combined filtering and parameter estimation approximations and robustness abstract the filtering problem for a non linear discrete time model is considered that includes as a special case the problem of combined filtering and parameter estimation for linear models the filter derived in the paper is shown to be robust in a specific sense with respect to small variations in the a priori distributions in the model

discrete time lq optimal control problems for infinite markov jump parameter systems optimal control problems for discrete time linear systems subject to markovian jumps in the parameters are considered for the case in which the markov chain takes values in a countably infinite set two situations are considered the noiseless case and the case in which an additive noise is appended to the model the solution for these problems relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution to the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd which turn out to be equivalent to the spectral radius of certain infinite dimensional linear operators in a banach space being less than one for the long run average cost ss and sd guarantee existence and uniqueness of a stationary measure and consequently existence of an optimal stationary control policy furthermore an extension of a lyapunov equation result is derived for the countably infinite markov state space case

analytic torsion and holomorphic determinant bundles in this paper we prove that in the case of holomorphic locally kahler fibrations the analytic and algebraic geometry constructions of determinant bundles for direct images coincide we calculate the curvature of the holomorphic hermitian connection for the quillen metric on the determinant bundle we study the behavior of the quillen metric under change of metrics in the fibers and also on the twisting vector bundles we thus generalize the conformal anomaly formula to kahler manifolds of arbitrary dimension we also study the quillen metrics on determinants associated with exact sequences of vector bundles we prove that the quillen metric is smooth on the grothendieck knudsen mumford determinant for arbitrary holomorphic fibrations

on the existence of maximal solution for generalized algebraic riccati equations arising in stochastic control abstract existence of maximal solution is proved for a generalized version of the well known standard algebraic riccati equations which arise in certain stochastic optimal control problems

on stabilization of bilinear uncertain time delay stochastic systems with markovian jumping parameters in this paper we investigate the stochastic stabilization problem for a class of bilinear continuous time delay uncertain systems with markovian jumping parameters specifically the stochastic bilinear jump system under study involves unknown state time delay parameter uncertainties and unknown nonlinear deterministic disturbances the jumping parameters considered here form a continuous time discrete state homogeneous markov process the whole system may be regarded as a stochastic bilinear hybrid system that includes both time evolving and event driven mechanisms our attention is focused on the design of a robust state feedback controller such that for all admissible uncertainties as well as nonlinear disturbances the closed loop system is stochastically exponentially stable in the mean square independent of the time delay sufficient conditions are established to guarantee the existence of desired robust controllers which are given in terms of the solutions to a set of either linear matrix inequalities lmis or coupled quadratic matrix inequalities the developed theory is illustrated by numerical simulation

comparison between two analytic torsions on orbifolds in this paper we establish an equality between the analytic torsion introduced by dar math z 194 2 193 216 1987 and the orbifold analytic torsion defined by ma trans am math soc 357 6 2205 2233 2005 on an even dimensional manifold with isolated conical singularities which in addition has an orbifold structure we assume the orbifold flat vector bundle is an honest vector bundle although the metric on the flat bundle may not be flat

lms algorithms for tracking slow markov chains with applications to hidden markov estimation and adaptive multiuser detection this paper analyzes the tracking properties of the least mean squares lms algorithm when the underlying parameter evolves according to a finite state markov chain with infrequent jumps first using perturbed liapunov function methods mean square error estimates are obtained for the tracking error then using recent results on two time scale markov chains mean ordinary differential equation and diffusion approximation results are obtained it is shown that a sequence of the centered tracking errors converges to an ordinary differential equation moreover a suitably scaled sequence of the tracking errors converges weakly to a diffusion process it is also shown that iterate averaging of the tracking algorithm results in optimal asymptotic convergence rate in an appropriate sense two application examples analysis of the performance of an adaptive multiuser detection algorithm in a direct sequence code division multiple access ds cdma system and tracking analysis of the state of a hidden markov model hmm with infrequent jumps are presented

adaptive sampled data based linear quadratic optimal control of stochastic systems the problem of sampled data sd based adaptive linear quadratic lq optimal control is considered for linear stochastic continuous time systems with unknown parameters and disturbances to overcome the difficulties caused by the unknown parameters and incompleteness of the state information and to probe into the influence of sample size on system performance a cost biased parameter estimator and an adaptive control design method are presented under the assumption that the unknown parameter belongs to a known finite set some sufficient conditions ensuring the convergence of the parameter estimate are obtained it is shown that when the sample step size is small the sd based adaptive control is lq optimal for the corresponding discretized system and sub optimal compared with that of the case where the parameter is known and the information is complete

orbifolds and analytic torsions dans cet article on calcule le comportement de metrique de quillen par immersions d orbifold on etend ainsi une formule de bismut lebeau au cas d orbifold

intersection r torsion and analytic torsion for pseudomanifolds pour une pseudovariete x n on definit un invariant i p la r torsion intersection parametrisee par la perversite p cet invariant est analogue a la torsion de reidemeister et est un invariant combinatoire

the interacting multiple model algorithm for systems with markovian switching coefficients an important problem in filtering for linear systems with markovian switching coefficients dynamic multiple model systems is the management of hypotheses which is necessary to limit the computational requirements a novel approach to hypotheses merging is presented for this problem the novelty lies in the timing of hypotheses merging when applied to the problem of filtering for a linear system with markovian coefficients the method is an elegant way to derive the interacting multiple model imm algorithm evaluation of the imm algorithm shows that it performs well at a relatively low computational load these results imply a significant change in the state of the art of approximate bayesian filtering for systems with markovian coefficients

