Parameter-dependent Lyapunov Function Method Research Articles

Fault Detection of Discrete-time LPV System Based on Event Triggering Mechanism

For discrete-time linear parameter varying systems with distributed time delays, the problem of fault detection under event triggering mechanism is studied. Based on the parameter dependent Lyapunov function method, the sufficient conditions for the system to be asymptotically stable and meet the H∞ performance criterion are given. The parameter matrix of fault detection filter is obtained by solving LMI technology. In addition, the event triggering strategy is introduced to save network resources.

Robust H∞ control for nonlinear course system of unmanned surface vessel with polytopic uncertainty based on sum of squares

In this paper, the nonlinear robust [Formula: see text] control is investigated for nonlinear course control systems of unmanned surface vessel (USV) with uncertain parameters and external disturbance. Firstly, we suppose that the part or all of the system parameters are unknown but within some ranges, due to the effect of different conditions such as the loading of ship. Then, the course system is modeled as a polynomial one with time invariant polytopic uncertainty. With the aid of parameter dependent Lyapunov function method and positive polynomial theory, the sufficient conditions are given for stability and stabilization with [Formula: see text] performance. These conditions are formulated in terms of parameter-dependent nonlinear matrix inequalities which can be verified by semidefinite programming relaxations based on the sum of squares technique. Finally, simulation results show the effectiveness of the approach.

Guaranteed cost nonlinear sampled-data control: applications to a class of chaotic systems

This paper addresses the guaranteed cost sampled-data controller synthesis and analysis problems with application to nonlinear chaotic systems. A linear parameter-varying (LPV) model is utilized to represent the nonlinear behaviour of the chaotic system while the gap between the measured and real parameters of the controller and plant are considered as bounded uncertainties. Using the LPV model coupled with the uncertainties, a modified parameter-dependent Lyapunov functional method is utilized and a sampled-data controller is developed that locally asymptotically stabilizes the nonlinear system with guaranteed predefined cost function upper bound. Moreover, employing the cost function upper bound minimization, a suboptimal sampled-data LPV controller is proposed. The central contribution of this work is to present a novel LMI-based formulation with the less conservative results, and thereby, an LMI-based LPV suboptimal sampled-data controller synthesis procedure is developed for nonlinear chaotic systems. The proposed procedure is readily solved by the aid of available off-the-shelf convex optimization techniques. Finally, the proposed sampled-data LPV controller is applied to the well-known chaotic Lorenz and Rossler systems, and the results verify the effectiveness and less conservativeness of the proposed method compared to some state-of-the-art techniques.

H<SUB align="right">∞ filtering for a class of networked control systems with redundant channels subject to randomly occurred packet dropouts and cyber attacks

This paper is concerned with the design of H∞ filter for the networked control systems subject to cyber attacks which occur randomly in the process of data transmission. Moreover, the unavoidable packet dropout with uncertain expectation is considered in order to get closer to the engineering practice. By increasing the received data, the redundant channel is equipped to enhance the system performance. A full-order filter is designed by means of the parameter-dependent Lyapunov function method such that the corresponding filtering error dynamics is stochastically stable in the mean square with a prescribed H∞ disturbance attenuation level. The desired filter parameters are derived via linear matrix inequality technique. Finally, the illustrative example of vehicle suspension system is presented to show the effectiveness of the proposed algorithm.

Robust Guaranteed-Cost Preview Repetitive Control for Polytopic Uncertain Discrete-Time Systems

In this paper, a robust guaranteed-cost preview repetitive controller is proposed for a class of polytopic uncertain discrete-time systems. In order to improve the tracking performance, a repetitive controller, combined with preview compensator, is inserted in the forward channel. By using the L-order forward difference operator, an augmented dynamic system is constructed. Then, the guaranteed-cost preview repetitive control problem is transformed into a guaranteed-cost control problem for the augmented dynamic system. For a given performance index, the sufficient condition of asymptotic stability for the closed-loop system is derived by using a parameter-dependent Lyapunov function method and linear matrix inequality (LMI) techniques. Incorporating the controller obtained into the original system, the guaranteed-cost preview repetitive controller is derived. A numerical example is also included, to show the effectiveness of the proposed method.

