h sup spl infin control for linear time varying systems controller parameterization in this correspondence the h sup spl infin control problem is studied for finite dimensional linear time varying fdltv systems state space formulas are derived for all fdltv controllers solving the problem these controllers are parameterized by the interconnection of the central controller with an exponentially stable free system having h sup spl infin norm strictly less than spl gamma our approach is drawn from some changes of variables a time varying version of a strict bounded real lemma and youla parameterization thus the proofs given are simple and clear

principle of proportional damages in a multiple criteria lqr problem a multiple criteria linear quadratic regulator lqr problem is considered the principle of proportional damages is worked out to minimize a norm of a difference between ideal and optimal values of the vector performance criteria while the distribution of the losses damages of the performance criteria are under control a multiple criteria lqr problem solution via principle of proportional damages is obtained as a linear form of state variables and is invariant to the norm which is minimized

a solution to the continuous time rm h _ infty fixed interval smoother problem the minimum variance fixed interval smoother is a state space realization of the wiener solution generalized for time varying problems it involves forward and adjoint wiener hopf factor inverses in which the gains are obtained by solving a riccati equation this technical note introduces a continuous time h smoother having the structure of the minimum variance version in which the gains are obtained by solving a riccati equation that possesses an indefinite quadratic term it is shown that the smoother exhibits an increase in mean square error the error is bounded and the upper error bound is greater than that for the h filter

a nash game approach to mixed h sub 2 h sub spl infin control the established theory of nonzero sum games is used to solve a mixed h sub 2 h sub spl infin control problem our idea is to use the two pay off functions associated with a two player nash game to represent the h sub 2 and h sub spl infin criteria separately we treat the state feedback problem and we find necessary and sufficient conditions for the existence of a solution both the finite and infinite time problems are considered in the infinite horizon case we present a full stability analysis the resulting controller is a constant state feedback law characterized by the solution to a pair of cross coupled riccati equations which may be solved using a standard numerical integration procedure we begin our development by considering strategy sets containing linear controllers only at the end of the paper we broaden the strategy sets to include a class of nonlinear controls it turns out that this extension has no effect on the necessary and sufficient conditions for the existence of a solution or on the nature of the controllers

robust state estimation for uncertain systems with averaged integral quadratic constraints this paper considers a robust state estimation problem for a new class of uncertain systems the new uncertainty class introduced in the paper involves structured uncertainties which are required to satisfy a certain averaged integral quadratic constraint this uncertainty class combines aspects of norm bounded and stochastic uncertainty descriptions the solution to the robust state estimation problem is obtained by solving a parametrized riccati differential equation of the game type

multiobjective boldmath ht hf control design an important question in feedback control design is how to achieve desired performance for dynamical systems subject to both model uncertainties and white noise for this purpose it is desirable to develop a systematic design technique that combines the good aspects of both cal h 2 lqg and cal h infty methods which provides the motivation for the development of multiobjective design framework in this paper encouraged by a time domain game approach for cal h 2 cal h infty control design two multiobjective control design problems are formulated and solved in the time domain results for both the finite time horizon and the infinite time horizon are presented it is shown that all the results can be obtained by solving the corresponding set of coupled riccati equations

h output feedback control for linear discrete time varying systems via the bounded real lemma in this paper we develop a solution to the discrete time output feedback control problem for linear time varying ltv systems the solution is developed along the strategy set up by doyle et al in 1989 and the main ingredient in its derivation is the extension of the well known bounded real lemma to a discrete time varying context developed by van der veen and verhaegen in 1995 this approach contributes to the conceptual simplicity and hence to the accessibility of the solution apart from that we treat the infinite horizon case for ltv system of non uniform state dimension and varying input and output dimension both situations can easily occur in practice for example in multirate sampled data control systems the algorithm that can be derived from the solution presented in then applied to the output feedback of a dynamical system changing from one operation point in its operation envelope to another

recursive state estimation for uncertain systems with an integral quadratic constraint this paper considers a robust state estimation problem for a class of uncertain systems where the noise and uncertainty are modeled deterministically via an integral quadratic constraint the robust state estimation problem involves constructing the set of all possible states at the current time consistent with given output measurements and the integral quadratic constraint

