finite horizon ℋ 2 ℋ control for a class of nonlinear markovian jump systems with probabilistic sensor failures this article is concerned with the mixed 2 control problem over a finite horizon for a class of nonlinear markovian jump systems with both stochastic nonlinearities and probabilistic sensor failures the stochastic nonlinearities described by statistical means could cover several types of well studied nonlinearities and the failure probability for each sensor is governed by an individual random variable satisfying a certain probability distribution over a given interval the purpose of the addressed problem is to design state feedback controllers such that the closed loop system achieves the expected 2 performance requirement with a guaranteed disturbance attenuation level the solvability of the addressed control problem is expressed as the feasibility of certain coupled matrix equations the controller gain at each time instant k can be obtained by solving the corresponding set of matrix equations a numerical example is given to illustrate the effectiveness and applicability of the proposed al

brief paper bounded nash type controls for uncertain linear systems this paper deals with multicriteria controls for systems coping with polytopic uncertainties the proposed controls are inspired by a nash strategy for exactly known systems reformulated as a nonconvex coupling between semi definite programming problems the extension to the uncertain case duplicates the linear matrix inequalities for all vertices of the polytope a new iterative algorithm using semi definite programming is provided to design bounded nash type controls for uncertain systems a numerical example is given to illustrate the design method

external non white noise theory and experiment abstract we consider a system under the influence of an external gaussian noise with a flat spectrum and finite cut off frequency the stationery properties of the system are studied as a function of the correlation time of the noise theoretical predictions based on an expansion in powers of the correlation time are corroborated by experimental measurements on an electric circuit with a digital noise generator the two main qualitative properties experimentally observed which can not be explained in a white noise limit theory are i appearance of relative extrema of the stationery distribution for high noise intensity when the correlation time is not too small ii dependence on the noise characteristics of the position of the maximum of the stationary distribution for low noise intensity

h 2 h control for stochastic systems with delay this paper is concerned with the h2 h control problem for stochastic linear systems with delay in state control and external disturbance dependent noise a necessary and sufficient condition for the existence of a unique solution to the control problem is derived the resulting solution is characterised by a kind of complex generalised forward backward stochastic differential equations with stochastic delay equations as forward equations and anticipated backward stochastic differential equations as backward equations especially we present the equivalent feedback solution via a new type of riccati equations to explain the theoretical results we apply them to a population control problem

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

infinite horizon stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper studies the infinite horizon mixed h 2 h control for discrete time stochastic systems with state and disturbance dependent noise we shall first establish a version of stochastic bounded real lemma sbrl which by itself has theoretical importance based on the sbrl it is shown that under the condition of exact observability the existence of a static state feedback h 2 h controller is equivalent to the solvability of four coupled matrix valued equations a suboptimal h 2 h controller design is given based on a convex optimization approach and an iterative algorithm is proposed to solve the four coupled matrix valued equations

stochastic h2 h control with x u v dependent noise finite horizon case in this paper the finite horizon mixed h 2 h control problem is studied for the systems governed by ito type nonlinear stochastic differential equations with state control and external disturbance dependent noise it is shown that the mixed h 2 h control under consideration is associated with the four cross coupled hamilton jacobi equations a discrete approximation algorithm is presented for solving the coupled generalized differential riccati equations arising from linear stochastic h 2 h control a necessary condition and a sufficient condition for the existence of the finite horizon stochastic h 2 h control are derived in particular some previous results on deterministic and stochastic h 2 h control can be viewed as corollaries of our main theorems

state feedback h type control of linear systems with time varying parameter uncertainty this paper is concerned with stabilisation and disturbance attenuation problems for linear systems with uncertain parameters we consider the case where the uncertainties are possibly unbounded but have a certain normal distribution and the case where the uncertainties are arbitrary but bounded criteria for the solvability of the disturbance attenuation problem are presented in terms of generalized riccati type matrix inequalities and equations the main part of the paper is devoted to the analysis and solution of these equations a numerical example is given to illustrate our results

theory of external two state markov noise in the presence of internal fluctuations a theory is presented to take into account internal fluctuations in the study of stochastically driven systems internal fluctuations are modeled by a master equation in which external noise is introduced external noise is modeled by a two state markov process a unified theory of internal and external fluctuations is described in terms of an effective integrodifferential master equation or its equivalent generating function representation two examples for which exact analytical results can be obtained are presented a discussion of the white noise limit of the theory is also given

fisher information in quantum statistics braunstein and caves braunstein s l and caves c m 1994 phys rev lett 72 3439 43 proposed to use helstrom s quantum information number to define meaningfully a metric on the set of all possible states of a given quantum system they showed that the quantum information is nothing other than the maximal fisher information in a measurement of the quantum system maximized over all possible measurements combining this fact with classical statistical results they argued that the quantum information determines the asymptotically optimal rate at which neighbouring states on some smooth curve can be distinguished based on arbitrary measurements on n identical copies of the given quantum system we show that the measurement which maximizes the fisher information typically depends on the true unknown state of the quantum system we close the resulting loophole in the argument by showing that one can still achieve the same optimal rate of distinguishability by a two stage adaptive measurement procedure when we consider states lying not on a smooth curve but on a manifold of higher dimension the situation becomes much more complex we show that the notion of distinguishability of close by states depends strongly on the measurement resources one allows oneself and on a further specification of the task at hand the quantum information matrix no longer seems to play a central role

