Parameter-dependent Linear Matrix Inequalities Research Articles

Polynomial filter-based adaptive fault-tolerant control for a class of nonlinear systems with multiplicative faults

In this article, the problem of fault-tolerant control is investigated for polynomial nonlinear systems (PNSs) subject to multiplicative faults and measurement noise. Firstly, a matrix Taylor expansion technique is applied to transform the PNS into a linear parameter varying system. Then the polynomial filter is constructed to get estimations of states and unmatched disturbances, which reduces the effect of measurement noise. A novel adaptive fault-tolerant controller is proposed to compensate for multiplicative faults and unmatched disturbances. Furthermore, the condition of the parameter-dependent linear matrix inequality (PDLMI) is deduced, which guarantees the boundedness of tracking errors and estimation errors, and the sum of squares (SOS) decomposition technique is utilized to solve PDLMI. Finally, the simulation of a rotary steerable drilling tool system confirms the feasibility of the proposed adaptive fault-tolerant control framework.

Lateral string stabilization of connected vehicles with time-varying longitude velocity based on gain-scheduling approach

This paper deals with the controller design for lateral string stabilization and vehicle following in connected vehicles with time-varying longitude velocity. The platoon of the vehicles is modeled based on LPV systems by considering the longitude velocity as scheduling parameter. To derive results less conservative than existing methods, polynomial functions are suggested to approximate various nonlinear functions of the scheduling parameter in the lateral dynamics. Approximation errors are considered as bounded uncertain parameters. Moreover, H∞ gain-scheduling dynamic output controller is designed by defining appropriate weighting functions and considering uncertain parameters in order to suppress the disturbances along the platoon. Towards this, new change of variables is proposed to derive sufficient conditions that guarantee H∞ performance in the form of parameter-dependent Linear Matrix Inequalities (LMIs). Since the measurements are available in sampling times and are transmitted through network with delay or packet dropouts, new method is proposed to determine the maximum sampling interval that guarantee the stability of the closed-loop LPV system. This method is derived based on modeling sampling process by delay operator with bounded L2 gain. The performance of the proposed gain-scheduling controller is investigated by numerical simulations. By considering real situations in which velocity in the longitude direction is variable in time, the prosperity of the proposed controller for tracking the proceeding vehicle in the platoon and attenuating of disturbances is validated.

Output feedback tracking control for polynomial nonlinear systems with measurement noises and mismatched disturbances

In this paper, the output feedback tracking control problem is investigated for polynomial nonlinear systems (PNSs) with measurement noises and mismatched disturbances. First, in order to suppress measurement noises, a polynomial observer is introduced to simultaneously estimate states and mismatched disturbances. Next, based on the idea of backstepping control, a novel output feedback controller is designed for PNSs to compensate mismatched disturbances. Command filters are employed to avoid the repeated derivatives of virtual control and measurement noises in the recursive controller design. Then, a sufficient condition in terms of the parameter-dependent linear matrix inequality (PDLMI) is derived to guarantee the boundedness of tracking errors and estimation errors. By utilizing the sum of squares (SOS) decomposition technique, the PDLMI is solved to obtain desired controller parameters. Finally, an example of dynamic point-the-bit rotary steerable drilling tool system is performed to demonstrate the effectiveness and feasibility of the proposed strategy.

Adaptive control and parameter-dependent anti-windup compensation for inertia-varying quadcopters*

A novel parameter-dependent anti-windup compensator is developed to improve the performance of a constrained model reference adaptive controller. The combined control structure solves the input saturation and stability problem for inertia-varying quadcopters. The control synthesis follows the conventional two-step anti-windup design paradigm where a nominal controller is designed without consideration of input saturation while the anti-windup compensator is designed to minimise deviations from nominal performance caused by saturated inputs. To account for the varying inertia of the quadcopter during package retrieval/delivery routines, inertia parameters of the vehicle/package are estimated with an online recursive identification technique. These estimates are used by the model reference adaptive controller and to schedule the parameter-dependent anti-windup compensator. Anti-windup performance and stability conditions are formulated as a set of parameter-dependent linear matrix inequalities, which when solved, yield a gain-scheduled anti-windup compensator that ensures stability and minimises deviation from nominal performance when saturation occurs. The effectiveness of the combined control scheme is demonstrated by simulations of an input-constrained quadcopter lifting a payload of unknown mass.