global solutions to a game theoretic riccati equation of stochastic control abstract in this paper the existence of global solutions to game theoretic riccati equations associated to a controlled stochastic differential equation with state dependent white noise is investigated one proves that if a stabilizing and attenuating feed back exists then a matrix differential game theoretic riccati equation of stochastic control has a unique global bounded stabilizing positive semidefinite solution this solution is periodic if the coefficients are periodic functions and it solves an algebraic riccati equation if the coefficients are constant conversly if such a solution exists it allows an explicit construction of a stabilizing and disturbance attenuating state feedback

h sub spl infin differential riccati equations convergence properties and finite escape phenomena the paper studies the transient and asymptotic behavior of the solution of the sign indefinite differential riccati equation dre arising in finite horizon h sub spl infin filtering and control problems differently from the sign definite h sub spl infin dre the solution of the h sub spl infin dre can have finite escape times even for nonnegative initial conditions sufficient and necessary conditions for boundedness and convergence are derived in correspondence to a fixed value of the h sub spl infin norm attenuation level spl gamma finally a stepwise spl gamma switching strategy is devised to guarantee boundedness as well as asymptotic performance

optimum h designs under sampled state measurements abstract we present the complete solution to the h optimal control problem when only sampled values of the state are available for linear time varying systems the optimum controller is characterized in terms of the solution of a particular generalized riccati differential equation with the optimum performance determined by the conjugate point conditions associated with a family of generalized riccati differential equations for the infinite horizon time invariant problem however the optimum controller is characterized in terms of the solution of a particular generalized algebraic riccati equation and the performance is determined in terms of the conjugate point conditions of a single generalized riccati equation defined on the longest sampling interval if the distribution of the sampling times is also taken as part of the general design uniform sampling turns out to be optimal for the infinite horizon case while for the finite horizon problem a nonuniform sampling generally leads to a better performance

robust spl hscr sub spl infin filtering for continuous time varying uncertain systems with deterministic input signals many dynamical systems involve not only process and measurement noise signals but also parameter uncertainty and known input signals when spl lscr sub 2 or spl hscr sub spl infin filters that were designed based on a nominal model of the system are applied the presence of parameter uncertainty will not only affect the noise attenuation property of the filter but also introduce a bias proportional to the known input signal and the latter may be very appreciable we introduce a finite horizon robust spl hscr sub spl infin filtering method that provides a guaranteed spl hscr sub spl infin bound for the estimation error in the presence of both parameter uncertainty and a known input signal this method is developed by using a game theoretic approach and the results generalize those obtained for cases without parameter uncertainty or without a known input signal it is also demonstrated via an example that the proposed method provides significantly improved signal estimates

the finite horizon singular h control problem with dynamic measurement feedback this paper is concerned with the finite horizon version of the h problem with measurement feedback given a finite dimensional linear time varying system together with a positive real number we obtain necessary and sufficient conditions for the existence of a possibly time varying dynamic compensator such that the l2 0 t1 induced norm of the closed loop operator is smaller than these conditions are expressed in terms of a pair of quadratic differential inequalities generalizing the well known riccati differential equations introduced recently in the context of finite horizon h control

quantum statistics in complex networks in this work we discuss the symmetric construction of bosonic and fermionic networks and we present a case of a network showing a mixed quantum statistics this model takes into account the different nature of nodes described by a random parameter that we call energy and includes rewiring of the links the system described by the mixed statistics is an inhomogeneous system formed by two class of nodes in fact there is a threshold energy epsilon s such that nodes with lower energy epsilon epsilon s decrease their connectivity in time

application of the min max certainty equivalence principle to the sampled data output feedback h control problem abstract we apply our certainty equivalence principle to the solution of the sampled data output feedback h control problem as expected the solution bears close resemblance to a kalman filter design

