adaptive control of linear systems with markov perturbations the stochastic model considered is a linear jump diffusion process x for which the coefficients and the jump processes depend on a markov chain z with finite state space first we study the optimal filtering and control problem for these systems with non gaussian initial conditions given noisy observations of the state x and perfect measurements of z we derive a new sufficient condition which ensures the existence and the uniqueness of the solution of the nonlinear stochastic differential equations satisfied by the output of the filter we study a quadratic control problem and show that the separation principle holds next we investigate an adaptive control problem for a state process x defined by a linear diffusion for which the coefficients depend on a markov chain the processes x and z being observed in independent white noises suboptimal estimates for the process x z and approximate control law are investigated for a large class of probability distributions of the initial state asymptotic properties of these filters and this control law are obtained upper bounds for the corresponding error are given

a quadratic bolza type problem in a riemannian manifold abstract a classical nonlinear equation d s x x v x s 0 on a complete riemannian manifold m is considered the existence of solutions connecting any two points x 0 x 1 m is studied i e for t 0 the critical points of the functional j t x 1 2 0 t x x ds 0 t v x s ds with x 0 x0 x t x1 when the potential v has a subquadratic growth with respect to x jt admits a minimum critical point for any t 0 infinitely many critical points if the topology of m is not trivial when v has an at most quadratic growth i e v x s d 2 x x k this property does not hold but an optimal arrival time t 0 exists such that if 0 m can be joined by a critical point of the corresponding functional for the existence and multiplicity results variational methods and ljusternik schnirelman theory are used the optimal value t 2 is fulfilled by the harmonic oscillator these ideas work for other related problems

robust linear filtering for discrete time hybrid markov linear systems in this paper we consider the robust linear filtering of hybrid discrete time markovian jump linear systems we assume that only an output of the system is available and therefore the values of the jump parameter are not known it is desired to design a dynamic linear filter such that the closed loop system is mean square stable and minimizes the stationary expected value of the square error we consider uncertainties on the parameters of the possible modes of operation of the system a linear matrix inequalities lmi formulation is proposed to solve the problem for the case in which there are no uncertainties on the modes of operation of the system we show that the lmi formulation provides a filter with the same stationary mean square error as the one obtained from the riccati equation approach

distributed robust estimation over randomly switching networks using h consensus the paper considers a distributed robust estimation problem over a network with markovian randomly varying topology the objective is to deal with network variations locally by switching observer gains at affected nodes only we propose sufficient conditions which guarantee a suboptimal h level of relative disagreement of estimates in such observer networks when the status of the network is known globally these sufficient conditions enable the network gains to be computed by solving certain lmis when the nodes are to rely on a locally available information about the network topology additional rank constraints are used to condition the gains given this information the results are complemented by necessary conditions which relate properties of the interconnection graph laplacian to the mean square detectability of the plant through measurement and interconnection channels

morse index of some min max critical points i application to multiplicity results on donne un resultat general sur des bornes inferieures pour des indices de morse de points critiques obtenus par des principes de min max en combinant cette information avec une inegalite semiclassique on obtient des estimations pointues sur la croissance de certaines valeurs critiques a partir desquelles on deduit de nouveaux resultats de multiplicite pour des solutions d equations elliptiques semi lineaires d ordre 2

distributed robust filtering with h consensus of estimates the paper addresses a problem of design of distributed robust filters using the recent vector dissipativity theory the main result is a sufficient condition which guarantees a suboptimal h level of disagreement of estimates in a network of filters it involves solving a convex optimization feasibility problem subject to lmi constraints the special case of balanced interconnection graphs is also considered a gradient descent type algorithm is presented which allows the nodes to compute their estimator parameters in a decentralized manner the proposed approach is applied to the problem of observer based robust synchronization of a nonlinear network to an isolated node

technical communique a linear distributed filter inspired by the markovian jump linear system filtering problem in this paper we introduce a consensus based distributed filter executed by a sensor network inspired by the markovian jump linear system filtering theory we show that the optimal filtering gains of the markovian jump linear system can be used as an approximate solution of the optimal distributed filtering problem this parallel allows us to interpret each filtering gain corresponding to a mode of operation of the markovian jump linear system as a filtering gain corresponding to a sensor in the network the approximate solution can be implemented distributively and guarantees a quantifiable level of performance

stationary filter for linear minimum mean square error estimator of discrete time markovian jump systems we derive in this paper a stationary filter for the linear minimum mean square error estimator lmmse of discrete time markovian jump linear systems mjlss we obtain the convergence of the error covariance matrix of the lmmse to a stationary value under the assumption of mean square stability of the mjls and ergodicity of the associated markov chain it is shown that there exists a unique solution for the stationary riccati filter equation and moreover this solution is the limit of the error covariance matrix of the lmmse the advantage of this scheme is that it is very easy to implement and all calculations can be performed off line leading to a linear time invariant filter