on nearly optimal controls of hybrid lqg problems the paper is concerned with hybrid control of a class of linear quadratic gaussian lqg systems modulated by a finite state markov chain it develops approximation schemes for systems involving singularly perturbed markov chains with weak and strong interactions which are useful for natural time scale separation and for large scale markovian systems the presentation encompasses three cases the recurrent markov chains inclusion of transient states and inclusion of absorbing states near optimality of the approximation schemes is obtained and a numerical example is presented computational results indicate our approximation schemes perform well

on robust stability of singular systems with random abrupt changes this paper deals with the class of continuous time singular linear systems with markovian switching sufficient conditions on stochastic stability and robust stochastic stability are developed in the lmi setting the developed sufficient conditions are used to check if either the nominal or the uncertain systems are regular impulse free and stochastically stable or robust stochastically stable

brief control of singularly perturbed systems with markovian jump parameters an h approach in this paper we study the problem of h control for singularly perturbed linear continuous time systems with markovian jump parameters the system under consideration is described by a state space model consisting of slow and fast dynamics with a continuous time discrete state markov process taking values on a finite set on the basis of reduced order technique our attention is focused on the designing of state feedback control such that both stochastic stability and a prescribed h performance for the full order system are achieved it has been shown that the above problem can be solved if a set of coupled riccati equations has solution furthermore the asymptotic structure of composite mode dependent controller is characterized which shows that the controller is independent of the singular perturbation e when e is sufficiently small

optimal estimation theory for dynamic systems with set membership uncertainty an overview in many problems such as linear and nonlinear regressions parameter and state estimation of dynamic systems state space and time series prediction interpolation smoothing and functions approximation one has to evaluate some unknown variable using available data the data are always associated with some uncertainty and it is necessary to evaluate how this uncertainty affects the estimated variables typically the problem is approached assuming a probabilistic description of uncertainty and applying statistical estimation theory an interesting alternative approach referred to as set membership or unknown but bounded ubb error description has been investigated since the late 1960s in this approach uncertainty is described by an additive noise which is known only to have given integral typically l2 of l1 or componentwise l bounds in this paper we review the main results of this theory with special attention to the most recent advances obtained in the case of componentwise bounds

asymptotically efficient parameter estimation using quantized output observations this paper studies identification of systems in which only quantized output observations are available an identification algorithm for system gains is introduced that employs empirical measures from multiple sensor thresholds and optimizes their convex combinations strong convergence of the algorithm is first derived the algorithm is then extended to a scenario of system identification with communication constraints in which the sensor output is transmitted through a noisy communication channel and observed after transmission the main results of this paper demonstrate that these algorithms achieve the cramer rao lower bounds asymptotically and hence are asymptotically efficient algorithms furthermore under some mild regularity conditions these optimal algorithms achieve error bounds that approach optimal error bounds of linear sensors when the number of thresholds becomes large these results are further extended to finite impulse response and rational transfer function models when the inputs are designed to be periodic and full rank

hybrid filtering for linear systems with non gaussian disturbances this paper is concerned with hybrid filtering of a non gaussian system coupled by a hidden switching process an optimal control approach is used to derive a finite dimensional recursive filter that is optimal in the sense of the most probable trajectory mpt estimate an approximate scheme is obtained when the probability distribution of the switching process converges to a limiting distribution which is often easier to obtain numerical examples are considered and computational experiments are reported in these examples our schemes outperform popular filtering schemes available in the literature

nonlinear filtering and control of a switching diffusion with small observation noise this paper is concerned with nonlinear filtering and control of a switching diffusion coupled by an unknown markov chain two statistical estimation methods are used to track the unknown markov chain computable approximate filters are obtained based on these methods the filters are then used to construct controls for the partially observed system these controls are shown to be asymptotically optimal as the observation noise tends to zero finally an example is considered and numerical experiments are reported

a crame spl acute r rao type estimation lower bound for systems with measurement faults a crame spl acute r rao type lower bound is presented for systems with measurements prone to discretely distributed faults which are a class of hybrid systems lower bounds for both the state and the markovian interruption variables fault indicators of the system are derived using the recently presented sequential version of the crame spl acute r rao lower bound crlb for general nonlinear systems because of the hybrid nature of the systems addressed the crlb cannot be directly applied due to violation of its associated regularity conditions to facilitate the calculation of the lower bound the hybrid system is first approximated by a system in which the discrete distribution of the fault indicators is replaced by an approximating continuous one the lower bound is then obtained via a limiting process applied to the approximating system the results presented herein facilitate a relatively simple calculation of a nontrivial lower bound for the state vector of systems with fault prone measurements the crlb type lower bound for the interruption process variables turns out to be trivially zero however a nontrivial non crlb type bound for these variables has been recently presented elsewhere by the authors the utility and applicability of the proposed lower bound are demonstrated via a numerical example involving a simple global positioning system gps aided navigation system where the gps measurements are fault prone due to their sensitivity to multipath errors

