Nonlinear H_∞ filtering for interconnected Markovian jump systems

1.INTRODUCTIONState esti mation or observer design has been an i m-portant research topic and has been widely used incontrol and signal processing in the last fewdecades[1~3].One of the esti mation approaches isKal man filtering,which is based on the assumptionthat the system model under considerationis availableandits disturbances are Gaussian noises with knownstatistics.However,the noise sources may not be ex-actly known and uncertainties may appear.There-fore,an alternative esti matio…     

Neural network-based H∞ filtering for nonlinear systems with time-delays

A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed.Firstly,neural networks are employed to approximate the nonlinearities.Next,the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion (LDI).Finally,based on the LDI model,a neural network-based nonlinear filter (NNBNF) is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality (LMI) constraints.Compared with the existing nonlinear filters,NNBNF is time-invariant and numerically tractable.The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.     

Robust H_∞ reliable control for uncertain singular systems with state delay

1 .INTRODUCTIONSingular systems have comprehensive practical back-ground,a great deal of results based on the theory ofregular systems have beenextendedtothe area of sin-gular systems[1 ,2]. However , in practical applica-tions ,since faults of control components often occur ,ani mportant reliability requirement for the design ofreliable systems is to guarantee the stability and basicperformance of the plant by a single controller whichcan tolerate sensor and actuator faults . Such the so-…     

Delay-dependent decentralized H∞ filtering for uncertain interconnected systems

This article considers delay dependent decentralized H∞ filtering for a class of uncertain intercon nected systems,where the uncertainties are assumed to be time varying and satisfy the norm-bounded conditions.First,combining the Lyapunov-Krasovskii functional approach and the delay integral inequality of matrices,a sufficient condition of the existence of the robust decentralized H∞ filter is derived,which makes the error systems asymptotically stable and satisfies the H∞ norm of the transfer function from noise input to error output less than the specified up-bound on the basis of the form of uncertainties.Then,the above sufficient condition is transformed to a system of easily solvable LMIs via a series of equivalent transformation.Finally,the numerical simulation shows the efficiency of the main results.     

H_∞ control for stochastic systems with time-delay

1.INTRODUCTION Physicalplantsareunavoidabletobeaffectedbydis turbance,time delayanduncertainty,whichmay makesomeunwantedinfluenceonthesystem’sper formanceandevenresultininstability.Howtoavoid andcounteractsuchdisadvantagesthroughfeedback designhasbeenaresearchtopicunderintensiveinves tigationrecently[1～7].Inpractice,twokindsofdisturbancesareoften encountered:stochastic(orrandom)disturbanceand deterministicdisturbance.Forthestochasticdistur bance,systemsunderconsiderationaremodeledand st…     

New algorithm for robust H_2/H_∞ filtering with error variance assignment

1 .INTRODUCTIONThedevelopmentofefficientlinearestimationalgo rithmshasbeenbasedinthepastmainlyonthemini mizationoftheL2 normofthecorrespondingestima tionerror .Thistypeofestimationassumesthatthemessagegeneratingprocesshasaknownstatisticalproperty .Unfort…     

Robust H_∞ control for uncertain descriptor systems with state and control delay

1 .INTRODUCTIONTi me delayis commonly encounteredin various en-gineering systems ,which often occursinthe trans-mission of information or material between differ-ent parts of a systemand is frequently a source ofinstability and poor performance[1]. Transporta-tion systems , communications systems , chemicalprocess , power systems are typical examples ofti me-delay systems . In the recent years , muchwork has been devoted to the analysis and synthe-sis of controller for state-delayed system…     

Krein space approach to robust H∞ filtering for linear uncertain systems

A novel Krein space approach to robust H ∞ filtering for linear uncertain systems is developed. The parameter uncertainty, entering into both states and measurement equations, satisfies an energy-type constraint. Then a Krein space approach is used to tackle the robust H ∞ filtering problem. To this end, a new Krein space formal system is designed according to the original sum quadratic constraint (SQC) without introducing any nonzero factors into it and, consequently, the estimate recursion is obtained through the filter gain in Krein space. Finally, a numerical example is given to demonstrate the effectiveness of the proposed approach.     

Neural network-based H∞ filtering for nonlinear systems with time-delays

A novel H∞ design methodology for a neural network-based nonlinear filtering scheme is addressed. Firstly, neural networks are employed to approximate the nonlinearities. Next, the nonlinear dynamic system is represented by the mode-dependent linear difference inclusion （LDI）. Finally, based on the LDI model, a neural network-based nonlinear filter （NNBNF） is developed to minimize the upper bound of H∞ gain index of the estimation error under some linear matrix inequality （LMI） constraints. Compared with the existing nonlinear filters, NNBNF is time-invariant and numerically tractable. The validity and applicability of the proposed approach are successfully demonstrated in an illustrative example.     