Non-fragile switched H∞ control for morphing aircraft with asynchronous switching

This paper deals with the problem of non-fragile linear parameter-varying (LPV) H∞ control for morphing aircraft with asynchronous switching. The switched LPV model of morphing aircraft is established by Jacobian linearization approach according to the nonlinear model. The data missing is taken into account in the link from sensors to controllers and the link from controllers to actuators, which satisfies Bernoulli distribution. The non-fragile switched LPV controllers are constructed with consideration of the uncertainties of controllers and asynchronous switching phenomenon. The parameter-dependent Lyapunov functional method and mode-dependent average dwell time (MDADT) method are combined to guarantee the stability and prescribed performance of the system. The sufficient conditions on the solvability of the problem are derived in the form of linear matrix inequalities (LMI). In order to achieve higher efficiency of the designing process, an algorithm is applied to divide the whole set into subsets automatically. Simulation results are provided to verify the effectiveness and superiority of the method in the paper.

Parameter‐dependent preview control with robust tracking performance

The problem of static output feedback preview tracking control is proposed for a class of polytopic uncertain discrete-time systems by combining parameter-dependent Lyapunov function method with linear matrix inequality (LMI) technique. First, the error system method of preview control theory is adopted and the difference operator is introduced, and then an augmented error system including previewed information is constructed, which transforms a tracking problem into a regulation problem. Then, a previewable reference signal is fully utilised through reformulation of the output equation for the derived augmented error system while considering the output feedback. Sufficient conditions for designing a robust static feedback preview controller are given in terms of solutions to a set of LMIs. Based on the criterion, a static output feedback controller with preview action is designed such that the output can asymptotically track the reference signal. Finally, the numerical simulation examples also illustrate the superiority of the desired preview controller for the uncertain system in the study.

Structured output-feedback controller synthesis with design specifications

ABSTRACTThis paper considers the problem of structured output-feedback controller synthesis with finite frequency specifications. Based on the orthogonal space information of input matrix, an improved parameter-dependent Lyapunov function method is first proposed. Then, a two-stage construction method is designed, which depends on an initial centralised controller. Corresponding design conditions for three types of output-feedback controllers are presented in terms of unified representations. Moreover, heuristic algorithms are provided to explore the desirable controllers. Finally, the effectiveness of these proposed methods is illustrated via some practical examples.

A new decentralised controller design method for a class of strongly interconnected systems

ABSTRACTIn this paper, two interconnected structures are first discussed, under which some closed-loop subsystems must be unstable to make the whole interconnected system stable, which can be viewed as a kind of strongly interconnected systems. Then, comparisons with small gain theorem are discussed and large gain interconnected characteristics are shown. A new approach for the design of decentralised controllers is presented by determining the Lyapunov function structure previously, which allows the existence of unstable subsystems. By fully utilising the orthogonal space information of input matrix, some new understandings are presented for the construction of Lyapunov matrix. This new method can deal with decentralised state feedback, static output feedback and dynamic output feedback controllers in a unified framework. Furthermore, in order to reduce the design conservativeness and deal with robustness, a new robust decentralised controller design method is given by combining with the parameter-dependent Lyapunov function method. Some basic rules are provided for the choice of initial variables in Lyapunov matrix or new introduced slack matrices. As byproducts, some linear matrix inequality based sufficient conditions are established for centralised static output feedback stabilisation. Effects of unstable subsystems in nonlinear Lur'e systems are further discussed. The corresponding decentralised controller design method is presented for absolute stability. The examples illustrate that the new method is significantly effective.