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

an extension to balanced truncation with application to structured model reduction balanced truncation is a standard method for model reduction possessing many desirable properties such as preservation of model stability and a priori error bounds balanced truncation is conducted using controllability and observability gramians generalized gramians can be found by solving a set of linear matrix inequalities in this paper we show that these linear matrix inequalities can be extended so that the number of decision variables are at least doubled leading to the concept of extended gramians herein it is shown that the desirable properties of balanced truncation also hold with extended gramians the extended gramians are especially useful for improving error bounds and for models possessing additional structural constraints as is demonstrated by means of examples herein

multiple solutions for semilinear elliptic systems with non homogeneous boundary conditions since the early seventies many authors have widely investigated existence and multiplicity of solutions for semilinear elliptic problems with dirichlet boundary conditions especially by means of variational methods see 22 and references therein in particular if is a real l2 function on a bounded domain rn p 2 and pi 2 if n 3 here 2 2n n 2 the following model problem 6u u p 2u in

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

observability through a matrix weighted graph observability of an array of identical linear time invariant systems with incommensurable output matrices is studied where an array is called observable when identically zero relative outputs imply synchronized solutions for the individual systems it is shown that the observability of an array is equivalent to the connectivity of its interconnection graph whose edges are assigned matrix weights moreover to better understand the relative behavior of distant units pairwise observability that concerns with the synchronization of a certain pair of individual systems in the array is studied this milder version of observability is shown to be closely related to certain connectivity properties of the interconnection graph as well pairwise observability is also analyzed using the circuit theoretic tool effective conductance the observability of a certain pair of units is proved to be equivalent to the nonsingularity of the matrix valued effective conductance between the associated pair of nodes of a resistive network with matrix valued parameters whose node admittance matrix is the laplacian of the array s interconnection graph

brief paper detection and estimation for abruptly changing systems the problem of state estimation and system structure detection for discrete stochastic dynamical systems with parameters which may switch among a finite set of values is considered the switchings are modelled by a markov chain with known transition probabilities a brief survey and a unified treatment of the existing suboptimal algorithms are provided the optimal algorithms require exponentially increasing memory and computations with time simulation results comparing the various suboptimal algorithms are presented

design of distributed decentralized estimators for formations with fixed and stochastic communication topologies this paper proposes a solution to the problem of synthesizing distributed decentralized estimators for a formation of agents the collected dynamics of the formation are modeled by a discrete lti system in the considered estimation structure each agent of the formation carries an estimate of the entire formation state agents of the formation can communicate information between each other through unidirectional links modeled with a fixed or a stochastic communication topology the design procedures are based on a set of convex optimization problems with linear matrix inequalities and result in the suboptimal choice of estimator gains which stabilize the estimation error dynamics and minimize a norm of the estimation error correlation matrix

on the bolza problem abstract we consider the following boundary value problem x v x 0 x 0 x 0 x t x 1 where t 0 x 0 x 1 r n are given we prove that this problem has infinitely many solutions provided v is even and superquadratic

on the uniform algebraic observability of multi switching linear systems the main objective of this paper is the characterisation of the notion of uniform algebraic observability for multi switching linear systems in particular it is shown that a multi switching linea

linear minimum mean square error estimation for discrete time markovian jump linear systems the linear minimum mean square error estimator lmmse for discrete time linear systems subject to abrupt changes in the parameters modeled by a markov chain spl theta k spl epsiv 1 n is considered the filter equations are derived from geometric arguments in a recursive form resulting in an on line algorithm suitable for computer implementation the author s approach is based on estimating x k 1 sub spl theta k i instead of estimating directly x k the uncertainty introduced by the markovian jumps increases the dimension of the filter to n n 1 where n is the dimension of the state variable an example where the dimension of the filter can be reduced to n is presented as well as a numerical comparison with the imm filter