a detector based approach for the h_ 2 control of markov jump linear systems with partial information in this paper we study the h 2 control for discrete time markov jump linear systems mjls with partial information we consider the case in which we do not have access to the markov jump parameter but instead there is a detector that emits signals which provides information on this parameter a salient feature of our formulation is that it encompasses for instance the cases with perfect information no information and cluster observations of the markov parameter which were previously analyzed in the markov jump control literature the goal is to derive a feedback linear control using the information provided by the detector in order to stochastically stabilize the closed loop system we present two lyapunov like equations for the stochastic stability of the system in addition we show that a linear matrix inequalities lmi formulation can be obtained in order to design a stochastically stabilizing feedback control in the sequel we deal with the h 2 control problem and we show that again an lmi optimization problem can be formulated in order to design a stochastically stabilizing feedback control with guaranteed h 2 cost we also present two special cases one of them always satisfied for the limit case in which the detector provides perfect information on the markov parameter and the bernoulli jump case under which lmi conditions become necessary and sufficient for the stochastic stabilizability of the system and the lmi optimization problems provide the optimal h 2 cost for the bernoulli jump case we show that our formulation generalizes previous ones the case with convex polytopic uncertainty on the parameters of the system and on the transition probability matrix is also considered the paper is concluded with some numerical examples

stochastic adaptive one step ahead optimal controllers based on input matching optimal adaptive controller based on the els algorithm is established using the input matching technique the control signal is reduced to a constant weighted sum of the measurable information state vector components using a one step ahead quadratic cost function to govern the behavior of the stochastic linear systems the control effort can be estimated globally the algorithm also predicts the convergence rate with no excitation condition the closed loop system is globally stable and the input converges to the one step ahead optimal input

quadratic control with partial information for discrete time jump systems with the markov chain in a general borel space this paper deals with the finite horizon quadratic optimal control problem of discrete time markov jump linear systems mjls considering the case in which the markov chain takes values in a general borel space s it is assumed that the controller has access to an output variable as well as the jump parameter the goal is to design a dynamic markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time it is shown that an optimal controller can be obtained from two s coupled difference riccati equations one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available by s coupled it is meant that the difference riccati equations are coupled via an integral over s this result which can be seen as a separation principle for discrete time mjls generalizes previous ones that were restricted to the markov chain taking values in a finite set

almost sure convergence rates for system identification using binary quantized and regular sensors abstract this paper presents almost sure convergence rates for system identification under binary quantized and regular sensors to accommodate practical model complexity constraints the system under consideration is represented by a modeled part together with an unknown but bounded unmodeled dynamics under uncorrelated noise sequences identification errors with different sensor types are studied and tight error bounds are obtained without information or constraints on noise moment conditions the results are then extended to correlated noise sequences whose remote past and distant future are asymptotically independent in both cases almost sure error bounds of the laws of iterated logarithms type are derived

lyapunov coupled equations for continuous time infinite markov jump linear systems this paper deals with lyapunov equations for continuous time markov jump linear systems mjls out of the bent which wends most of the literature on mjls we focus here on the case in which the markov chain has a countably infinite state space it is shown that the infinite mjls is stochastically stabilizable ss if and only if the associated countably infinite coupled lyapunov equations have a unique norm bounded strictly positive solution it is worth mentioning here that this result do not hold for mean square stabilizability mss since ss and mss are no longer equivalent in our set up see e g j baczynski optimal control for continuous time lq problems with infinite markov jump parameters ph d thesis federal university of rio de janeiro ufrj coppe 2000 to some extent a decomplexification technique and tools from operator theory in banach space and in particular from semigroup theory are the very technical underpinning of the paper

parameter estimation in systems with binary valued observations and structural uncertainties this paper studies identification of linear systems with binary valued observations generated via fixed thresholds in addition to stochastic measurement noises the systems are also subject to structural uncertainties including deterministic unmodelled dynamics nonlinear model mismatch and sensor observation bias since binary valued observations can supply only limited information on the signals truncated empirical measures are introduced to extract further information for system identification an effective identification algorithm is constructed based on the proposed empirical measures optimal identification errors time complexity optimal input design and impact of disturbances unmodelled dynamics observation bias and nonlinear model mismatch are thoroughly investigated in a stochastic information framework asymptotic upper and lower bounds are established on identification errors numerical experiments are presented to demonstrate the effectiveness of the algorithms and the main results

least mean square algorithms with markov regime switching limit we analyze the tracking performance of the least mean square lms algorithm for adaptively estimating a time varying parameter that evolves according to a finite state markov chain we assume the markov chain jumps infrequently between the finite states at the same rate of change as the lms algorithm we derive mean square estimation error bounds for the tracking error of the lms algorithm using perturbed lyapunov function methods then combining results in two time scale markov chains with weak convergence methods for stochastic approximation we derive the limit dynamics satisfied by continuous time interpolation of the estimates unlike most previous analyzes of stochastic approximation algorithms the limit we obtain is a system of ordinary differential equations with regime switching controlled by a continuous time markov chain next to analyze the rate of convergence we take a continuous time interpolation of a scaled sequence of the error sequence and derive its diffusion limit somewhat remarkably for correlated regression vectors we obtain a jump markov diffusion finally two novel examples of the analysis are given for state estimation of hidden markov models hmms and adaptive interference suppression in wireless code division multiple access cdma networks

spectral geometry of singular riemannian spaces on considere la trace du noyau de la chaleur et l application de la methode de l equation de la chaleur au theoreme d indice pour la caracteristique d euler et des complexes signatures

symplectic structures on gauge theory we study certain natural differential forms and their equivariant extensions on the space of connections these forms are defined using the family local index theorem when the base manifold is symplectic they define a family of symplectic forms on the space of connections we will explain their relationships with the einstein metric and the stability of vector bundles these forms also determine primary and secondary characteristic forms and their higher level generalizations

mean field stochastic linear quadratic optimal control with markov jump parameters abstract this paper considers a class of mean field stochastic linear quadratic optimal control problems with markov jump parameters the new feature of these problems is that means of state and control are incorporated into the systems and the cost functional based on the modes of markov chain the corresponding decomposition technique of augmented state and control is introduced it is shown that under some appropriate conditions there exists a unique optimal control which can be explicitly given via solutions of two generalized difference riccati equations a numerical example sheds light on the theoretical results established