Robust H∞ control for neutral stochastic uncertain systems with time-varying delay

The problem of robust H∞ control for uncertain neutral stochastic systems with time-varying delay is discussed.The parameter uncertaintie is assumed to be time varying norm-bounded.First,the stochastic robust stabilization of the stochastic system without disturbance input is investigated by nonlinear matrix inequality method.Then,a full-order stochastic dynamic output feedback controller is designed by solving a bilinear matrix inequality(BMI),which ensures a prescribed stochastic robust H∞ performance level for the resulting closed-loop system with nonzero disturbance input and for all admissible uncertainties.An illustrative example is provided to show the feasibility of the controller and the potential of the proposed technique.     

Extended parameter-dependent H∞filtering for uncer tain continuous-time state-delayed systems

The design of robust H∞ filtering problem of polytopic uncertain linear time-delay systems is addressed. The uncertain parameters are supposed to reside in a polytope. A parameter-dependent Lyapunov function approach is proposed for the design of filters that ensure a prescribed H∞performance level for al ad-missible uncertain parameters, which is different from the quadratic framework that entails fixed matrices for the entire uncertainty do-main. This idea is realized by careful y selecting the structure of the matrices involved in the products with system matrices. An extended H∞ sufficient condition for the existence of robust esti-mators is formulated in terms of linear matrix inequalities, which can be solved via efficient interior-point algorithms.     

ROBUST H∞ FILTERING FOR UNCERTAIN DISCRETE-TIME STATE-DELAYED SYSTEMS： APARAMETER-DEPENDENT LYAPUNOV APPROACH

This paper is concerned with the problem of robust H_∞ filtering for linear discrete-time systems with multiple state delays and polytopic uncertain parameters. Attention is focused on the design of full-order, reduced-order and zeroth-order robust H_∞ filters on the basis of a recently published parameter-dependent Lyapunov stability result. Sufficient conditions for the existence of such filters are formulated in terms of linear matrix inequalities, upon which admissible filters can be obtained from convex optimization problems. The proposed methodology has been shown, via a numerical example, to be much less conservative than previous filter design methods in the quadratic framework.     

L ∞-estimates of mixed finite element methods for general nonlinear optimal control problems

This paper investigates L~∞-estimates for the general optimal control problems governed by two-dimensional nonlinear elliptic equations with pointwise control constraints using mixed finite element methods.The state and the co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is approximated by piecewise constant functions.The authors derive L~∞-estimates for the mixed finite element approximation of nonlinear optimal control problems.Finally,the numerical examples are given.     

Robust H_∞ Control with Exponent Stability for Time-Delay Uncertain Systems

1 .ＩＮＴＲＯＤＵＣＴＩＯＮＩｔｉｓｗｅｌｌ ｋｎｏｗｎｔｈａｔｔｈｅｓｔａｂｉｌｉｚａｔｉｏｎｏｆｔｈｅｓｙｓｔｅｍｓｗｉｔｈｔｉｍｅｄｅｌａｙｓｉｎｄｉｆｆｅｒｅｎｔｓｔａｔｅｓｉｓａｔｏｕｇｈｐｒｏｂｌｅｍｂｅ ｃａｕｓｅｔｈｅｔｉｍｅｄｅｌａｙｓｉｎａｓｙｓｔｅｍｍａｙｉｎｄｕｃｅａｎｉｎｓｔａｂｉｌｉｔｙｏｆｔｈｅｐｅｒｆｏｒｍａｎｃｅｓｏｆｔｈｅｃｌｏｓｅｄ ｌｏｏｐｓｃｈｅｍｅｓ.Ｔｈｅｒｅｆｏｒｅ,ｔｈｅｓｕｂｊｅｃｔｏｆｓｔａｂｉｌｉｔｙａｎｄｃｏｎｔｒｏｌｆｏｒｔｉｍｅ ｄｅｌａｙ…     

Robust H∞ output feedback controller design for uncertain discrete-time switched systems via switched Lyapunov functions

The H∞ output feedback control problem for uncertain discrete-time switched systems is reasearched. A new characterization of stability and H∞ performance for the switched system under arbitrary switching is obtained by using switched Lyapunov function.Then,based on the characterization,a linear matrix inequality (LMI)approach is developed to design a switched output feedback controller which guarantees the stability and H∞ performance of the closed-loop system.A numerical example is presented to demonstrate the application of the proposed method.