robust stochastic maximum principle for multi model worst case optimization this paper develops a version of the robust maximum principle applied to the minimax mayer problem formulated for stochastic differential equations with a control dependent diffusion term the parametric families of first and second order adjoint stochastic processes are introduced to construct the corresponding hamiltonian formalism the hamiltonian function used for the construction of the robust optimal control is shown to be equal to the sum of the standard stochastic hamiltonians corresponding to each possible value of the parameter the cost function is defined on a finite horizon and contains the mathematical expectation of a terminal term a terminal condition given by a vector function is also considered the optimal control strategies adapted for available information for the wide class of multi model systems given by a stochastic differential equation with parameters from a given finite set are constructed this problem belongs to the class of minimax stochastic optimization problems the p

condensation and topological phase transitions in a dynamical network model with rewiring of the links growing network models with both heterogeneity of the nodes and topological constraints can give rise to a rich phase structure we present a simple model based on preferential attachment with rewiring of the links rewiring probabilities are modulated by the negative fitness of the nodes and by the constraint for the network to be a simple graph at low temperatures and high rewiring rates this constraint induces a bose einstein condensation of paths of length 2 i e a new phase transition with an extended condensate of links the phase space of the model includes further transitions in the size of the connected component and the degeneracy of the network

remarks on the time varying h riccati equations in this paper we establish some useful properties of three riccati equations appearing in the standard h control problems for continuous and discrete time time varying systems we then give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent riccati equations with a coupling inequality

risk sensitive control and dynamic games for partially observed discrete time nonlinear systems solves a finite horizon partially observed risk sensitive stochastic optimal control problem for discrete time nonlinear systems and obtains small noise and small risk limits the small noise limit is interpreted as a deterministic partially observed dynamic game and new insights into the optimal solution of such game problems are obtained both the risk sensitive stochastic control problem and the deterministic dynamic game problem are solved using information states dynamic programming and associated separated policies a certainty equivalence principle is also discussed the authors results have implications for the nonlinear robust stabilization problem the small risk limit is a standard partially observed risk neutral stochastic optimal control problem

existence of similarity transformation converting bmis to lmis under a mild condition we investigate the existence of a similarity transformation regarding robust hinfin stability analysis and observer controller synthesis problems the observer based controller is capable of disturbance rejection in the presence of unknown but bounded disturbance we present results which illustrate plainly the role of the similarity transformation in converting a bmi problem into an lmi problem in a unified fashion applicable to both continuous and discrete time problems with or without uncertainty finally the validity and applicability of the approach are illuminated by examples

h norm computation for ltv systems using nonlinear optimal control algorithms we discuss the computation for 2 induced norms of finite horizon linear time varying systems it is well known that 2 induced norm calculating problems can be converted into optimal control problems so with the help of optimal control algorithms we propose a numerical technique for 2 induced norm computation our approach is as follows first we present a new computational method for nonlinear optimal control problems that is numerically reliable stable and robust analysing the convergence property under some assumptions next by modifying the presented method we propose an algorithm for the 2 induced norm calculation of finite horizon linear time varying systems which is essentially different from all other existing methods finally the effectiveness of our algorithm is demonstrated by simulation

h filtering for a class of uncertain nonlinear systems abstract this paper investigates the problem of h filtering for a class of uncertain continuous time nonlinear systems with real time varying parameter uncertainty and unknown initial state we develop an infinite horizon h filtering methodology which provides both robust stability and a guaranteed h performance for the filtering error irrespective of the parameter uncertainty