index theory nontrivial solutions and asymptotically linear second order hamiltonian systems abstract in this paper we consider the existence and multiplicity of solutions of second order hamiltonian systems we propose a generalized asymptotically linear condition on the gradient of hamiltonian function classify the linear hamiltonian systems prove the monotonicity of the index function and obtain some new conditions on the existence and multiplicity for generalized asymptotically linear hamiltonian systems by global analysis methods such as the leray schauder degree theory the morse theory the ljusternik schnirelman theory etc

multiple solutions for prescribed boundary value problem we in this paper consider the semilinear elliptic boundary value problem u f x u in and u g on and the corresponding bolza problem x v t x 0 x 0 x0 x t x1 where is

decentralized determinantal assignment problem fixed and almost fixed modes and zeros the decentralized determinantal assignment problem ddap is defined as the unifying description for the study of pole and zero assignment problems under decentralized output state feedback dof dsf and decentralized squaring down dsd respectively ddap is reduced to a linear problem of zero assignment of polynomial combinants and a multilinear problem of restricted decomposability of multivectors the decentralization characteristic dc and the decentralized polynomial grassmann representative d s gr of ddap are defined the fixed zero polynomial of ddap is then determined as the zero polynomial of d s gr the canonical d s gr cd r s gr and the decentralized plucker matrix dpm of ddap are introduced and necessary conditions for arbitrary assignment of the non fixed zeros are given in terms of the dpm the family of strongly zero non assignable sna systems is defined and for such systems the notion of the fixed zero is extended to that of the almost fixed zero afz an

quality of trial functions in quadratic isoparametric representation of an arc an examination is made of displacement trial functions found in the quadratic isoparametric representation of an arc special attention is given to the quality of curvature change description and to effective manipulation of the trial functions various interpolation formulae are derived which have relevance to curved shell finite element design under love kirchhoff assumptions

extended h 2 and h norm characterizations and controller parametrizations for discrete time systems this paper presents new synthesis procedures for discrete time linear systems it is based on a recently developed stability condition which contains as particular cases both the celebrated lyapunov theorem for precisely known systems and the quadratic stability condition for systems with uncertain parameters these new synthesis conditions have some nice properties a they can be expressed in terms of lmi linear matrix inequalities and b the optimization variables associated with the controller parameters are independent of the symmetric matrix that defines a quadratic lyapunov function used to test stability this second feature is important for several reasons first structural constraints as those appearing in the decentralized and static output feedback control design can be addressed less conservatively second parameter dependent lyapunov function can be considered with a very positive impact on the design of robust h 2 and h x control problems third the design of controller with mixed

analytical and numerical results for vibration analysis of multi stepped and multi damaged circular arches this paper investigates the in plane linear dynamic behaviour of multi stepped and multi damaged circular arches under different boundary conditions cracked cross sections are modelled as massless elastic rotational hinges in damaged configuration cracks can be located both at the interface between two adjacent portions as well as inside the portion itself for each arch portion bounded by two cracks the differential equations of motion have been established considering axial extension transverse shear effects and rotatory inertia the equilibrium equations of arch portions are combined in the coupled fundamental system in terms of radial displacement tangential displacement and rotation analytical and numerical solutions for multi stepped arches in undamaged as well as in damaged configurations are proposed the analytical solution is based on the euler characteristic exponent procedure involving the roots of characteristic polynomials while the numerical method is focused on the generalized differential quadrature gdq method and the generalized differential quadrature element gdqe technique numerical results are shown in terms of the first 10 analytical and numerical frequencies of multi stepped and multi damaged arches with different boundary conditions finally convergence and stability characteristics of the gdqe procedure are investigated the convergence rate of the natural frequencies is shown to be very fast and the stability of the numerical procedure is very good

optimal linear filtering under parameter uncertainty this paper addresses the problem of designing a guaranteed minimum error variance robust filter for convex bounded parameter uncertainty in the state output and input matrices the design procedure is valid for linear filters that are obtained from the minimization of an upper bound of the error variance holding for all admissible parameter uncertainty the results provided generalize the ones available in the literature to date in several directions first all system matrices can be corrupted by parameter uncertainty and the admissible uncertainty may be structured assuming the order of the uncertain system is known the optimal robust linear filter is proved to be of the same order as the order of the system in the present case of convex bounded parameter uncertainty the basic numerical design tools are linear matrix inequality lmi solvers instead of the riccati equation solvers used for the design of robust filters available in the literature to date the paper that contains the most important and very recent results on robust filtering is used for comparison purposes in particular it is shown that under the same assumptions our results are generally better as far as the minimization of a guaranteed error variance is considered some numerical examples illustrate the theoretical results