identification of systems with regime switching and unmodeled dynamics this paper is concerned with persistent identification of systems that involve deterministic unmodeled dynamics and stochastic observation disturbances and whose unknown parameters switch values possibly large jumps that can be represented by a markov chain two classes of problems are considered in the first class the switching parameters are stochastic processes modeled by irreducible and aperiodic markov chains with transition rates sufficiently faster than adaptation rates of the identification algorithms in this case tracking real time parameters by output observations becomes impossible and we show that an averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and can be estimated with periodic inputs and least squares type algorithms upper and lower error bounds are established that explicitly show impact of unmodeled dynamics in contrast the second class of problems represents systems whose state transitions occur infrequently an adaptive algorithm with variable step sizes is introduced for tracking the time varying parameters convergence and error bounds are derived numerical results are presented to illustrate the performance of the algorithm

on the adaptive stabilization of linear systems abstract the problem of adaptively stabilizing a linear system to zero is addressed a new result is presented showing that a finite family of linear systems is adaptively stabilizable if and only if the family is simultaneously stabilizable in the wellknown algebraic sense this result is all the more surprising as the observations available consist of the signal corrupted by additive white gaussian noise

distributed estimation algorithms for nonlinear systems in this paper we consider the problem of combining the local conditional distributions of a random variable which have been generated by local observers having access to their private information sufficient statistics for the local distributions are communicated to a coordinator who attempts to reconstruct the global centralized distribution using only the communicated statistics we obtain a distributed processing algorithm which recovers exactly the centralized conditional distribution the results can be applied in designing distributed hypothesis testing algorithms for event driven systems

optimal policies for passive learning controllers abstract this paper deals with the optimal control of unknown parameter partially observed linear discrete time systems the objective of the paper is to find a suitable cost functional for which passive learning controllers are optimal it is shown that if there are parameter uncertainties in the observation equation then a quadratic functional can be found such that a passively adaptive closed loop control law is optimal with respect to this functional if there are also parameter uncertainties in the system equation then a quadratic functional can be found such that a passively adaptive open loop feedback control law is optimal with respect to this functional

the certainty equivalence property in stochastic control theory in this paper we will give a general formulation of the certainty equivalence principle for stochastic optimal control problems special attention is paid to the question what do we mean by a certainty equivalence control law it is then shown that in this context the lqg problem is indeed certainty equivalent

regime switching stochastic approximation algorithms with application to adaptive discrete stochastic optimization this work is devoted to a class of stochastic approximation problems with regime switching modulated by a discrete time markov chain our motivation stems from using stochastic recursive algorithms for tracking markovian parameters such as those in spreading code optimization in cdma code division multiple access wireless communication the algorithm uses constant step size to update the increments of a sequence of occupation measures it is proved that least squares estimates of the tracking errors can be developed assume that the adaptation rate is of the same order of magnitude as that of the time varying parameter which is more difficult to deal with than that of slower parameter variations due to the time varying characteristics and markovian jumps the usual stochastic approximation sa techniques cannot be carried over in the analysis by a combined use of the sa method and two time scale markov chains asymptotic properties of the algorithm are obtained which are distinct from the usual sa

two time scale approximation for wonham filters this paper is concerned with approximation of wonham filters a focal point is that the underlying hidden markov chain has a large state space to reduce computational complexity a two time scale approach is developed under time scale separation the state space of the underlying markov chain is divided into a number of groups such that the chain jumps rapidly within each group and switches occasionally from one group to another such structure gives rise to a limit wonham filter that preserves the main features of the filtering process but has a much smaller dimension and therefore is easier to compute using the limit filter enables us to develop efficient approximations and useful filters for hidden markov chains the main advantage of our approach is the reduction of dimensionality

optimal control of unknown parameter systems the problem is discussed of finding a cost functional for which an adaptive control law is optimal the system under consideration is a partially observed linear stochastic system with unknown parameters it is well known that an optimal finite dimensional filter for this problem can be derived when the parameters belong to a finite set since the optimal filter involves the evaluation of a finite set of a posteriori probabilities for each of the parameter values given the observations a natural adaptive control scheme is i develop the optimal linear feedback law given each parameter ii use the a posteriori probabilities to form the weighted average convex combination of the individual control policies and iii use the weighted average as the control law a quadratic cost functional is devised for which this strategy is optimal in a general case and it is shown that the probing effect identified with dual control problems is inherent in the standard linear quadratic gaussian problem with parameter uncertainty

hidden markov processes an overview of statistical and information theoretic aspects of hidden markov processes hmps is presented an hmp is a discrete time finite state homogeneous markov chain observed through a discrete time memoryless invariant channel in recent years the work of baum and petrie 1966 on finite state finite alphabet hmps was expanded to hmps with finite as well as continuous state spaces and a general alphabet in particular statistical properties and ergodic theorems for relative entropy densities of hmps were developed consistency and asymptotic normality of the maximum likelihood ml parameter estimator were proved under some mild conditions similar results were established for switching autoregressive processes these processes generalize hmps new algorithms were developed for estimating the state parameter and order of an hmp for universal coding and classification of hmps and for universal decoding of hidden markov channels these and other related topics are reviewed