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

quantum estimation for non differentiable models state estimation is a classical problem in quantum information in optimization of an estimation scheme to find a lower bound to the error of the estimator is a very important step so far all the proposed tractable lower bounds use a derivative of the density matrix however sometimes we are interested in quantities with singularity e g concurrence etc in this paper lower bounds to a mean square error of an estimator are derived for a quantum estimation problem without smoothness assumptions our main idea is to replace the derivative by difference as is done in classical estimation theory we applied the inequalities to several examples and derived an optimal estimator for some of them

lqg control with an h sup infinity performance bound a riccati equation approach an lqg linear quadratic gaussian control design problem involving a constraint on h sup infinity disturbance attenuation is considered the h sup infinity performance constraint is embedded within the optimization process by replacing the covariance lyapunov equation by a riccati equation whose solution leads to an upper bound on l sub 2 performance in contrast to the pair of separated riccati equations of standard lqg theory the h sup infinity constrained gains are given by a coupled system of three modified riccati equations the coupling illustrates the breakdown of the separation principle for the h sup infinity constrained problem both full and reduced order design problems are considered with an h sup infinity attenuation constraint involving both state and control variables an algorithm is developed for the full order design problem and illustrative numerical results are given

mixed h 2 h autopilot design of bank to turn missiles using fuzzy basis function networks this paper presents a novel mixed h2 h autopilot design for bank to turn missiles based on sliding control theory the proposed autopilot utilizes a fuzzy basis function network to approximate the unknown nonlinear functions of bank to turn missile dynamics enabling a mixed h2 h controller with weight updating laws to be applied to attenuate the effects of approximation errors and external disturbances moreover the mixed h2 h autopilot design can minimize h2 performance criteria under a desired h disturbance rejection constraint unlike general mixed h2 h control problems the proposed h2 h autopilot with self tuning fuzzy basis function network can avoid solving coupled riccati equations by adequately selecting diagonal weighting matrices in the h2 performance criterion and h constraint therefore the proposed h2 h control approach can be implemented efficiently computer simulation results are presented to illustrate the effectiveness of the proposed mixed h2 h autopilot for btt missiles

brief paper stochastic h2 h control for discrete time systems with state and disturbance dependent noise this paper is to study the discrete time stochastic h 2 h control with state and external disturbance dependent noise a necessary and sufficient condition for the existence of h 2 h control is presented which transforms the h 2 h controller design into solving four coupled matrix valued equations moreover a recursive algorithm for solving the four coupled matrix valued equations is also given

brief paper h filtering for nonlinear discrete time stochastic systems with randomly varying sensor delays this paper is concerned with the h filtering problem for a general class of nonlinear discrete time stochastic systems with randomly varying sensor delays where the delayed sensor measurement is governed by a stochastic variable satisfying the bernoulli random binary distribution law in terms of the hamilton jacobi isaacs inequalities preliminary results are first obtained that ensure the addressed system to possess an l 2 gain less than a given positive scalar c next a sufficient condition is established under which the filtering process is asymptotically stable in the mean square and the filtering error satisfies the h performance constraint for all nonzero exogenous disturbances under the zero initial condition such a sufficient condition is then decoupled into four inequalities for the purpose of easy implementation furthermore it is shown that our main results can be readily specialized to the case of linear stochastic systems finally a numerical simulation example is used to demonstrate the effectiveness of the results derived

strong consistency and asymptotic efficiency for adaptive quantum estimation problems it is shown that for an adaptive quantum estimation scheme based on locally unbiased measurements the sequence of maximum likelihood estimators is strongly consistent and asymptotically efficient

a numerical algorithm to find all feedback nash equilibria in scalar affine quadratic differential games this note deals with solving scalar coupled algebraic riccati equations these equations arise in finding linear feedback nash equilibria of the scalar n player affine quadratic differential game a numerical procedure is provided to compute all the stabilizing solutions the main idea is to reformulate the riccati equations into an extended eigenvalue eigenvector problem for a specific parametrized matrix u in i r 2 n times 2 n since the size of u increases exponentially on n the algorithm only applies for games where the number of players is not too large

some remarks on general nonlinear stochastic h_ infty control with state control and disturbance dependent noise this technical note studies the nonlinear stochastic h control of ito type differential systems with all the state control input and external disturbance dependent noise x u v dependent noise for short a sufficient condition is given for the finite infinite horizon h control of such a system by means of an hamilton jacobi inequality hji instead of three coupled hamilton jacobi equations hjes as in previous literature

mixed h 2 h control via state feedback for nonlinear systems this paper studies a mixed h 2 h control problem with internal stability by means of memoryless state feedback for smooth nonlinear control systems the problem consists of combining the performance requirements of quadratic optimal controllers with the robustness properties of h controllers it is shown that under appropriate assumptions the problem is solvable if a pair of cross coupled hamilton jacobi isaacs equations allows smooth solutions our approach to the mixed h 2 h nonlinear control problem is drawn from the concepts of non zero sum differential game lasalle s invariance principle and completion of squares analogous results are also developed for discrete time nonlinear systems by using the taylor expansion argument finally all the results obtained in affine systems are generalized to non affine nonlinear systems

nonlinear stochastic h_2 h_ infty control with x u v dependent noise infinite horizon case for general nonlinear stochastic ito systems with state control and external disturbance dependent noise the infinite horizon mixed h2 hinfin control is studied it turns out that in order to solve the h2 hinfin control one only needs to solve four cross coupled hamilton jacobi equations a necessary condition and a sufficient condition for the existence of the solution of h2 hinfin controlis respectively presented which extends the previous results to more general models