h sup spl infin optimal control for singularly perturbed systems ii imperfect state measurements for pt i see ibid vol 29 no 2 p 401 423 1993 in this paper we study the h sup spl infin optimal control of singularly perturbed linear systems under general imperfect measurements for both finite and infinite horizon formulations using a differential game theoretic approach we first show that as the singular perturbation parameter say spl epsiv 0 approaches zero the optimal disturbance attenuation level for the full order system under a quadratic performance index converges to a value that is bounded above by and in some cases equal to the maximum of the optimal disturbance attenuation levels for the slow and fast subsystems under appropriate slow and fast quadratic cost functions with the bound being computable independently of e and knowing only the slow and fast dynamics of the system we then construct a controller based on the slow subsystem only and obtain conditions under which it delivers a desired performance level even though the fast dynamics are completely neglected the ultimate performance level achieved by this slow controller can be uniformly improved upon however by a composite controller that uses some feedback from the output of the fast subsystem we construct one such controller via a two step sequential procedure which uses static feedback from the fast output and dynamic feedback from an appropriate slow output each one obtained by solving appropriate spl epsiv independent lower dimensional h sup spl infin optimal control problems under some informational constraints we provide a detailed analysis of the performance achieved by this lower dimensional spl epsiv independent composite controller when applied to the full order system and illustrate the theory with some numerical results on some prototype systems

stochastic h sub 2 h sub spl infin control with state dependent noise this paper discusses the stochastic h sub 2 h sub spl infin control problem with state dependent noise by means of the stabilization exact observability and stochastic detectability of stochastic systems the infinite horizon stochastic h sub 2 h sub spl infin control design is developed for the finite horizon h sub 2 h sub spl infin control problem our results generalize the corresponding deterministic ones to the stochastic models finally the observer based suboptimal stochastic h sub 2 h sub spl infin control is discussed in which the state variables cannot be measured directly and a feasible design algorithm is proposed

linear estimation in krein spaces i theory the authors develop a self contained theory for linear estimation in krein spaces the derivation is based on simple concepts such as projections and matrix factorizations and leads to an interesting connection between krein space projection and the recursive computation of the stationary points of certain second order or quadratic forms the authors use the innovations process to obtain a general recursive linear estimation algorithm when specialized to a state space structure the algorithm yields a krein space generalization of the celebrated kalman filter with applications in several areas such as h sup spl infin filtering and control game problems risk sensitive control and adaptive filtering

optimal and robust noncausal filter formulations the paper describes an optimal minimum variance noncausal filter or fixed interval smoother the optimal solution involves a cascade of a kalman predictor and an adjoint kalman predictor a robust smoother involving h sub spl infin predictors is also described filter asymptotes are developed for output estimation and input estimation problems which yield bounds on the spectrum of the estimation error these bounds lead to a priori estimates for the scalar spl gamma in the h sub spl infin filter and smoother design the results of simulation studies are presented which demonstrate that optimal robust and extended kalman smoothers can provide performance benefits

on the structure of a two degree of freedom h loop shaping controller explicit state space formulae are presented for a two degree of freedom 2 dof controller that stabilizes an augmented plant with respect to unstructured additive coprime factor perturbations whilst simultaneously providing robust model following the 2 dof problem was known to inherit certain features of the mcfarlane glover loop shaping design method from which it is derived in this paper the precise structure of one admissible controller is derived that structure is shown to comprise a state estimator an on line step response model and an augmented state estimate feedback law the formulae derived herein are applied to a classical nonlinear stabilization problem

sampled data h optimal control of time varying systems the sampled data h optimal control problem is studied for time varying systems the problem consists of finding all sampled data controllers with a piece wise constant control signal for which the l2 induced norm from the continuous time disturbance to the continuous time output is less than a specified bound a game theoretic approach is used to obtain a complete solution to the problem in the finite horizon time varying case the solution involves a mixed discrete continuous riccati equation and a variable transformation which takes the problem to a standard discrete finite dimensional h filtering problem

an uncertainty averaging approach to optimal guaranteed cost control of uncertain systems with structured uncertainty this paper presents an optimal state feedback guaranteed cost control result for a class of uncertain linear time varying systems with structured uncertainty the cost function considered is a quadratic cost function defined over a finite time interval the solution of the optimal control problem is obtained by solving a parametrized riccati differential equation of the game type