brief paper on the adaptive control of a class of systems with random parameters and disturbances the adaptive control of discrete time parameter linear stochastic systems with random parameters is investigated it is shown that systems whose unknown autoregressive parameters undergo bounded martingale difference disturbances may be stabilized by the application of the so called modified least squares adaptive control algorithm asymptotically the sample mean square performance criterion is equal to the one step ahead minimum variance control loss which equals the prediction error variance when the system parameters are known plus a term which is bounded by a quantity proportional to the square of the bound on the parameter disturbance this latter term may be interpreted as the increase in the prediction error variance due to the random parameter variation

embedding adaptive jlqg into lq martingale control with a completely observable stochastic control matrix with jump linear quadratic gaussian jlqg control one refers to the control under a quadratic performance criterion of a linear gaussian system the coefficients of which are completely observable while they are jumping according to a finite state markov process with adaptive jlqg one refers to the more complicated situation that the finite state process is only partially observable although many practically applicable results have been developed jlqg and adaptive jlqg control are lagging behind those for linear quadratic gaussian lqg and adaptive lqg the aim of this paper is to help improve the situation by introducing an exact transformation which embeds adaptive jlqg control into lqm linear quadratic martingale control with a completely observable stochastic control matrix by lqm control the authors mean the control of a martingale driven linear system under a quadratic performance criterion with the lqm transformation the adaptive jlqg control can be studied within the framework of robust or minimax control without the need for the usual approach of averaging or approximating the adaptive jlqg dynamics to show the effectiveness of the authors transformation it is used to characterize the open loop optimal feedback olof policy for adaptive jlqg control

fast identification n widths and uncertainty principles for lti and slowly varying systems the optimal worst case uncertainty that can be achieved by identification depends on the observation time in the first part of the paper this dependence is evaluated for selected linear time invariant systems in the l sup 1 and h sup spl infin norms and shown to be derivable from a monotonicity principle the minimal time required is shown to depend on the metric complexity of the a priori information set two notions of n width or metric dimension are introduced to characterize this complexity in the second part of the paper the results are applied to systems in which the law governing the evolution of the uncertain elements is not time invariant such systems cannot be identified accurately the inherent uncertainty is bounded in the case of slow time variation the n widths and related optimal inputs provide benchmarks for the evaluation of actual inputs occurring in adaptive feedback systems

asymptotically optimal controls of hybrid linear quadratic regulators in discrete time this work develops asymptotically optimal controls for a class of discrete time hybrid systems involving singularly perturbed markov chains having weak and strong interactions the state space of the underlying markov chain is decomposed into a number of recurrent classes and a group of transient states using a hierarchical control approach by aggregating the states in each recurrent class into a single state a continuous time quadratic limit control problem in which the resulting limit markov chain has much smaller state space is derived using the optimal control for the limit problem a control for the original problem is constructed which is shown to be nearly optimal finally a numerical example is given to demonstrate the effectiveness of the approximation scheme

optimal adaptive control and stabilization of families of linear systems a natural adaptive linear quadratic regulator is studied the optimal control is shown to be the best estimate given the observation of the linear quadratic control computed assuming that the true parameter were known moreover this optimal control is stabilizing the new ingredient that makes these results possible is the introduction of the concept of entropy into linear quadratic control

stabilizing control law for hybrid models this note is concerned with the adaptive stabilizing control problem for jump markov systems a new control law is proposed based on a simple set of algebraic sufficient conditions it is shown that this approach can be used for a class of stochastic models for which the more restrictive solution proposed by caines and zhang 1992 does not apply

optimal stochastic adaptive control with quadratic index the discrete time stochastic control system with complete observation is considered with quadratic loss function when the constant coefficients of the system are unknown the parameter estimates given by the recursive least squares method are used to define the feedback gain and the adaptive control is taken to be either a linear state feedback disturbed by a sequence of random vectors with variances tending to zero or only the disturbance without the feedback term in accordance with stopping times defined on the trajectory of the system it is proved that the parameter estimates are strongly consistent and the loss function reaches its minimum i e the adaptive control is optimal

nonlinear filtering for systems with random structure this note studies the nonlinear filtering problem for a linear system with random structure governed by a finite state markov process a characterization of the optimal mean square filter is derived and some suboptimal filter approximations are presented

optimal control for continuous time linear quadratic problems with infinite markov jump parameters the subject matter of this paper is the optimal control problem for continuous time linear systems subject to markovian jumps in the parameters and the usual infinite time horizon quadratic cost what essentially distinguishes our problem from previous ones inter alia is that the markov chain takes values on a countably infinite set to tackle our problem we make use of powerful tools from semigroup theory in banach space and a decomplexification technique the solution for the problem relies in part on the study of a countably infinite set of coupled algebraic riccati equations icare conditions for existence and uniqueness of a positive semidefinite solution of the icare are obtained via the extended concepts of stochastic stabilizability ss and stochastic detectability sd these concepts are couched into the theory of operators in banach space and parallel to the classical linear quadratic lq case bound up with the spectrum of a certain infinite dimensional linear operator

stabilization of jump linear gaussian systems without mode observations systems such as those subject to abrupt changes including failure or those with uncertain dynamic model or more than one possible model can be naturally modelled as jump linear jl systems because of their applications in fields such as tracking fault tolerant control manufacturing process and robots jl systems have drawn extensive attention the optimal control and stabilization problem for jl systems when the mode system model is not assumed to be directly and perfectly observed a realistic assumption in many applications is nonlinear and prohibitive both analytically and computationally because of the dual effect the main contribution of this work is the sufficient condition for stabilization for a class of adaptive controllers when the mode is not directly observed we first present the optimal controller under an assumption of a certain type of mode availability using this optimal feedback gain we derive a condition that ensures the stabilizing property for a class of adaptive cont