attaining the ultimate precision limit in quantum state estimation we derive a bound on the precision of state estimation for finite dimensional quantum systems and prove its attainability in the generic case where the spectrum is non degenerate our results hold under an assumption called local asymptotic covariance which is weaker than unbiasedness or local unbiasedness the derivation is based on an analysis of the limiting distribution of the estimator s deviation from the true value of the parameter and takes advantage of quantum local asymptotic normality a useful asymptotic characterization of identically prepared states in terms of gaussian states we first prove our results for the mean square error of a special class of models called d invariant and then extend the results to arbitrary models generic cost functions and global state estimation where the unknown parameter is not restricted to a local neighbourhood of the true value the extension includes a treatment of nuisance parameters i e parameters that are not of interest to the experimenter but nevertheless affect the precision of the estimation as an illustration of the general approach we provide the optimal estimation strategies for the joint measurement of two qubit observables for the estimation of qubit states in the presence of amplitude damping noise and for noisy multiphase estimation

a state space algorithm for the solution of the 2 block superoptimal distance problem a state space algorithm for computing the solution of the 2 block superoptimal distance problem sodp is presented given a rational and antistable matrix function r s r 11 s r 12 s find all stable approximations q s that lexicographically minimize the singular values of the error function e s r 11 s r 12 s q s conditions are given for which the superoptimal approximation is unique in addition an a priori upper bound on the macmillan degree of the approximation is given the algorithm may be stopped after minimizing a given number of singular values this premature termination of the algorithm carries with it an expected saving in the computational effort and a predictable reduction in the macmillan degree of the approximation the algorithm only requires standard linear algebraic computations and is therefore easily implemented

robust h infinity control in the presence of stochastic uncertainty this paper considers a robust h infinity state feedback control problem for linear uncertain systems with stochastic uncertainty the uncertainty class considered in the paper involves uncertain multiplicative white noise perturbations which satisfy a certain variance constraint a state feedback controller is presented which guarantees a prescribed level of disturbance attenuation for all admissible stochastic uncertainties

necessary and sufficient conditions for mixed h sub 2 and h sub infinity optimal control it is shown that d s bernstein and w m hadad s ibid vol 34 no 3 p 293 1989 necessary condition for full order mixed h sub 2 and h sub infinity optimal control is also sufficient and that j c doyle et al s proc amer control conf p 2065 1989 sufficient condition for full order mixed h sub 2 and h sub infinity optimal control is also necessary they are duals of one another

a maximum entropy principle for contractive interpolants abstract in this paper a maximum entropy principle is established for a class of continuous contractive m n matrix valued functions g with preassigned fourier coefficients gj j for j 0 1 the function g in this class which achieves the maximum entropy is characterized in a number of different ways and its entropy is computed in terms of a hankel operator based on the prescribed matrices 0 1 a pair of seemingly new szego type formulas are obtained enroute and some applications to nevanlinna pick interpolation are indicated

on the relaxation of fluctuations in the steady state of the stratonovich model a detailed investigation has been carried out of the relaxation of fluctuations in the steady state of the stratonovich model also known as the random growing rate model the autocorrelation time of this system driven by parametric white noise in the linear term has been measured for an electronic circuit model computed by digital simulation and calculated by use of a continued fraction expansion method the results are all consistent with each other and with those obtained from the matrix continued fraction method of jung and risken 1985 provided that explicit account is taken of the ways in which any macroscopic real physical system is bound to differ from the idealisation represented by the original form of the stratonovich model in particular it is necessary to recognise the existence of weak additive noise and a small additive constant the physical origins of some earlier seemingly discrepant calculations and experimental data are discussed

mixed norm h 2 h and entropy covariance control a convex optimisation approach in this paper we develop a covariance control problem to address a tradeoff between h 2 performance and h disturbance attenuation in particular we formulate a mixed norm h 2 h and entropy

pareto optimal strategy for linear stochastic systems with h constraint in finite horizon abstract in this paper we derive conditions for the existence of pareto efficient strategy and pareto solution under h constraint for the linear quadratic lq finite horizon cooperative differential game of stochastic systems with state control and disturbance multiplicative noise firstly we present a stochastic bounded real lemma sbrl with any initial condition for the considered stochastic system next a necessary and sufficient condition for pareto optimal strategy under the h constraint is researched by two cross coupled generalized differential riccati equations gdres which is the key contribution of this paper another contribution is that the pareto solution for every controller is given under the pareto efficient strategy and worst case external disturbance finally a practical example is given to illustrate the effectiveness of our results

brief trading robustness with optimality in nonlinear control the mixed h 2 h control problem is studied for a class of nonlinear systems a procedure providing a sub optimal solution to this problem is discussed and analyzed in detail the sub optimal state feedback control law can be obtained solving two hamilton jacobi equations and a simple one parameter static minimization problem a simple one dimensional example is discussed in detail and applications to the optimal robust stabilization of the angular velocities of a rigid body are included