a game theoretic approach to a finite time disturbance attenuation problem a disturbance attenuation problem over a finite time interval is considered by a game theoretic approach where the control restricted to a function of the measurement history plays against adversaries composed of the process and measurement disturbances and the initial state a zero sum game formulated as a quadratic cost criterion subject to linear time varying dynamics and measurements is solved by a calculus of variation technique by first maximizing the quadratic cost criterion with respect to the process disturbance and initial state a full information game between the control and the measurement residual subject to the estimator dynamics results the resulting solution produces an n dimensional compensator which expresses the controller as a linear combination of the measurement history a disturbance attenuation problem is solved based on the results of the game problem for time invariant systems it is shown that under certain conditions the time varying controller becomes time invariant on the infinite time interval the resulting controller satisfies an h sub infinity norm bound

robust kalman filtering for uncertain systems abstract this paper studies the problem of kalman filter design for uncertain systems the system under consideration is subjected to time varying norm bounded parameter uncertainties in both the state and measurement matrices the problem we address is the design of a state estimator such that the covariance of the estimation error is guaranteed to be within a certain bound for all admissible uncertainties a riccati equation approach is proposed to solve the above problem furthermore a suboptimal covariance upper bound can be computed by a convex optimization

product of nonnegative operators and infinite dimensional h riccati equations in this paper we collect some useful properties of the product of nonnegative operators in a hilbert space we then apply them to the standard h control problem for infinite dimensional time varying systems and give necessary and sufficient conditions for the existence of a suboptimal controller by three conditions involving two independent riccati equations with a coupling inequality

the problem of optimal robust sensor scheduling abstract this paper considers the sensor scheduling problem which consists of estimating the state of an uncertain process based on measurements obtained by switching a given set of noisy sensors the noise and uncertainty models considered in this paper are assumed to be unknown deterministic functions which satisfy an energy type constraint known as an integral quadratic constraint the problem of optimal robust sensor scheduling is formulated and solution to this problem is given in terms of the existence of suitable solutions to a riccati differential equation of the game type and a dynamic programming equation furthermore a real time implementable method for sensor scheduling is also presented

continuous time tracking problems in an h sub spl infin setting a game theory approach this paper investigates the problem of finite horizon h sub spl infin tracking for linear time varying systems three tracking problems are considered depending on whether the reference signal is perfectly known in advance measured on line or previewed in fixed interval of time ahead no a priori knowledge of a dynamic model for the reference signal is assumed a game theory approach to the latter tracking problems is presented where given a specific reference signal the controllers play against nature which can choose any initial state and any bounded energy disturbance input and measurement noise necessary and sufficient conditions for the existence of a saddle point equilibrium are determined and h sub spl infin tracking controllers for both the cases of state and output feedback are derived tracking problems for time invariant systems on infinite horizon are also analyzed and time invariant tracking controllers are obtained for zero initial conditions

h control of nonlinear time varying systems with finite time horizon the finite time horizon h control problems for nonlinear time varying systems are considered where the initial state is unknown they are solved by using both static state feedback and dynamic output feedback controllers a class of nonlinear h controllers is parameterized as nonlinear fractional transformation on contractive nonlinear parameters the solvability for nonlinear finite time horizon h control problem requires suitable solutions to some hamilton jacobi inequalities equations

a dynamic games approach to controller design disturbance rejection in discrete time it is shown that the discrete time disturbance rejection problem formulated in finite and infinite horizons and under perfect state measurements can be solved by making direct use of some results on linear quadratic zero sum dynamic games for the finite horizon problem an optimal minimax controller exists and can be expressed in terms of a generalized time varying discrete time riccati equation the existence of an optimum also holds in the infinite horizon case under an appropriate observability condition with the optimal control given in terms of a generalized algebraic riccati equation also being stabilizing in both cases the corresponding worst case disturbances turn out to be correlated random sequences with discrete distributions which means that the problem viewed as a dynamic game between the controller and the disturbance does not admit a pure strategy saddle point results for the delayed state measurement and the nonzero initial state cases are presented

state feedback h_ infty control for a class of nonlinear stochastic systems this paper discusses the h infty control problem for a class of nonlinear stochastic systems with both state and disturbance dependent noise by means of hamilton jacobi equations both infinite and finite horizon nonlinear stochastic h infty control designs are developed some results on nonlinear h infty control of deterministic systems are generalized to a stochastic setting we introduce some useful concepts such as zero state observability and zero state detectability which together with the stochastic lasalle invariance principle yield some valuable consequences in infinite horizon nonlinear stochastic h infty control

