. We apply a predictive scheme to compensate for the C–A delay, and propose to design a controller for each network-induced delay. Using the augmentation technique twice, the tracking problem of the NCS is converted to a feedback control problem for delay-free stochastic systems. The stochastic stability and the H∞ performance of the obtained closed-loop stochastic system are analyzed in terms of a linear matrix inequality and a linear matrix equality. Then, we propose the controller design method by solving a nonlinear trace minimization problem. Finally, an example on the control of a helicopter is given to illustrate the proposed design approach.

Robust pole assignment for synthesizing feedback control systems using recurrent neural networks.

This paper presents a neurodynamic optimization approach to robust pole assignment for synthesizing linear control systems via state and output feedback. The problem is formulated as a pseudoconvex optimization problem with robustness measure: i.e., the spectral condition number as the objective function and linear matrix equality constraints for exact pole assignment. Two coupled recurrent neural networks are applied for solving the formulated problem in real time. In contrast to existing approaches, the exponential convergence of the proposed neurodynamics to global optimal solutions can be guaranteed even with lower model complexity in terms of the number of variables. Simulation results of the proposed neurodynamic approach for 11 benchmark problems are reported to demonstrate its superiority.

Simple Tracking Output Feedback H∞ Control for Switched Linear Systems: Lateral Vehicle Control Application

In this paper, the problem of the switched H∞tracking output feedback control problem is studied. The control design problem is addressed in the context of discrete-time switched linear systems. Then, the design of continuous-time case becomes trivial. Linear Matrix Inequality (LMI) and Linear Matrix Equality (LME) representations are used to express all sufficient conditions to solve the control problem. Some transformations leading to sufficient conditions for the control problem are also used. All conditions are established for any switching using a switched Lyapunov function and a common Lyapunov function. The effectiveness of the proposed control approach is shown through a steering vehicle control implementation. Interesting simulation results are obtained using real data acquired by an instrumented car.

정적 출력궤환 기반 강인 고장포용 제어기 설계

This paper addresses the robust fault tolerant controller design problems of static output systems with disturbance. The fault is expressed by the abrupt chattering of system parameters. The design conditions are derived in terms of linear matrix inequalities and linear matrix equalities. An illustrative example is provided to verify performances of the proposed controller.

Positive Semidefinite Generalized Diffusion Tensor Imaging via Quadratic Semidefinite Programming

The positive definiteness of a diffusion tensor is important in magnetic resonance imaging because it reflects the phenomenon of water molecular diffusion in complicated biological tissue environments. To preserve this property, we represent it as an explicit positive semidefinite (PSD) matrix constraint and some linear matrix equalities. The objective function is the regularized linear least squares fitting for the log-linearized Stejskal--Tanner equation. The regularization term is the heuristic nuclear norm of the PSD matrix, since we expect it to be of low rank. In this way, we establish a convex quadratic semidefinite programming (SDP) model, whose global solution exists. The optimal solution could be solved by three efficient methods. While there are two state-of-the-art solvers---SDPT3 and QSDP---for the primal problem, we design a new augmented Lagrangian based alternating direction method (ADM) for the dual problem. Sensitivity analyses on the coefficients of the optimal diffusion tensor and the ...