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

output tracking of high order stochastic nonlinear systems with application to benchmark mechanical system this note considers output tracking of high order stochastic nonlinear systems without imposing any restriction on the high order and the drift and diffusion terms by using the backstepping design technique a smooth state feedback controller is given to guarantee that the solution process is bounded in probability and the error signal between the output and the reference signal can be regulated into a small neighborhood of the origin in probability a practical example of stochastic benchmark mechanical system and simulation are provided to demonstrate the effectiveness of the control scheme

state feedback ℋ control for stochastic time delay nonlinear systems with state and disturbance dependent noise this article focuses on the state feedback control problem for the stochastic nonlinear systems with state and disturbance dependent noise and time varying state delays based on the maxmin optimisation approach both the delay independent and the delay dependent hamilton jacobi inequalities hjis are developed for synthesising the state feedback controller for a general type of stochastic nonlinear systems it is shown that the resulting control system achieves stochastic stability in probability and the prescribed disturbance attenuation level for a class of stochastic affine nonlinear systems the delay independent as well as delay dependent matrix valued inequalities are proposed the resulting control system satisfies global asymptotic stability in the mean square sense and the required disturbance attenuation level by modelling the nonlinearities as uncertainties in corresponding stochastic time delay systems the sufficient conditions in terms of a linear matrix inequality lmi and a bili

an iterative method for nonlinear stochastic optimal control based on path integrals this paper proposes a new iterative solution method for nonlinear stochastic optimal control problems based on path integral analysis first we provide an iteration law for solving a stochastic hamilton jacobi bellman shjb equation associated to this problem which is a nonlinear partial differential equation pde of second order each iteration procedure of the proposed method is represented by a cauchy problem for a linear parabolic pde and its explicit solution is given by the feynman kac formula second we derive a suboptimal feedback controller at each iteration by using the path integral analysis third the convergence property of the proposed method is investigated here some conditions are provided so that the sequence of solutions for the proposed iteration converges and the shjb equation is satisfied finally numerical simulations demonstrate the effectiveness of the proposed method

on global existence of solutions to coupled matrix riccati equations in closed loop nash games presents comparison and global existence results for solutions of coupled matrix riccati differential equations appearing in closed loop nash games and in mixed h sub 2 h sub spl infin type problems convergence of solutions is established for the diagonal case solutions of the corresponding algebraic equations are discussed using numerical examples

asymptotic properties of maximum likelihood estimators and likelihood ratio tests under nonstandard conditions abstract large sample properties of the likelihood function when the true parameter value may be on the boundary of the parameter space are described specifically the asymptotic distribution of maximum likelihood estimators and likelihood ratio statistics are derived these results generalize the work of moran 1971 chant 1974 and chernoff 1954 some of chant s results are shown to be incorrect the approach used in deriving these results follows from comments made by moran and chant the problem is shown to be asymptotically equivalent to the problem of estimating the restricted mean of a multivariate gaussian distribution from a sample of size 1 in this representation the gaussian random variable corresponds to the limit of the normalized score statistic and the estimate of the mean corresponds to the limit of the normalized maximum likelihood estimator thus the limiting distribution of the maximum likelihood estimator is the same as the distribution of the projection of the gaussian random v

reliable mixed l2 h fuzzy static output feedback control for nonlinear systems with sensor faults this paper is concerned with the design of reliable mixed l 2 h static output feedback sof fuzzy controllers for nonlinear continuous time systems with complete sensor faults the takagi and sugeno t s fuzzy model is employed to represent a nonlinear system a sufficient condition for the existence of reliable mixed l 2 h sof fuzzy controllers is presented in terms of a set of quadratic matrix inequalities qmis which not only guarantees that the closed loop fuzzy system satisfies a desired h disturbance attenuation constraint for all admissible operating regimes including the normal and sensor fault cases but also provides different upper bounds on the l 2 performance criterion for different operating regimes a suboptimal reliable fuzzy controller is obtained by the proposed iterative linear matrix inequality ilmi algorithm for minimizing the normal l 2 performance bound while maintaining acceptable lower levels of the bounds in the sensor fault cases finally a numerical example is given to illustrate the effectiveness of the proposed design method

mixed h sub 2 h sub spl infin fuzzy output feedback control design for nonlinear dynamic systems an lmi approach this study introduces a mixed h sub 2 h sub spl infin fuzzy output feedback control design method for nonlinear systems with guaranteed control performance first the takagi sugeno fuzzy model is employed to approximate a nonlinear system next based on the fuzzy model a fuzzy observer based mixed h sub 2 h sub spl infin controller is developed to achieve the suboptimal h sub 2 control performance with a desired h sub spl infin disturbance rejection constraint a robust stabilization technique is also proposed to override the effect of approximation error in the fuzzy approximation procedure by the proposed decoupling technique and two stage procedure the outcome of the fuzzy observer based mixed h sub 2 h sub spl infin control problem is parametrized in terms of the two eigenvalue problems evps one for observer and the other for controller the evps can be solved very efficiently using the linear matrix inequality lmi optimization techniques a simulation example is given to illustrate the design procedures and performances of the proposed method

relationship between nash equilibrium strategies and h_ 2 h_ infty control of stochastic markov jump systems with multiplicative noise this technical note is concerned with discussing the relationship between nash equilibrium strategies and the finite horizon h 2 h control of time varying stochastic systems subject to markov jump parameters and multiplicative noise it is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term furthermore necessary and sufficient conditions for the finite horizon h 2 h control of stochastic markov jump systems are presented via coupled matrix valued equations

finite horizon h_ 2 h_ infty control for discrete time stochastic systems with markovian jumps and multiplicative noise in this note we consider the finite horizon mixed h 2 h control problem for discrete time stochastic linear systems subject to markov jump parameters and multiplicative noise firstly we derive a stochastic bounded real lemma sbrl which is used to establish a necessary and sufficient condition for the existence of the mixed h 2 h control via the solvability of four coupled difference matrix valued recursions cdmrs moreover a state feedback h 2 h controller is designed by means of the solutions of cdmrs

a state space approach to super optimal h sup infinity control problems a numerically stable algorithm is presented for solving the strengthened or super optimal model matching problem the steps of the algorithm follows closely those given by n j young 1986 except that for each step a reliable implementation using state space models is provided