Estimation of Toolface for Dynamic Point-the-bit Rotary Steerable Systems via Nonlinear Polynomial Filtering

In this article, the estimation problem of Toolface is investigated for the dynamic point-the-bit rotary steerable system (DPRSS), and it is essentially a nonlinear filtering problem under strong interference. First, the DPRSS is modeled by a continuous-time nonlinear system, which involves polynomial nonlinearities and strong interference whose amplitude is much larger than that of system states. By employing the Carleman approximation approach, a linear parameter varying system is derived from the polynomial nonlinear system, and a novel polynomial filter is constructed. Subsequently, several sufficient conditions in terms of parameter-dependent linear matrix inequalities (PDLMIs) are obtained to ensure the input-to-state stability of the filtering error system. Furthermore, the filter parameter can be calculated by solving PDLMIs through the sum of squares decomposition method. Finally, an experimental study on the DPRSS prototype is provided to show the effectiveness and applicability of the developed filtering scheme.

Formula omitted] state-feedback control for discrete-time cyber-physical uncertain systems under DoS attacks

This paper investigates the packet-based state-feedback control problem for uncertain discrete-time cyber-physical systems. The presence of Denial of Service (DoS) attacks is considered, and the dynamics of the closed-loop system under attacks is modeled as a switched uncertain system. The H2 performance criteria is employed to assess the robustness of the system. Moreover, three strategies are considered in the control design: i) the use of a full packet of controllers, ii) the zero-input strategy, which sets the control to zero in the presence of an attacker, and iii) the hold strategy, that keeps the same control input during the DoS attack. The conditions are formulated as parameter-dependent linear matrix inequalities, and the Lyapunov theory was employed to derive the conditions. Numerical experiments are employed to illustrate the efficacy of the method when considering the H2 performance criteria.

Robust gain-scheduled output feedback H2 controller synthesis with reduced conservativeness: An application to EMS system

This article investigates the design problem of gain-scheduled output feedback (GSOF) [Formula: see text] controller exploiting uncertain scheduling parameters for continuous-time linear parameter-varying (LPV) systems. The problem of coexistence of absolute and proportional uncertainties on the scheduling parameters is considered to address more practical situations. This challenging issue has been tackled by introducing a novel admissible region for the actual and measured scheduling parameters. Furthermore, all the system matrices of the LPV system are assumed to be polynomially dependent on the scheduling parameters with arbitrary degrees. Both Lyapunov and auxiliary matrices are considered to be parameter-dependent. The merit of the proposed method lies in its less conservativeness in comparison with the available approaches. The design method is presented in terms of solutions to a set of parameter-dependent linear matrix inequalities (LMIs) including parameter searches for two scalar values. The application of the provided method on an electromagnetic suspension (EMS) system is considered to demonstrate the applicability and benefits of the proposed approach for practical systems.

Robust Static Output-Feedback Control for MJLS with Non-Homogeneous Markov Chains: A Comparative Study Considering a Wireless Sensor Network with Time-Varying PER.

This paper deals with the problem of control through a semi-reliable communication channel, such as wireless sensor networks (WSN). Particularly, the case investigated is the one where the packet loss rate of the network is time-varying due to, for instance, variation in the distance between the nodes. Considering this practical motivation, the control system is modeled using a formulation based on discrete-time Markov jump linear systems (MJLS) with non-homogeneous Markov chains (time-varying transition probabilities). New control design conditions based on parameter-dependent linear matrix inequalities are proposed in order to solve this problem. The purpose is to demonstrate that this strategy is suitable to handle the networked control problem by comparing the temporal behavior of the closed-loop system with the Markovian controller and a standard proportional-integral-derivative (PID) controller. The case study presented in the paper considers the problem of the remote control of a Vertical Take-Off and Landing (VTOL) vehicle through a wireless communication channel. The network packet loss model employed in the case study is based on data collected on a wireless network workbench, which was previously developed and validated by the authors.

Event-based asynchronous and resilient filtering for singular Markov jump LPV systems against deception attacks

This article addresses the issue of dissipative asynchronous and resilient filter design for singular Markov jump linear parameter-varying (SMJLPV) systems against deception attacks under the dynamic event-triggered transmission protocol. Firstly, an improved dynamic event-triggered transmission protocol is provided to further relieve the channel congestion caused by the bandwidth limited communication network. Then, the deception attack, which can potentially destroy the integrity of the system, is modelled as a random variable satisfying Bernoulli distribution. Since the filter cannot identify the original system mode accurately, the hidden-Markov-model (HMM) is established to describe the phenomenon that two modes are out of synchronization. By augmenting the states of the original system and the filter, the filtering error systems are converted into SMJLPV systems with partially known transition rates (TRs). Based on the parameter-dependent linear matrix inequalities (PDLMIs), a cooperative design technique for the asynchronous filter and the weighting matrix of the dynamic event-triggered transmission protocol is proposed. Lastly, a numerical instance and a resistance-inductance-capacitance (RLC) switch circuit system are employed to verify the effectiveness of the theoretical results.