intersection homology ii in 19 20 we introduced topological invariants ih x called intersection homology groups for the study of singular spaces x these groups depend on the choice of a perversity p a perversity is a function from 2 3 to the non negative integers such that both c and c 2 c are positive and increasing functions of c 2 1 the group ihr is defined for spaces x called pseudomanifolds a pseudomanifold of dimension n is a space that admits a stratification x x n x n z x n 3 x 1 x 0

the analysis of elliptic families i metrics and connections on determinant bundles in this paper we construct the quillen metric on the determinant bundle associated with a family of elliptic first order differential operators we also introduce a unitary connection on and calculate its curvature our results will be applied to the case of dirac operators in a forthcoming paper

analytic torsion and r torsion for unimodular representations let m be a closed c manifold of dimension n both r torsion and analytic torsion are smooth invariants of acyclic orthogonal or unitary representations p of the fundamental group 7i m the reidemeister franz torsion or r torsion tm p of p is defined in terms of the combinatorial structure of m given by its smooth triangulations the analytic torsion tm p was introduced by ray and singer rs as an analytic counterpart of r torsion in order to define the analytic torsion one has to choose a riemannian metric on m then tm p is a certain weighted alternating product of regularized determinants of the laplacians on differential qforms of m with values in the flat bundle e defined by p it was conjectured by ray and singer rs that tm p trm p for all acyclic orthogonal or unitary representations p this conjecture was proved independently by cheeger c and the author mu the restriction to orthogonal or unitary representations is certainly a limitation of the applicability of this result if 7i m is infinite because an infinite discrete group will have in general many nonorthogonal finite dimensional representations it is the purpose of the present paper to remove this limitation we call a representation p r m gl e on a finite dimensional real or complex vector space e unimodular if i det p y i 1 for all y e i m then we define r torsion and analytic torsion for unimodular representations and the main result is that for odd dimensional manifolds m the equality of the two torsions extends to all unimodular representations

optimal adaptive lqg control for systems with finite state process parameters the situation where a totally observed process y t is generated by a stochastic differential equation whose parameters evolve on a finite set 1 n according to a stochastic differential equation is considered the optimal control law is sought with respect to quadratic loss functions on y t and the control u t the auxiliary p d e technique of hijab 6 is used together with a nonlinear filter to obtain the solution whose existence depends upon that of a smooth solution to the auxiliary p d e and strong solutions to the system s d e under the given control inputs

the adaptive lqg problem part i this paper is concerned with a rigorous study of the dual control problem of fel dbaum i e the lqg optimal control problem in the presence of bayesian parameter uncertainty the solution of this problem involves two parts one relating to filtering and one to control although we establish our filtering result in complete generality in the last section most of the paper concentrates on the finite parameter case to ease the exposition the control result that we establish is incomplete in the sense that the smoothness of the optimal cost function is assumed rather than proved nevertheless our results and methods are such that we arrive at a new proof of the classical separation theorem showing that the well known lqg feedback law is optimal within the widest possible class of admissible controls as this new proof avoids all talk of dependence of the sigma algebra on the control weak solutions measure transformation techniques etc we feel that this result will help to clarify what is involved in the classical separation theorem

riemannian geometry over different normed division algebras we develop a unifed theory to study geometry of manifolds with different holonomy groups they are classified by 1 real complex quaternion or octonion number in the appropriate cases and 2 being special or not specialty is an orientation with respect to the corresponding normed algebra mathbb a for example special riemannian mathbb a manifolds are oriented riemannian calabi yau hyperkahler and g 2 manifolds respectively for vector bundles over such manifolds we introduce special mathbb a connections they include holomorphic hermitian yang mills anti self dual and donaldson thomas connections similarly we introduce special frac 1 2 mathbb a lagrangian submanifolds as maximally real submanifolds they include special lagrangian complex lagrangian cayley and co associative submanifolds we also discuss geometric dualities from this viewpoint fourier transformations on mathbb a geometry for flat tori and a conjectural syz mirror transformation from special mathbb a geometry to special frac 1 2 mathbb a lagrangian geometry on mirror special mathbb a manifolds

control of discrete time hybrid stochastic systems a realistic stochastic control problem for hybrid systems with markovian jump parameters can have switching parameters in both the state and the measurement equations furthermore both the base and jump states in general are not perfectly observed there are only two existing controllers for this problem both with complexity exponentially increasing with time the authors present another control algorithm for stochastic systems with markovian jump parameters this algorithm is derived through the use of stochastic dynamic programming and is designed to be used for realistic stochastic control problems i e with noisy state observations this scheme has fixed computational requirements at each stage and a natural parallel implementation simulation results are used to compare the algorithm with previous schemes

jump linear quadratic gaussian control in continuous time the optimal quadratic control of continuous time linear systems that possess randomly jumping parameters which can be described by finite state markov processes is addressed the systems are also subject to gaussian input and measurement noise the optimal solution for the jump linear quadratic gaussian jlqc problem is given this solution is based on a separation theorem the optimal state estimator is sample path dependent if the plant parameters are constant in each value of the underlying jumping process then the controller portion of the compensator converges to a time invariant control law however the filter portion of the optimal infinite time horizon jlqc compensator is not time invariant thus a suboptimal filter which does converge to a steady state solution under certain conditions is derived and a time invariant compensator is obtained