stochastic h2 h control of nonlinear systems with time delay and state dependent noise this paper investigates the problem of h2 h control for nonlinear stochastic systems with time delay and state dependent noise firstly a sufficient condition for the existence of the nonlinear stochastic h2 h control with time delay is presented in terms of coupled hamilton jacobi equations hjes secondly by using the fuzzy approach the stochastic h2 h controller can be designed via solving a set of linear matrix inequalities instead of coupled hjes finally two numerical examples are employed to show the effectiveness of the results obtained

robust optimal reference tracking design method for stochastic synthetic biology systems t s fuzzy approach at present the development in the nascent field of synthetic gene networks is still difficult most newly created gene networks are nonfunctioning due to intrinsic parameter fluctuations uncertain interactions with unknown molecules and external disturbances of intra and extracellular environments on the host cell how to design a completely new gene network that is to track some desired behaviors under these intrinsic and extrinsic disturbances on the host cell is the most important topic in synthetic biology in this study the intrinsic parameter fluctuations uncertain interactions with unknown molecules and environmental disturbances are modeled into the nonlinear stochastic systems of synthetic gene networks in vivo four design specifications are introduced to guarantee the stochastic synthetic gene network which can achieve robust optimal tracking of a desired reference model in spite of these intrinsic and extrinsic disturbances on the host cell however the robust optimal reference tracking design problem of nonlinear synthetic gene networks is still hard to solve in order to simplify the design procedure of the robust optimal nonlinear stochastic tracking design for synthetic gene networks the takagi sugeno t s fuzzy method is introduced to solve the nonlinear stochastic minimum error tracking design problem hence the robust optimal reference tracking design problem under four design specifications can be solved by the linear matrix inequality lmi constrained optimization method using convex optimization techniques further a simple design procedure is developed for synthetic gene networks to meet the four design specifications to achieve robust optimal reference tracking finally an eigenvalue shifted design method is also proposed as an expedient scheme to improve the stochastic optimal tracking design method of synthetic gene oscillators

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

brief paper a unified design for state and output feedback h control of nonlinear stochastic markovian jump systems with state and disturbance dependent noise for a class of continuous time nonlinear stochastic markovian jump systems with state and disturbance dependent noise both the state and output feedback h control problems are studied based on the solvability of a set of coupled hamilton jacobi inequalities hjis we give a unified design for both state and dynamic output feedback h control via a common function u r t i e u x r t is a state feedback h control while u email protected r t is the desired output feedback h control

state space algorithm for the computation of superoptimal matrix interpolating functions a state space algorithm is studied which generates the unique superoptimal nehari extension of a general rational matrix the procedure is to use a set of all pass transformations to sequentially minimize each frequency dependent singular value of the interpolating function in a dimension peeling algorithm these all pass transformations are determined by the maximal schmidt pairs of a sequence of hankel operators the process terminates when the original problem is reduced to one of rank one at this stage all the available degrees of freedom have been exhausted the work is an extension of that by young 1986 and gives a concrete state space implementation of his operator theoretic arguments in addition bounds are given on the minimum achievable values for s1 e sup ersi e j i 1 2 rank g0 and also the mcmillan degree of the final superoptimal extension here si denotes the ith singular value of a frequency dependent matrix and the numbering is taken to be in decrea

the effect of multiplicative noise on the relaxation time of a real non linear physical system a comparison of experiment and theory for the random growing rate model rgrm it is found that the theoretical behaviour of the relaxation time t for the random growing rate model rgrm under the influence of multiplicative noise of intensity q a monotonic decrease of t 1 towards a limiting value as q to infinity differs markedly from that actually measured in electronic simulators of that system a new electronic analogue experiment is described in which a distinct minimum in t 1 q has been observed for the first time with clear evidence for an increase of t 1 q with q at large q in good qualitative agreement with an earlier analogue experiment the discrepancy between experiment and the theoretical solutions of the idealised equation is attributed to the profound influence exerted by the very weak additive noise which must also in some measure always be present in a real physical system

mixed control the discrete time case abstract a stochastic h and a mixed stochastic h 2 h control problem for discrete time systems are considered and solved conditions for existence of a solution are derived based on the solvability of an equivalent minimax problem in this framework it is possible to consider at the same time both stochastic and deterministic disturbances highlighting their mutual effects the controller can be designed by solving a system of three coupled riccati equations such equations display how the h 2 type minimization problem and the h type constraint influence each other

a new approximate stationary probability distribution for processes driven by ornstein uhlenbeck noise a novel approximate probability distribution for a class of nonlinear processes driven by multiplicative linear ornstein uhlenbeck noise is presented a comparison is made with other approximate distributions reported in the literature

event based h_ infty state estimation for time varying stochastic dynamical networks with state and disturbance dependent noises in this paper the event based finite horizon h infty state estimation problem is investigated for a class of discrete time varying stochastic dynamical networks with state and disturbance dependent noises also called x v dependent noises an event triggered scheme is proposed to decrease the frequency of the data transmission between the sensors and the estimator where the signal is transmitted only when certain conditions are satisfied the purpose of the problem addressed is to design a time varying state estimator in order to estimate the network states through available output measurements by employing the completing the square technique and the stochastic analysis approach sufficient conditions are established to ensure that the error dynamics of the state estimation satisfies a prescribed h infty performance constraint over a finite horizon the desired estimator parameters can be designed via solving coupled backward recursive riccati difference equations finally a numerical example is exploited to demonstrate the effectiveness of the developed state estimation scheme

constructive epsilon nash equilibria for nonzero sum differential games in this paper a class of infinite horizon nonzero sum differential games and their nash equilibria are studied and the notion of epsilon alpha nash equilibrium strategies is introduced dynamic strategies satisfying partial differential inequalities in place of the hamilton jacobi isaacs partial differential equations associated with the differential games are constructed these strategies constitute local epsilon alpha nash equilibrium strategies for the differential game the proposed methods are illustrated on a differential game for which the nash equilibrium strategies are known and on a lotka volterra model with two competing species simulations indicate that both dynamic strategies yield better performance than the strategies resulting from the solution of the linear quadratic approximation of the problem