Spatially Local Piecewise Fuzzy Control for Nonlinear Delayed DPSs With Random Packet Losses

This article introduces a spatially local piecewise fuzzy control (SLPFC) for nonlinear delayed distributed parameter systems (DPSs) with random packet losses. Due to the limited bandwidth of the channels, the random packet losses could occur simultaneously in the communication channels from the sensor to the controller and from the controller to the actuator, which are assumed to obey the Bernoulli random binary distribution. An SLPFC design is given such that, for all possible random packet losses, the closed-loop delayed DPS is mean square exponentially stable. Delay-dependent conditions are obtained and then two procedures are given for designing the spatially local piecewise fuzzy controller: one casts the controller design into an iterative linear matrix inequality (LMI) algorithm and the other casts the controller design into a parameter-dependent LMI problem. Two examples are provided to illustrate the usefulness of the presented design approach.

Static output-feedback control for Cyber-physical LPV systems under DoS attacks

This paper is concerned with the static output-feedback secure control problem for Cyber-physical linear parameter varying systems under Denial of Service (DoS) attacks. A scenario where the number of consecutive DoS attacks is bounded is considered. A packet-based output control method for the design of gain-scheduling output-feedback controllers that diminish the influence of malicious attack on the system behavior is presented. Moreover, the technique may also be adapted to design a fixed robust or gain-scheduled controller. The system dynamic during the attack is modeled as a switching linear parameter varying system. The proposed conditions are written in the form of parameter-dependent Linear Matrix Inequalities and no structural constraints on the systems matrices are imposed. Differently from existing approaches, a lifted condition that considers the free of attack dynamics in the construction of the Lyapunov function is introduced. Numerical experiments illustrate the potential of the proposed approach and its ability to guarantee the stability of the closed-loop system under DoS attacks.

Robust Model Predictive Control for Takagi-Sugeno Model With Bounded Disturbances—Pólya Approach

This paper proposes a general robust model predictive control (MPC) approach for the constrained Takagi-Sugeno (T-S) fuzzy model with additive bounded disturbances. We adopt the homogeneous polynomially parameter-dependent (HPP) Lyapunov matrix with the arbitrary complexity degree and the corresponding HPP control law for the controller design. By applying the Polya’s theorem and the extended nonquadratic boundedness property, a systematic approach to construct a set of sufficient conditions for assessing robust stability described by parameter-dependent linear matrix inequalities (LMIs) is established. The proposed approach is an improvement over existing approaches in terms of control performance and stabilizable model range. Numerical examples are provided to show the effectiveness of the proposed robust MPC approach.

Dynamic event-based dissipative asynchronous control for T–S fuzzy singular Markov jump LPV systems against deception attacks

In this article, the issue of dissipative asynchronous control for continuous-time T–S fuzzy singular Markov jump linear parameter-varying systems against dual deception attacks under the dynamic event-triggered transmission protocol (DETP) is investigated. Firstly, the DETP is offered to further abate the channel congestion caused by the limited bandwidth. Meanwhile, the mutually independent random variables subject to Bernoulli distribution are utilized to model the dual deception attacks, which can destroy the integrity of the considered system to some degree. Besides, since the controller can not accurately receive the system information, a hidden Markov model is established to depict the asynchronous phenomenon. Specifically, in the light of the parameter-dependent Lyapunov functional, the stochastic admissible criterion of the closed-loop system with certain dissipative performance and uncertain transition rates is obtained. Ulteriorly, based on the parameter-dependent linear matrix inequalities, a cooperative design technique of asynchronous controller and the weighting matrix of the DETP is proposed. Finally, two examples of chaotic systems and electric truck-trailer systems under the DETP are given to illustrate the feasibility of the proposed method.

H model reduction design in finite frequency ranges for discrete-time Takagi-Sugeno fuzzy systems

This paper addresses the problem of H∞ model reduction design in finite frequency ranges for discrete-time nonlinear systems. With the aid of the generalised Kalman-Yakubovich-Popov (gKYP) lemma, the Lyapunov theory, and some matrix inequality techniques, sufficient conditions for the finite frequency model reduction problem are derived. The design conditions are given in terms of sufficient parameter-dependent linear matrix inequalities that can be solved through relaxations based on semi-definite programming. The advantages of the proposed approach are illustrated through numerical examples and comparisons with other available techniques.

H<SUB align="right">∞ model reduction design in finite frequency ranges for discrete-time Takagi-Sugeno fuzzy systems

This paper addresses the problem of H∞ model reduction design in finite frequency ranges for discrete-time nonlinear systems. With the aid of the generalised Kalman-Yakubovich-Popov (gKYP) lemma, the Lyapunov theory, and some matrix inequality techniques, sufficient conditions for the finite frequency model reduction problem are derived. The design conditions are given in terms of sufficient parameter-dependent linear matrix inequalities that can be solved through relaxations based on semi-definite programming. The advantages of the proposed approach are illustrated through numerical examples and comparisons with other available techniques.