Asynchronous H∞ control for unmanned aerial vehicles: switched polytopic system approach

This study is concerned with the H∞ control for the full-envelope unmanned aerial vehicles (UAVs) in the presence of missing measurements and external disturbances. With the dramatic parameter variations in large flight envelope and the locally overlapped switching laws in flight, the system dynamics is modeled as a locally overlapped switched polytopic system to reduce designing conservatism and solving complexity. Then, considering updating lags of controller's switching signals and the weighted coefficients of the polytopic subsystems induced by missing measurements, an asynchronous H∞ control method is proposed such that the system is stable and a desired disturbance attenuation level is satisfied. Furthermore, the sufficient existing conditions of the desired switched parameter-dependent H∞ controller are derived in the form of linear matrix inequality (LMIs) by combining the switched parameter-dependent Lyapunov function method and average dwell time method. Finally, a numerical example based on a highly maneuverable technology (HiMAT) vehicle is given to verify the validity of the proposed method.

Robust Fault-Tolerant Tracking Control for Nonlinear Networked Control System: Asynchronous Switched Polytopic Approach

This paper is concerned with the robust fault-tolerant tracking control problem for networked control system (NCS). Firstly, considering the locally overlapped switching law widely existed in engineering applications, the NCS is modeled as a locally overlapped switched polytopic system to reduce designing conservatism and solving complexity. Then, switched parameter dependent fault-tolerant tracking controllers are constructed to deal with the asynchronous switching phenomenon caused by the updating delays of the switching signals and weighted coefficients. Additionally, the global uniform asymptotic stability in the mean (GUAS-M) and desired weightedl2performance are guaranteed by combining the switched parameter dependent Lyapunov functional method with the average dwell time (ADT) method, and the feasible conditions for the fault-tolerant tracking controllers are obtained in the form of linear matrix inequalities (LMIs). Finally, the performance of the proposed approach is verified on a highly maneuverable technology (HiMAT) vehicle’s tracking control problem. Simulation results show the effectiveness of the proposed method.

Distributed H∞ filtering for a class of sensor networks with uncertain rates of packet losses

In this paper, the distributed H∞ filtering problem is discussed for a class of sensor networks with uncertain rates of packet losses. The packet losses occur randomly in measurements from local sensor and in transmission from the neighbor sensors are mutually independent but obey Bernoulli distribution. Different from the most results on packet losses, the rates of packet losses are assumed to be uncertain and norm-bounded. We aim to design a linear full-order filter such that the estimation error converges to zero asymptotically in the mean square while the disturbance rejection attenuation is constrained to a given level by means of the H∞ performance index. By using the parameter-dependent Lyapunov function method, the sufficient conditions are obtained for ensuring the stochastic stability as well as prescribed H∞ performance for the overall filtering error dynamics. These conditions are characterized in terms of the feasibility of a set of linear matrix inequalities (LMIs), and then the explicit expression is given for the desired filter parameters. Finally, one simulation example is employed to demonstrate the effectiveness of the proposed filter design technique in this paper.

Leader-Following Consensus of Linear Multiagent Systems with State Observer under Switching Topologies

The leader-following consensus problem of higher order multiagent systems is considered. The dynamics of each agent are given in general form of linear system, and the communication topology among the agents is assumed to be directed and switching. To track the leader, two kinds of distributed observer-based consensus protocols are proposed for each following agent, whose distributed observers are used to estimate the leader’s state and tracking error based on the relative outputs of the neighboring agents, respectively. Some sufficient consensus conditions are established by using parameter-dependent Lyapunov function method under a class of directed interaction topologies. As special cases, the consensus conditions for balanced and undirected interconnection topology cases can be obtained directly. The protocol design technique is based on algebraic graph theory, Riccati equation, and Sylvester equation. Finally, a simulation example is given to illustrate our obtained result.

Output chattering attenuation between two tracking controllers

In this paper, an output chattering attenuation scheme is proposed for two tracking controllers. The controllers have integral actions and are used to eliminate the steady-state tracking errors. By designing a compensator and reducing the discontinuous switching, the output chattering at the switching points can be attenuated significantly. Moreover, combining with the generalized Kalman-Yakubovich-Popov (KYP) lemma and the parameter-dependent Lyapunov function method, this problem can be characterized in terms of linear matrix inequality (LMI) formulation. Finally, the simulation results demonstrate the effectiveness of the proposed method.