h filtering for linear periodic systems with parameter uncertainty abstract this paper focuses on h filtering for a class of linear periodic systems with a certain type of norm bounded time varying parameter uncertainty which appears in both the state and output matrices the problem addressed is the design of a linear periodic estimator that guarantees both the quadratic stability and and prescribed h performance on infinite horizon for the estimation error for all admissible parameter uncertainties a solution to this problem is obtained via a riccati equation approach

robust maximum principle for multi model lq problem this paper presents the version of the robust maximum principle in the context of multi model control formulated as the minimax bolza problem the cost function contains a terminal term as well as an integral one a fixed horizon and terminal set are considered the necessary conditions of the optimality are derived for the class of uncertain systems given by an ordinary differential equation with parameters from a given finite set this problem consists in the control design providing a good behaviour for a given class of multi model system it is shown that the design of the minimax optimal controller is reduced to a finite dimensional optimization problem given at the corresponding simplex set containing the weight parameters to be found the robust optimal control may be interpreted as a mixture with the optimal weights of the controls which are optimal for each fixed parameter value the proof is based on the recent results obtained for minimax mayer problem boltyanski and poznyak 1999a the mini

solution of the state feedback singular h control problem for linear time varying systems a procedure for the solution of the h control problem when the system is time varying and the feedthrough matrix between the control input and the controlled output is not full column rank is proposed

game theory approach to optimal linear state estimation and its relation to the minimum h sub infinity norm estimation a possible game theory approach to optimal state estimation is presented it is found that in a certain differential game the minimizer s policy is identical to the one obtained by optimal estimation in the minimum h sub infinity norm sense this interpretation of h sub infinity optimal state estimation provides better insight into the mechanism of h sub infinity optimal filtering especially in the case where the exogenous signals are not energy bounded

quadratic stabilization with an h performance bound of uncertain linear time varying systems in this paper we deal with linear time varying systems subject to uncertain parameters in the so called one block norm bounded form we consider the problem of designing a controller which guarantees the quadratic stabilization of the closed loop system while keeping the norm of the operator mapping the exogenus input to the controlled output under a prespecified level necessary and sufficient conditions for the existence of such a controller are given

a game theoretic approach to h control for time varying systems a representation formula for all controllers that satisfy an mathcal l infty type constraint is derived for time varying systems it is now known that a formula based on two indefinite algebraic riccati equations may be found for time invariant systems over an infinite time support see j c doyle et al ieee trans automat control ac 34 1989 pp 831 847 k glover and j c doyle systems control lett 11 1988 pp 167 172 k glover et al siam j control optim 29 1991 pp 283 324 m green et al siam j control optim 28 1990 pp 1350 1371 d j n limebeer et al in proc ieee conf on decision and control austin tx 1988 g tadmor math control systems signal processing 3 1990 pp 301 324 in the time varying case two indefinite riccati differential equations are required a solution to the design problem exists if these equations have a solution on the optimization interval the derivation of the representation formula illustrated in this paper mak

model validation for robust control of uncertain systems with an integral quadratic constraint this paper presents a new approach to the model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint the proposed model validation algorithm is based on the solution to a game type riccati differential equation and a set of state equations closely related to a robust kalman filtering problem

h control with output feedback for time varying discrete systems h problems with state feedback are considered for time varying discrete systems first quadratic games related to h problems are studied a necessary and sufficient condition for the existence of a stabilizing controller such that the norm of the operator from the disturbance to the output is less than a prescribed number is given in terms of a riccati equation