Iterative LMI approach to robust static output feedback control of uncertain polynomial systems with bounded actuators

This paper presents a novel static output feedback stabilization of polynomial systems with bounded actuators. We propose a new sufficient condition for static output feedback design for nominal polynomial systems with constraints on input magnitudes. In the proposed stabilization condition, the system matrices and the Lyapunov matrices are separated, and hence parameterization of the controller is independent of the Lyapunov matrices. The main result is the novel parameter-dependent Lyapunov functions that are readily applied to robust static output feedback design of polynomial systems subject to parametric uncertainty. The proposed design conditions are bilinear in the decision variables. Hence, we provide iterative algorithms to solve the design problems. At each iteration, the design condition is cast as parameter-dependent linear matrix inequalities using the sum-of-squares technique and can be efficiently solved. The proposed approach leads to enhanced static output feedback design with computationally tractable formulation. Effectiveness of the proposed approach is demonstrated by numerical examples.

Synchronization of Cohen-Grossberg fuzzy cellular neural networks with time-varying delays

Abstract In this paper, a class of Cohen-Grossberg fuzzy cellular neural networks (CGFCNNs) with time-varying delays are considered. Initially, the sufficient conditions are proposed to ascertain the existence and uniqueness of the solutions for the considered dynamical system via homeomorphism mapping principle. Then synchronization of the considered delayed neural networks is analyzed by utilizing the drive-response (master-slave) concept, in terms of a linear matrix inequality (LMI), the Lyapunov-Krasovskii (LK) functional, and also using some free weighting matrices. Next, this result is extended so as to establish the robust synchronization of a class of delayed CGFCNNs with polytopic uncertainty. Sufficient conditions are proposed to ascertain that the considered delayed networks are robustly synchronized by using a parameter-dependent LK functional and LMI technique. The restriction on the bounds of derivative of the time delays to be less than one is relaxed. In particular, the concept of fuzzy theory is greatly extended to study the synchronization with polytopic uncertainty which differs from previous efforts in the literature. Finally, numerical examples and simulations are provided to illustrate the effectiveness of the obtained theoretical results.

Dynamic Event-Triggered State Estimation for Continuous-Time Polynomial Nonlinear Systems With External Disturbances

This article is concerned with the problem of state estimation for continuous-time polynomial nonlinear (CTPN) systems with unknown but bounded disturbances. The Taylor polynomial expansion technique is employed to realize the conversion from polynomial nonlinear systems to linear-parameter-varying systems related to the estimate. Moreover, for the purpose of saving the communication resources, an event-triggered sampling scheme is first introduced in the state estimation for CTPN systems, where the event-triggered condition is changed dynamically and the Zeno behavior is excluded. Based on the matrix inequality approach, a sufficient condition is derived in terms of the parameter-dependent linear matrix inequality (LMI) such that the estimation error system is input-to-state stable. Then, the desired estimator parameters can be obtained by solving the parameter-dependent LMI via the sum of squares decomposition technique. Finally, two examples with one concerning the permanent magnet synchronous motor systems are provided to demonstrate the usefulness of proposed method.

State-Feedback Control for Cyber-Physical LPV Systems Under DoS Attacks

This letter addresses the state-feedback control problem for Cyber-physical Linear Parameter Varying systems. Both the feedback state and the time-varying parameter are affected by denial of service (DoS) attacks. The main goal is to design gain-scheduled state-feedback controllers that can mitigate the interference of this type of attack in the system. The system under attack is modeled as a switched linear parameter-varying system, and new conditions in the form of parameter-dependent Linear Matrix Inequalities are presented to provide stabilizing controllers with exponential decay rate. Moreover, lifted conditions based on the use of post-attack dynamics, that may improve the performance of the obtained controllers are presented. Numerical experiments illustrate the effectiveness of the proposed method.

Stability analysis and robust performance of periodic discrete-time uncertain systems via structured Lyapunov functions

This paper is concerned with stability and H2 analysis of periodic discrete-time uncertain systems. New conditions based on structured Lyapunov functions are provided in the form of parameter-dependent Linear Matrix Inequalities (LMIs). The Lyapunov functions make use of the periodic dynamic of the system to provide less conservative results in terms of scalar decision variables, LMI rows and H2 guaranteed cost. The proposed techniques are necessary and sufficient conditions to certify the stability of periodic discrete-time uncertain systems. Numerical experiments illustrate the improvement granted by the methods proposed in this paper over existing techniques.