on the adaptive control for jump parameter systems vianonlinear filtering in this paper we first present an error analysis for the process of estimates generated by the wonham filter when it is used for the estimation of the finite set valued jump markov parameters of a random parameter linear stochastic system and further give bounds on certain functions of these estimates we then consider a certainty equivalence adaptive linear quadratic gaussian feedback control law using the estimates generated by the nonlinear filter and demonstrate the global existence of solutions to the resulting closed loop system a stochastic lyapunov analysis establishes that the certainty equivalence law stabilizes the markov jump parameter linear system in the mean square average sense the conditions for this result are that certain products of i the parameter process jump rate and ii the solution of the control riccati equation and its second derivatives should be less than certain given bounds an example is given where the controlled linear system has state dimension 2 finally the stabilizing properties of certainty equivalence laws which depend on i the maximum likelihood estimate of the parameter value and ii a modified version of this estimate are established under certain conditions

tracking and identification of regime switching systems using binary sensors this work is concerned with tracking and system identification for time varying parameters the parameters are markov chains and the observations are binary valued with noise corruption to overcome the difficulties due to the limited measurement information wonham type filters are developed first then based on the filters two popular estimators namely mean squares estimator msq and maximum posterior map estimator are constructed for the mean squares estimator we derive asymptotic normality in the sense of weak convergence and in the sense of strong approximation the asymptotic normality is then used to derive error bounds when the markov chain is infrequently switching we derive error bounds for map estimators when the markovian parameters are fast varying we show that the averaged behavior of the parameter process can be derived from the stationary measure of the markov chain and that can be estimated using empirical measures upper and lower error bounds on estimation errors are also established

averaged dynamics and pole assignment for a class of stochastic systems for a linear system with markov jump parameters the moment liapunov exponents are computed explicitly in terms of averaged dynamics besides giving a necessary and sufficient condition for moment stability the computation suggests that control design for these systems can be aimed at assigning desired closed loop eigenvalues this is shown to be equivalent to a decentralized control problem to which the homotopy method applies and the control gains are obtained by continuation from the solution of the decoupled no jump problem

optimal control of jump linear gaussian systems this paper investigates the problem of controlling a discrete time linear system with jump parameters a review of the literature is presented as well as a development of the application of dynamic programming to this class of control problems dynamic programming has been applied by many researchers and it was observed that no closed form analytical solution could be constructed because of the dual aspects of the controller the main contribution of the present work is an algorithm suitable for computer implementation for the optimal dual control the construction of the algorithm is based on transforming the dynamic programming relations into a space of sufficient statistics and using a finite dimensional optimization procedure to obtain the optimal control as a function of the statistics this is achieved by first developing a suitable recursive realization of a filter which generates the sufficient statistics for the problem and then embedding this filter into the dynamic programming equations

robust output feedback h control of uncertain markovian jump systems with mode dependent time delays this paper describes the synthesis of robust output feedback h control for a class of uncertain markovian jump linear systems with time delays which are time varying and depend on the system modes of operation under the assumption of known bounds of system uncertainties and the control system gain variations we present sufficient conditions on the existence of robust stochastic stability and disturbance h attenuation through the changes of variables and schur complements these sufficient conditions can be rewritten in a set of coupled linear matrix inequalities with which robust control can be easily constructed as an added advantage the control design depends only on the measured parameter of markovian jumping at time t which might be corrupted by measurement noises numerical examples are provided to demonstrate the effectiveness of the proposed approach

transition probability bounds for the stochastic stability robustness of continuous and discrete time markovian jump linear systems this paper considers the robustness of stochastic stability of markovian jump linear systems in continuous and discrete time with respect to their transition rates and probabilities respectively the continuous time discrete time system is described via a continuous valued state vector and a discrete valued mode which varies according to a markov process chain by using stochastic lyapunov function approach and kronecker product transformation techniques sufficient conditions are obtained for the robust stochastic stability of the underlying systems which are in terms of upper bounds on the perturbed transition rates and probabilities analytical expressions are derived for scalar systems which are straightforward to use numerical examples are presented to show the potential of the proposed techniques

frequency domain tracking characteristics of adaptive algorithms the problem of tracking time varying linear systems is discussed the focus is on the model quality in terms of the mean square error mse between the true momentary transfer function and the estimated one this mse is thus a function of frequency the exact expression for the mse is complicated but simple expressions that are asymptotic in the model order are developed for model structures of finite impulse response fir character simulations verify that these simple expressions are quite reliable and insightful even for moderate model orders expressions are developed for three basic adaptation algorithms recursive identification algorithms viz the least mean squares algorithm the recursive least squares algorithm with exponential forgetting and a tracking algorithm based on the kalman filter the results apply both to slowly time varying systems and to the model recovery after an abrupt change in the system dynamics

the solution of a partially observed stochastic optimal control problem in terms of predicted miss the explicit solution of a partially observed lq problem driven by a combination of a wiener process and an unobserved finite state jump markov process is given applications of the model include guidance problems where the jump markov process models evasive maneuvers acceleration values of the target or systems subject to a sequence of failures that can be modeled by a jump markov process

stochastic dynamic programming caution and probing the purpose of this paper is to unify the concepts of caution and probing put forth by feldbaum 14 with the mathematical technique of stochastic dynamic programming originated by bellman 5 the decomposition of the expected cost in a stochastic control problem recently developed in 8 is used to assess quantitatively the caution and probing effects of the system uncertainties on the control it is shown how in some problems because of the uncertainties the control becomes cautious less aggressive while in other problems it will probe by becoming more aggressive in order to enhance the estimation identification while controlling the system following this a classification of stochastic control problems according to the dominant effect is discussed this is then used to point out which are the stochastic control problems where substantial improvements can be expected from using a sophisticated algorithm versus a simple one