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

brief a transformation approach for solving the hamilton jacobi bellman equation in h2 deterministic and stochastic optimal control of affine nonlinear systems in this paper we present a transformation approach for solving the hamilton jacobi bellman equations hjbes arising in h 2 or quadratic cost control of nonlinear deterministic and stochastic systems we show that the hjbe can be solved analogously to a scalar quadratic equation and we give a parameterization of solutions to the hjbe characterizing the solution of the optimal control problem the procedure is also generalized to include nonsmooth or viscosity solutions of the s hjbe

multi player non zero sum games online adaptive learning solution of coupled hamilton jacobi equations in this paper we present an online adaptive control algorithm based on policy iteration reinforcement learning techniques to solve the continuous time ct multi player non zero sum nzs game with infinite horizon for linear and nonlinear systems nzs games allow for players to have a cooperative team component and an individual selfish component of strategy the adaptive algorithm learns online the solution of coupled riccati equations and coupled hamilton jacobi equations for linear and nonlinear systems respectively this adaptive control method finds in real time approximations of the optimal value and the nzs nash equilibrium while also guaranteeing closed loop stability the optimal adaptive algorithm is implemented as a separate actor critic parametric network approximator structure for every player and involves simultaneous continuous time adaptation of the actor critic networks a persistence of excitation condition is shown to guarantee convergence of every critic to the actual optimal value function for that player a detailed mathematical analysis is done for 2 player nzs games novel tuning algorithms are given for the actor critic networks the convergence to the nash equilibrium is proven and stability of the system is also guaranteed this provides optimal adaptive control solutions for both non zero sum games and their special case the zero sum games simulation examples show the effectiveness of the new algorithm

finite correlation time effects in nonequilibrium phase transitions i dynamic equation and steady state properties abstract we determine an approximate renormalized equation of evolution for an arbitrary nonlinear single degree of freedom system externally driven by gaussian parametric fluctuations of finite correlation time the renormalization scheme used here gives a second order equation with a time and state dependent diffusion coefficient we are able to calculate the diffusion coefficient in closed form the steady state distribution can easily be obtained from the evolution equation we are thus able to determine the parameter dependence of the steady state distribution and in particular the influence of a correlation time of the fluctuations which does not vanish on the steady state distribution

brief a mixed h2 h adaptive tracking control for constrained non holonomic systems in this study a pid type controller incorporating an adaptive control scheme for the mixed h 2 h tracking performance is developed for constrained non holonomic mechanical systems under unknown or uncertain plant parameters and external disturbances by virtue of the skew symmetric property of the non holonomic mechanical systems and an adequate choice of a state variable transformation sufficient conditions are developed for the adaptive mixed h 2 h tracking control problems in terms of a pair of coupled algebraic equations instead of a pair of coupled non linear differential equations the coupled algebraic equations can be solved analytically

reduced order h sub spl infin filtering for stochastic systems this paper deals with the reduced order h sub spl infin filtering problem for stochastic systems necessary and sufficient conditions are obtained for the existence of solutions to the continuous time and discrete time problems in terms of certain linear matrix inequalities lmis and a coupling nonconvex rank constraint condition furthermore when these conditions are feasible an explicit parametrization of all desired reduced order filters corresponding to a feasible solution is given in particular when the reduced order filter is restricted to be a static one then simple conditions expressed by lmis only without any rank constraints are derived and a parametrization of all solutions is also given finally an illustrative example is provided to show the effectiveness of the proposed approach

derivation of the maximum entropy h controller and a state space formula for its entropy the problem of maximizing the entropy of a stabilized closed loop system is solved the solution exploits the parametrization of all closed loop systems that meet an h norm bound the central solution of this set is shown to maximize the entropy at infinity and for this case a particularly simple formula is derived for the maximum value of the entropy

mixed h sub 2 h sub infinity control a convex optimization approach the problem of finding an internally stabilizing controller that minimizes a mixed h sub 2 h sub infinity performance measure subject to an inequality constraint on the h sub infinity norm of another closed loop transfer function is considered this problem can be interpreted and motivated as a problem of optimal nominal performance subject to a robust stability constraint both the state feedback and output feedback problems are considered it is shown that in the state feedback case one can come arbitrarily close to the optimal even over full information controllers mixed h sub 2 h sub infinity performance measure using constant gain state feedback moreover the state feedback problem can be converted into a convex optimization problem over a bounded subset of n n and n q where n and q are respectively the state and input dimensions real matrices using the central h sub infinity estimator it is shown that the output feedback problem can be reduced to a state feedback problem in this case the dimension of the resulting controller does not exceed the dimension of the generalized plant

solutions to the h general distance problem which minimize an entropy integral abstract we pose and solve the problem of minimizing the entropy of an h norm bounded and stabilized closed loop solution proceeds via the equivalent error system distance problem the central member of the admissible class is shown to minimize the entropy at infinity and in that case an explicit state space formula is derived for the minimum value of the entropy links between entropy h 2 norms and h 2 optimal control are given