differential games finite time partial state stabilisation of nonlinear dynamical systems and optimal robust control abstracttwo player zero sum differential games are addressed within the framework of state feedback finite time partial state stabilisation of nonlinear dynamical systems specifically finite time partial state stability of the closed loop system is guaranteed by means of a lyapunov function which we prove to be the value of the game this lyapunov function verifies a partial differential equation that corresponds to a steady state form of the hamilton jacobi isaacs equation and hence guarantees both finite time stability with respect to part of the system state and the existence of a saddle point for the system s performance measure connections to optimal regulation for nonlinear dynamical systems with nonlinear nonquadratic cost functionals in the presence of exogenous disturbances and parameter uncertainties are also provided furthermore we develop feedback controllers for affine nonlinear systems extending an inverse optimality framework tailored to the finite time partial state stabilisation pr

a new parametrization of h suboptimal controllers elementary state space concepts are used to derive a transparent solution to the h control problem on an infinite horizon the main contribution of this solution is a novel representation of suboptimal controllers in terms of a pair of parametric riccati equations with a coupling constraint unlike the classical parametrization in terms of linear fractional transformation this state space representation has a homogeneous riccati formulation which should help to make the most of the suboptimal controller diversity potential applications include the design of reduced order controllers and more generally the selection of suboptimal controllers to meet or optimize additional constraints

h optimal terminal state control for linear systems with lumped and distributed time delays in this paper we consider a linear time varying system whose state equation is affected by time delays and subject to unknown square integrable disturbances using a differential games approach we provide a necessary and sufficient condition for the existence of an optimal control law minimizing the h norm of the operator mapping the disturbance to the weighted control and terminal state an example which illustrates the proposed technique is also provided at the end of the paper

risk sensitive estimation and a differential game a large deviation result is employed to solve the state estimation problem of a continuous time gauss markov system with an exponential cost the exponential cost is the expected value of an exponential function of the state estimation error a scalar spl theta appearing in the cost termed as the risk factor determines the penalty on the higher order moments of the error in contrast to the minimum variance estimate penalty on large deviations of the estimation error is possible

shannon and von neumann entropy of random networks with heterogeneous expected degree entropic measures of complexity are able to quantify the information encoded in complex network structures several entropic measures have been proposed in this respect here we study the relation between the shannon entropy and the von neumann entropy of networks with given expected degree sequence we find in different examples of network topologies that when the degree distribution contains some heterogeneity an intriguing correlation emerges between the two entropic quantities this results seems to suggest that heterogeneity in the expected degree distribution is implying an equivalence between a quantum and a classical description of networks which respectively corresponds to the von neumann and the shannon entropy

h sub infinity control and filtering for sampled data systems h sub infinity control and filtering problems for sampled data systems are studied necessary and sufficient conditions are obtained for the existence of controllers and filters that satisfy a specified h sub infinity performance bound when these conditions hold explicit formulas for a controller and a filter satisfying the h sub infinity performance bound are also given

game theory approach to finite time horizon optimal estimation in this game a measurement record is given and the first player looks for the best estimate of a prespecified combination of the system states in the presence of a hostile process noise signal and system initial condition that are applied by his adversary it turns out that the game possesses a saddle point solution which leads to an optimal smoothed estimate that is identical to the corresponding l sub 2 optimal estimate a similar game in which the estimate is restricted to be causal is formulated and solved this game provides for the first time a saddle point equilibrium interpretation to finite time h sub infinity optimal filtered estimation the two games are very closely related it is shown that in the first game the first player s strategy which is the optimal smoothed estimate is a linear fractional transformation of the h sub infinity optimal filter which applies a nonzero free contracting q parameter it therefore achieves a unity h sub infinity norm bound for the operator that relates the exogeneous signals to the estimation error

robust h sub spl infin output feedback control for nonlinear systems in this paper we present a new approach to the solution of the output feedback robust h sub spl infin control problem we employ the recently developed concept of information state for output feedback dynamic games and obtain necessary and sufficient conditions for the solution to the robust control problem expressed in terms of the information state the resulting controller is an information state feedback controller and is intrinsically infinite dimensional stability results are obtained using the theory of dissipative systems and our results are expressed in terms of dissipation inequalities

entropy and huhpm approach for complex networks abstract the general formulas of the network for the power exponents of the degree distribution and the entropy are presented based on an open liouville equation for the driven network the proposed harmonious unifying hybrid preferential models huhpm have been studied using the obtained formalism in which the simulating results are quite consistent with the theoretical results