ℋ ∞ model reduction for linear parameter-varying systems with distributed delay

This paper is concerned with the ℋ∞ model reduction for linear parameter-varying (LPV) systems with both discrete and distributed delays. For a given stable system, our attention is focused on the construction of reduced-order models, which approximate the original system well in an ℋ∞ norm sense. First, a sufficient condition is proposed for the asymptotic stability with an ℋ∞ performance of the error system by using the parameter-dependent Lyapunov functional method. Then, the decoupling technique is applied, such that there does not exist any product term between the Lyapunov matrices and the system matrices in the parametrised linear matrix inequality (PLMI) constraints; thus a new sufficient condition is obtained. Based on the new condition, two different approaches are developed to solve the model reduction problem. One is the convex linearisation approach and the other is the projection approach. Finally, a numerical example is provided to demonstrate the effectiveness of the proposed design method.

Analyzing and controlling the network synchronization regions

In this paper, the commonly concerned issue of synchronization regions of complex dynamical networks is investigated, for the case when the synchronous state is an equilibrium point. Some simple sufficient conditions for a network to have or have no unbounded synchronization regions of the form ( - ∞ , α 1 ) are established, where α 1 is a constant. In addition, a sufficient condition for the existence of a bounded synchronization region of the form ( α 2 , α 3 ) is derived, where α 2 and α 3 are constants, by using the parameter-dependent Lyapunov function method. Furthermore, some effective controller design methods are presented that can change the synchronization regions, thereby managing the synchronizability of the network. Finally, some numerical examples are given to show that a dynamical network may have disconnected synchronization regions, particularly it may have the coexistence of unbounded and bounded synchronization regions in the form of ( - ∞ , α 1 ) ∪ ( α 2 , α 3 ) .

Parameter-Dependent Lyapunov Function Method for a Class of Uncertain Nonlinear Systems with Multiple Equilibria

First, a new linear matrix inequality (LMI) characterization of extended strict positive realness is presented for linear continuous-time systems. Then a class of nonlinear systems with multiple equilibria subject to polytopic uncertainty is addressed by the parameter-dependent Lyapunov function method. New sufficient conditions for global convergence are presented. This allows the Lyapunov function to be parameter dependent. Furthermore, an LMI-based controller design method is also given, and reduced-order controllers can be designed by performing a structural constraint on the introduced slack variables. Several numerical examples are included to demonstrate the applicability of the proposed method.

Special decentralized control problems in discrete-time interconnected systems composed of two subsystems

In this paper, some special decentralized control problems are addressed for discrete-time interconnected systems. First it is pointed out that some subsystems must be unstable to ensure stability of the overall system in some special cases. Then a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. In addition, a decentralized controller design method based on linear matrix inequality is also given by using parameter-dependent Lyapunov function method developed for the study of robust stability. A special linear star coupled dynamical network is also considered. The central subsystem must be unstable to stabilize the whole network under a special coupling. Several examples are given to illustrate the results.

A quasi-LMI approach to computing stabilizing parameter ranges of multi-loop PID controllers

This paper addresses the problem of determining the parameter ranges of multi-loop PID (proportional-integral-derivative) controllers which stabilize a given process. An effective computational scheme is established by converting the considered problem to a quasi-LMI problem connected with robust stability test. The descriptor model approach is employed together with linearly parameter-dependent Lyapunov function method. Examples are given for illustration. The results are believed to facilitate real time tuning of multi-loop PID controllers for practical applications.

SOME SPECIAL DECENTRALIZED CONTROL PROBLEMS IN CONTINUOUS-TIME INTERCONNECTED SYSTEMS

In this paper, some decentralized control problems composed of two subsystems are addressed from a special perspective. First, it is pointed out that some subsystems must be unstable to stabilize the overall interconnected system in some special cases. Then, a special kind of decentralized control problem is studied. This kind of problem can be viewed as harmonic control among independent subsystems. Research results show that two unstable systems can generate a stable system through some effective cooperations. And a linear matrix inequality method is provided for decentralized controller design by using the parameter-dependent Lyapunov function method. Two examples are given to illustrate the results.