output feedback h2 h consensus control for stochastic time varying multi agent systems with x u v dependent noises abstract in this paper the output feedback h 2 h consensus control problem is investigated for discrete time varying stochastic multi agent systems with state control and disturbance dependent noises also called x u v dependent noises two new concepts for the h 2 and h consensus requirements are proposed to quantify the transient behavior of the consensus over a finite horizon for the addressed time varying multi agent systems we aim to design an output feedback consensus controller such that the closed loop multi agent systems achieve the prescribed h 2 and h consensus performances over a finite horizon by using the completing squares method and stochastic analysis techniques sufficient conditions are derived for the existence of the desired output feedback h 2 h consensus controller in terms of the solution to two coupled backward recursive riccati difference equations rdes moreover an iterative algorithm is proposed for solving the rdes by resorting to the moore penrose pseudo inverse a numerical example is utilized to illustrate the effectiveness of the proposed h 2 h consensus control strategy

on nonlinear h_ infty filtering for discrete time stochastic systems with missing measurements in this paper the h infin filtering problem is investigated for a general class of nonlinear discrete time stochastic systems with missing measurements the system under study is not only corrupted by state dependent white noises but also disturbed by exogenous inputs the measurement output contains randomly missing data that is modeled by a bernoulli distributed white sequence with a known conditional probability a filter of very general form is first designed such that the filtering process is stochastically stable and the filtering error satisfies h infin performance constraint for all admissible missing observations and nonzero exogenous disturbances under the zero initial condition the existence conditions of the desired filter are described in terms of a second order nonlinear inequality such an inequality can be decoupled into some auxiliary ones that can be solved independently by taking special form of the lyapunov functionals as a consequence a linear time invariant filter design problem is discussed for the benefit of practical applications and some simplified conditions are obtained finally two numerical simulation examples are given to illustrate the main results of this paper

a polynomial approach to minimax frequency domain optimization of multivariable feedback systems the properties of a feedback system where the plant has rational transfer matrix h and the compensator has transfer matrix g can be characterized through the system functions s i hg and t g i hg 1 good disturbance attenuation robustness limited bandwidth and compensator roll off may be obtained by minimizing a criterion of the form z where z v s t w1 wls t w2 w2t v with respect to the compensator transfer matrix g here v w1 and w2 are suitable rational weighting matrices the solution of the problem can be reduced to a pair of matrix polynomial equations since the optimal solution is highly non unique special solutions with additional optimality properties are considered as well the paper includes a discussion of the numerical solution of the polynomial equations and of the question how to choose the weighting matrices to ensure required feedback system properties an example illustrates the results

technical communique infinite horizon h2 h control for stochastic systems with markovian jumps this paper studies robust h 2 h control problem for systems subjected to multiplicative noise and markovian parameter jumps a necessary sufficient condition for the existence of h 2 h control is presented by means of two coupled algebraic riccati equations respectively finally a suboptimal h 2 h controller design algorithm is also obtained by solving a convex optimization problem

robust stabilization subject to structured uncertainties and mean power constraint abstract this paper deals with a robust stabilization problem for discrete time systems subject to multiple disturbances occurring in controller and actuating channel where both linear structured uncertainties and white gaussian noises are included the desired control law is aimed to robustly stabilize the system and to satisfy some pre specified mean power constraint simultaneously by the philosophy of the mixed h 2 h control a solvability condition is first derived for single input systems that reveals the intrinsic relation between the unstable poles of the plant and the disturbance parameters together with two cross coupled algebraic riccati equations the result is further generalized to multiple input systems with a sufficient condition given again by the unstable poles of the plant an example is included to illustrate the current results

robust h filter design for neutral stochastic uncertain systems with time varying delay abstract in this paper the robust h filtering problem for a class of neutral stochastic systems is discussed the system under consideration contains parameter uncertainties ito type stochastic disturbances time varying delay the parameter uncertainties are assumed to be time varying norm bounded using the stochastic lyapunov stability theory and ito s differential rule a full order filter is designed for all admissible uncertainties and time varying delay which is expressed in the form of linear matrix inequality lmi the dynamics of the filtering error systems are guaranteed to be robust stochastically mean square asymptotically stable while achieving a prescribed stochastic robust h performance level at the end of this paper a numerical example is given to demonstrate the usefulness of the proposed method

stochastic h infty we consider stochastic linear plants which are controlled by dynamic output feedback and subjected to both deterministic and stochastic perturbations our objective is to develop an h infty type theory for such systems we prove a bounded real lemma for stochastic systems with deterministic and stochastic perturbations this enables us to obtain necessary and sufficient conditions for the existence of a stabilizing compensator which keeps the effect of the perturbations on the to be controlled output below a given threshhold gamma 0 in the deterministic case the analogous conditions involve two uncoupled linear matrix inequalities but in the stochastic setting we obtain coupled nonlinear matrix inequalities instead the connection between h infty theory and stability radii is discussed and leads to a lower bound for the radii which is shown to be tight in some special cases

mixed control design numerical optimization approaches this paper presents some new approaches to mixed performance control problems of linear systems the design techniques proposed in this paper are based on numerical search of the norm bounded stable transfer matrix q in the and suboptimal controller parameterizations so that the additional performance specifications are satisfied the design problems are then converted to some finite dimensional non linear unconstrained optimization problems by explicitly parameterizing the or norm bounded stable transfer matrix q for any fixed order finally some two stage optimization algorithms are applied to find the optimal parameters numerical examples have shown significant performance improvements of the proposed algorithms over those in the existing literature