optimal design of networked control systems computer control via asynchronous communication channels we study a linear discrete time partially observed system perturbed by white noises the observations are transmitted to the controller and its outputs are sent to the actuators via communication channels that provide random transmission times and may lose messages various signals may incur independent delays and arrive at the destination point out of order under certain assumptions a recursive minimum variance state estimator is proposed a finite horizon linear quadratic optimal control problem is also solved

a separation principle for the continuous time lq problem with markovian jump parameters in this paper we devise a separation principle for the finite horizon quadratic optimal control problem of continuous time markovian jump linear systems driven by a wiener process and with partial observations we assume that the output variable and the jump parameters are available to the controller it is desired to design a dynamic markovian jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time as in the case with no jumps we show that an optimal controller can be obtained from two coupled riccati differential equations one associated to the optimal control problem when the state variable is available and the other one associated to the optimal filtering problem this is a separation principle for the finite horizon quadratic optimal control problem for continuous time markovian jump linear systems for the case in which the matrices are all time invariant we analyze the asymptotic behavior of the solution of the derived interconnected riccati differential equations to the solution of the associated set of coupled algebraic riccati equations as well as the mean square stabilizing property of this limiting solution when there is only one mode of operation our results coincide with the traditional ones for the lqg control of continuous time linear systems

joint identification of plant rational models and noise distribution functions using binary valued observations system identification of plants with binary valued output observations is of importance in understanding modeling capability and limitations for systems with limited sensor information establishing relationships between communication resource limitations and identification complexity and studying sensor networks this paper resolves two issues arising in such system identification problems first regression structures for identifying a rational model contain non smooth nonlinearities leading to a difficult nonlinear filtering problem by introducing a two step identification procedure that employs periodic signals empirical measures and identifiability features rational models can be identified without resorting to complicated nonlinear searching algorithms second by formulating a joint identification problem we are able to accommodate scenarios in which noise distribution functions are unknown convergence of parameter estimates is established recursive algorithms for joint identification and their key properties are further developed

an exact formula for a linear quadratic adaptive stochastic optimal control law for a linear quadratic adaptive stochastic optimal control problem a formula for the optimal control is obtained by applying variational methods to an equivalent problem obtained from the girsanov transformation the formula does depend on a quantity defined through a martingale representation of the conditional remaining cost

anti self dual yang mills connections over complex algebraic surfaces and stable vector bundles on presente une correspondance entre la geometrie algebrique et la geometrie differentielle des fibres vectoriels soit une surface algebrique projective x qui a un plongement donne x cp n et soit une metrique de kahler sur x dont la classe de cohomologie associee est duale a la classe de section d hyperplan h un fibre sur x est stable par rapport au plongement projectif si et seulement si il admet une connexion irreductible d hermite einstein par rapport a la metrique cette connexion est alors unique

on a partially observable lqg problem for systems with markovian jumping parameters in this paper a variant of the lqg problem for systems with markovian jumping parameters is studied it is assumed that the system is partially observable in the sense that we do not have access to the jumping parameter via nonlinear filtering the problem is recast as one with complete information it is then shown that a certain averaged control is an optimal policy vis a vis a modified quadratic cost apart from its intrinsic theoretical interest this result has an important bearing on a number of different analyses related with the original quadratic cost

performance analysis of general tracking algorithms a general family of tracking algorithms for linear regression models is studied it includes the familiar least mean square gradient approach recursive least squares and kalman filter based estimators the exact expressions for the quality of the obtained estimates are complicated approximate and easy to use expressions for the covariance matrix of the parameter tracking error are developed these are applicable over the whole time interval including the transient and the approximation error can be explicitly calculated

control of nonlinear systems with markovian parameter changes the control of hybrid systems in which a totally observed state process is generated by a nonlinear stochastic differential equation whose parameters are functions of a random jump process called the plant regime is considered regime transitions typically represent target maneuvers in a tracking system the control task is split between a jump detection and identification jdi filter and a discrete adaption or reconfiguration a design that takes into account the errors of the jdi device and the plant nonlinearities to produce a near optimal passively adaptive control law with an easily implemented affine structure is presented

identification input design for consistent parameter estimation of linear systems with binary valued output observations input design is of essential importance in system identification for providing sufficient probing capabilities to guarantee convergence of parameter estimates to their true values this paper presents conditions on input signals that characterize their probing richness for strongly consistent parameter estimation of linear systems with binary valued output observations necessary and sufficient conditions on periodic signals are derived for sufficient richness these conditions are further studied under different system configurations including open loop and feedback systems and different scenarios of noises including actuator noise input measurement noise and output measurement noise in addition to system parameter estimation essential properties of identifiability and input conditions are also derived when sensor thresholds or noise distribution functions are unknown the findings of this paper provide a foundation to study identification of systems that either use binary valued or quantized sensors or involve communication channels which mandate quantization of signals

spreading code optimization and adaptation in cdma via discrete stochastic approximation the aim of this paper is to develop discrete stochastic approximation algorithms that adaptively optimize the spreading codes of users in a code division multiple access cdma system employing linear minimum mean square error mmse receivers the proposed algorithms are able to adapt to slowly time varying channel conditions one of the most important properties of the algorithms is their self learning capability they spend most of the computational effort at the global optimizer of the objective function tracking analysis of the adaptive algorithms is presented together with mean square convergence an adaptive step size algorithm is also presented for optimally adjusting the step size based on the observations numerical examples illustrating the performance of the algorithms in multipath fading channels show substantial improvement over heuristic algorithms