a variational approach to spl hscr sup spl infin control with transients this paper presents a variational approach to spl hscr sup spl infin control with transients in the state feedback case the approach here provides a precise description with equality instead of inequality in the necessary and sufficient conditions for the existence of a linear controller furthermore the solution existence and uniqueness are proved in terms of certain properties of the indefinite riccati equations derived in this paper the linear time variant ltv plant on finite horizon is considered first and then the results are extended to the linear time invariant lti plant on the infinite horizon by this approach it can be directly concluded that only suboptimal spl hscr sup spl infin state feedback control can be achieved in an input output point of view and that the performance measure spl gamma spl mu sup 1 2 used in this paper is a strict upper bound

characterization of ℋ index for linear time varying systems the increasing interest in index in fault detection has led to some recent development in time domain investigation this paper at first presents a necessary and sufficient condition of the index in finite time horizon for linear time varying systems it is shown that the feasibility of the index which is given when the index is greater than a predefined value is equivalent to the existence of a certain backward differential riccati equation under a constraint the square system as a special case is discussed the corresponding results are extended to systems with unknown initial condition with a modified definition of the index the condition for weighted index to emphasize the signal effect at different time instant is also derived by transformation the result is also compared with the famous bounded real lemma the connection with the linear time invariant lti case is also discussed finally examples are given to illustrate the main results

model validation for iqc uncertain systems with fixed initial conditions abstract the paper considers a model validation problem for a class of uncertain systems in which the uncertainty is described by an integral quadratic constraint and the uncertain system has zero initial condition the problem is solved by applying methods from linear quadratic optimal control with a fixed endpoint this leads to a method for model validation which is based around a robust kalman filter structure the paper also yields a result on robust set valued state estimation for uncertain systems in which the initial condition is known to be zero

h sub infinity state estimation for linear periodic systems this note deals with the h sub infinity state estimation problem for linear periodic systems the question addressed is the design of an unbiased linear periodic and asymptotically stable estimator that achieves a prescribed h sub infinity performance on an infinite horizon necessary and sufficient conditions for the existence of a periodic estimator have been derived asymptotic properties of the finite horizon estimation problem when the time horizon tends to infinity are also investigated

a characterization of all solutions to the four block general distance problem all solutions to the four block general distance problem which arises in h infty optimal control are characterized the procedure is to embed the original problem in an all pass matrix which is constructed it is then shown that part of this all pass matrix acts as a generator of all solutions special attention is given to the characterization of all optimal solutions by invoking a new descriptor characterization of all pass transfer functions as an application necessary and sufficient conditions are found for the existence of an h infty optimal controller following that a descriptor representation of all solutions is derived

h optimal sampled data control in continuous time systems we consider the design of h optimal discrete time digital controllers in continuous time systems an apparent difficulty especially in utilizing modern transform domain analysis in this context stems from the absence of an appropriate transfer function model for the hybrid time discrete and continuous closed loop system this difficulty is overcome through the introduction of an equivalent difference equation model for the continuous time system with distributed inputs and outputs equivalence being in the sense that the continuous and discrete time inputs and outputs are essentially identical using the interplay between the discrete and the continuous time models solutions of the well known purely continuous time and purely discrete time standard problems extend to solutions of the problem at hand they comprise riccati equation characterizations of feasible combinations of sampling rates and bounds on the closed loop induced input output norm and parameterization of compensators we consid

mixed h2 h control in a stochastic framework abstract this paper deals with a mixture of h 2 and h in the following way we have two inputs and one output one input signal is a white noise stochastic process and represents errors e g resulting from measurement noise the other input has a more deterministic character if one has a reference signal e g a step as input one cannot model this as white noise but it fits nicely into this new class of inputs the objective is to minimize the effect of these signals on the output of the system we define a cost function which enables us to combine these two exogenous inputs even though they are structurally different the analysis of this function leads to a standard h riccati equation we motivate this cost function by looking at two theoretical applications the derivation of robust performance bounds and a tracking problem