state space solutions to standard h sub 2 and h sub infinity control problems simple state space formulas are derived for all controllers solving the following standard h sub infinity problem for a given number gamma 0 find all controllers such that the h sub infinity norm of the closed loop transfer function is strictly less than gamma it is known that a controller exists if and only if the unique stabilizing solutions to two algebraic riccati equations are positive definite and the spectral radius of their product is less than gamma sup 2 under these conditions a parameterization of all controllers solving the problem is given as a linear fractional transformation lft on a contractive stable free parameter the state dimension of the coefficient matrix for the lft constructed using the two riccati solutions equals that of the plant and has a separation structure reminiscent of classical lqg i e h sub 2 theory this paper is intended to be of tutorial value so a standard h sub 2 solution is developed in parallel

dynamical properties of non markovian stochastic differential equations we study nonstationary non markovian processes defined by langevin type stochastic differential equations with an ornstein uhlenbeck driving force we concentrate on the long time limit of the dynamical evolution we derive an approximate equation for the correlation function of a nonlinear nonstationary non markovian process and we discuss its consequences non markovicity can introduce a dependence on noise parameters in the dynamics of the correlation function in cases in which it becomes independent of these parameters in the markovian limit several examples are discussed in which the relaxation time increases with respect to the markovian limit for a brownian harmonic oscillator with fluctuating frequency the non markovicity of the process decreases the domain of stability of the system and it can change an infradamped evolution into an overdamped one

relations between maximum entropy h control and combined h lqg control abstract the maximum entropy h control problem and a combined h lqg control problem are presented in a unified way and shown to be equivalent in the case of a full order controller and equalized h lqg weights the result links two separate approaches which have distinctly different methods of solution only two decoupled algebraic riccati equations are needed to state the controller maximum value of the entropy and minimum value of the auxiliary cost

on a class of approximate solutions to multi objective h 2 h problems a class of matrix function optimization problems is considered in which the cost functional is the h 2 norm of an affine function of the decision variables and there are several constraints involving h 2 and h x norms of other affine functions such problems arise naturally in feedback control theory as closed loop transfer functions are affine functions of the socalled youla parameter and control objectives can often be expressed as prescribed upper bounds on the h 2 and h x norms of these functions a procedure for obtaining approximate solutions to such problems is described which involves solving a sequence of h 2 problems with a single weighted h 2 constraint this procedure hinges upon a weighting updating scheme in which roughly speaking a multiplication operator is applied to an additively corrected version of the weighting function at each step with both the operator and the additive correction being defined on the basis of the solution of the current auxiliary quadratic problem it is shown

properties of feedback nash equilibria in scalar lq differential games in this paper we study the scalar linear quadratic differential game with state feedback information structure using a geometric approach we present a complete characterization when this game will have no one or multiple equilibria furthermore we investigate the effect on this solution structure of some characteristics of the game i e the number of players the entrance of new players the level of asymmetry and the impact entrance of an additional player has on the closed loop stability of the game for that purpose we distinguish three types of the game the economic game the regulator game and the mixed game the analysis is restricted to the case the involved cost depend only on the state and control variables

robust h sub spl infin filtering of stationary continuous time linear systems with stochastic uncertainties the problem of applying h sub spl infin filters on stationary continuous time linear systems with stochastic uncertainties in the state space signal model is addressed these uncertainties are modeled via white noise processes the relevant cost function is the expected value of the standard h sub spl infin performance index with respect to the uncertain parameters the solution is obtained via a stochastic bounded real lemma that results in a modified riccati inequality this inequality is expressed in the form of a linear matrix inequality whose solution provides the filter parameters the method proposed is also applied to the case where in addition to the stochastic uncertainty other deterministic parameters of the system are not perfectly known and are assumed to lie in a given polytope the problem of mixed h sub 2 h sub spl infin filtering for the above system is also treated the theory developed is demonstrated by a practical example

an analysis of the pole zero cancellations in h optimal control problems of the first kind the aim of this paper is to study the pole zero cancellations which occur in a class of h infty optimal control problems which may be embedded in the configuration of fig 1 h infty control problems are said to be of the first kind if both p 12 s and p 21 s are square but not necessarily of the same size it is primarily this class of problems which will concern us here a general bound on the mcmillan degree of all controllers which are stabilizing and lead to a closed loop which satisfies bf mathcal r s infty leqq rho rho need not be optimal in the l infty norm sense is derived as illustrated in fig 1 bf mathcal r s is the transfer function relating y 1 s to u 1 s if the mcmillan degree of p s in fig 1 is n we show that in the single loop siso case the corresponding unique h infty optimal controller never requires more than n 1 states in the multivariable case there is a continuum of optimal controllers whose mcmil

robust h sub spl infin filtering for nonlinear stochastic systems this paper describes the robust h sub spl infin filtering analysis and synthesis of nonlinear stochastic systems with state and exogenous disturbance dependent noise we assume that the state and measurement are corrupted by stochastic uncertain exogenous disturbance and that the system dynamic is modeled by ito spl circ type stochastic differential equations for general nonlinear stochastic systems the h sub spl infin filter can be obtained by solving second order nonlinear hamilton jacobi inequalities when the worst case disturbance is considered in the design procedure a mixed h sub 2 h sub spl infin filtering problem is also solved by minimizing the total estimation error energy it is found that for a class of special nonlinear stochastic systems the h sub spl infin filtering design can be given via solving several linear matrix inequalities instead of hamilton jacobi inequalities a few examples show that the proposed methods are effective