a newton like method for solving rank constrained linear matrix inequalities this paper presents a newton like algorithm for solving systems of rank constrained linear matrix inequalities though local quadratic convergence of the algorithm is not a priori guaranteed or observed in all cases numerical experiments including application to an output feedback stabilization problem show the effectiveness of the algorithm

the uniqueness characteristics of mixed finite element methods in linear elasticity having established the non uniqueness in general of quadratic linear functionals in elasticity the investigative work on this topic is reviewed whence it is noted that there is no existing formal approach for the identification of either the causes of singular solutions or suitable remedial measures that might ensure their elimination a comparison of the weighted averages obtained from the single field and reissner s principles is then used to identify a higher order uniqueness criterion for the latter a detailed consideration of the application of the new condition to the arch equations demonstrates how and why singular solutions can be obtained and thence how suitable forms of remedial action can often be identified finally several other classes of problem are briefly investigated in order to show how the criterion can be used to explain the full range of known behaviour of the mixed methods

stability results for discrete time linear systems with markovian jumping parameters stability results for discrete time linear systems subject to random jumps in the parameters are obtained first necessary and sufficient conditions for mean square stability mss including the case in which the system is driven by an independent wide sense stationary random sequence are derived it is shown that mss is equivalent to the spectral radius of an augmented matrix being less than one or to the existence of a solution of a certain lyapunov equation in addition it is shown that the lyapunov equation can be derived in four equivalent forms and as a by product each one gives risc to an easier to check sufficient condition these results give inter alia a unified and rather complete picture for mss of markovian jump linear systems next we derive sufficient conditions for almost sure stability of the noiseless ease finally we conclude by presenting an illustrative application to adaptive filtering where a mild condition for almost sure convergence is provided

technical communique fixed modes in multivariable systems using constrained controllers a general expression is derived relating an arbitrary output feedback controller to the resulting closed loop characteristic polynomial in terms of suitably defined zero polynomials of the system this expression is then used to characterize the fixed modes of a multivariable system with respect to controllers of any desired structure

a new discrete time robust stability condition a new robust stability condition for uncertain discrete time systems with convex polytopic uncertainty is given it enables to check stability using parameter dependent lyapunov functions which are derived from lmi conditions it is shown that this new condition provides better results than the classical quadratic stability besides the use of a parameter dependent lyapunov function this condition exhibits a kind of decoupling between the lyapunov and the system matrices which may be explored for control synthesis purposes a numerical example illustrates the results

infinitely many solutions for quasilinear elliptic equations with lack of symmetry abstract in this paper we look for weak solutions of the quasilinear elliptic model problem div a x u u 1 2 a t x u u 2 g x u h x in u 0 on where r n is a bounded domain n 2 the real terms a x t a t x t a t x t and g x t are caratheodory functions on r and h r is a given measurable map we prove that even if a t x t 0 under suitable assumptions infinitely many solutions exist in spite of the lack of symmetry a suitable supercritical growth is allowed for the nonlinear term g x t we use a variant of the variational perturbation techniques introduced by rabinowitz in rabinowitz 1982 but by means of a weak version of the cerami palais smale condition

multiplicity of periodic solutions for a class of second order perturbed hamiltonian systems abstract consider the following second order perturbed hamiltonian systems u t f u u g t u t r u 0 u t u 0 u t 0 t 0 where f u k u w u k w c 2 r n r g c 2 r r n r with g t t u g t u k and w is even but g t u maybe has no parity in u assume that w is superquadratic and g is subquadratic at the infinity and k satisfies pinched condition the existence of infinitely many periodic solutions of the above perturbed systems is proved via the bolle s perturbation method which is a generalization of 21 theorem 1 2 and 3 theorem 2 in some sense

nonlinear oscillations and boundary value problems for hamiltonian systems we prove the existence of solutions of various boundary value problems for nonautonomous hamiltonian systems with forcing terms begin gathered dot x t h p t x t p t g t hfill dot p t h x t x t p t f t hfill end gathered