a two ellipsoid overlap test for on line failure detection the problem of failure detection in dynamic systems is addressed the approach is based on modelling and estimation methods and uses some known statistical tools as well as geometric arguments a test decision is derived which is based on the overlap between the confidence regions associated with two estimates one obtained using online measurements and the other based on a priori information the algorithm proposed here is suitable for on line detection of abrupt changes and failures in the applications where fast on line decisions are of importance the implementation of a necessary and sufficient condition is shown to result in a scalar test which does not call for any optimization procedure and so offers the advantage of low computational expenditure

worst case input output identification we consider worst case l1 identification of causal linear shift invariant systems from time series many results are given on general aspects of identification algorithm performance existence of optimal algorithms robust convergence and input experiment design the identification methodology studied here is compatible with the modelling requirements of modern robust control design

a polynomial time algorithm for computing an arrow debreu market equilibrium for linear utilities we provide the first polynomial time exact algorithm for computing an arrow debreu market equilibrium for the case of linear utilities our algorithm is based on solving a convex program using the ellipsoid algorithm and simultaneous diophantine approximation as a side result we prove that the set of assignments at equilibrium is convex and the equilibrium prices themselves are log convex our convex program is explicit and intuitive which allows maximizing a concave function over the set of equilibria on the practical side ye developed an interior point algorithm lecture notes in comput sci 3521 springer new york 2005 pp 3 5 to find an equilibrium based on our convex program we also derive separate combinatorial characterizations of equilibrium for arrow debreu and fisher cases our convex program can be extended for many nonlinear utilities and production models our paper also makes a powerful theorem theorem 6 4 1 in m grotschel l lovasz and a schrijver geometric algorithms and combinatorial optimization 2nd ed springer verlag berlin heidelberg 1993 even more powerful in theorems 12 and 13 in the area of geometric algorithms and combinatorial optimization the main idea in this generalization is to allow ellipsoids to contain not the whole convex region but a part of it this theorem is of independent interest

a frequency domain approach to control of singular systems in this paper singular control systems are studied from the frequency domain point of view the proper stable factorization of a singular system is derived the stability of the closed loop system consisting of a singular system and controller is addressed most significantly all proper stabilizing controllers are parameterized for a given singular system

parameter estimation algorithms for a set membership description of uncertainty abstract the problem of parameter estimation when the data are corrupted by unknown but bounded errors mainly consists in characterizing the minimal parameter set consistent with the measurements the model and the error description two different approaches are reviewed and compared in this paper the first one based on a recursive parameter ellipsoidal bounding algorithm the other on an orthotopic bounding set obtained by solving linear programming problems the original ellipsoidal algorithm modified for higher efficiency has been compared with the linear programming method although the orthotopic description may result in a more accurately defined parameter region it is time consuming when a large number of measurements is present conversely the ellipsodal bounding algorithm often provides a loose approximation to the parameter region but allows a fast data preprocessing producing a smaller number of constraints that can be subsequently fed to the linear programming algorithm a combined use of the two procedures is outlined and tested on simulated and real data the latter being relative to the tuning of an a d converter resulting in a remarkable reduction in the computing time

descriptor observer approaches for multivariable systems with measurement noises and application in fault detection and diagnosis in this paper new descriptor observer design approaches are presented for multivariable systems with measurement noises if the system matrix is stable the proposed modified proportional and derivative observer technique allows us not only to decouple the measurement noise in any forms completely but also obtain accurate estimations of both system states and measurement noises if the system is detectable and the noise is bounded it has been shown that two design parameters can provide more degrees of freedom in this context the derivative gain parameter is chosen to reduce the amplification of the noise and the proportional gain is then selected to guarantee the stability of the error dynamics for systems with both measurement output noises and input disturbances a modified proportional derivative and integral observer is constructed to asymptotically estimate states input disturbances and output noises at the same time the applications of the proposed observers for systems with actuator and sensor faults are also discussed numerical examples are given to illustrate the design procedures and the simulation results show the satisfactory tracking performance

brief paper state estimation in the presence of bounded disturbances this contribution proposes a robust recursive algorithm for the state estimation of linear models with unknown but bounded disturbances corrupting both the state and measurement vectors a novel approach based on state bounding techniques is presented the proposed algorithm can be decomposed into two steps time updating and observation updating that uses a switching estimation kalman like gain matrix particular emphasis will be given to the design of a weighting factor that ensures the stability of the estimation error

identification of probabilistic system uncertainty regions by explicit evaluation of bias and variance errors a procedure is developed for identification of probabilistic system uncertainty regions for a linear time invariant system with unknown dynamics on the basis of time sequences of input and output data the classical framework is handled in which the system output is contaminated by a realization of a stationary stochastic process given minor and verifiable prior information on the system and the noise process frequency response pulse response and step response confidence regions are constructed by explicitly evaluating the bias and variance errors of a linear regression estimate in the model parametrizations use is made of general forms of basis functions conservatism of the uncertainty regions is limited by focusing on direct computational solutions rather than on closed form expressions using an instrumental variable method for identification the procedure is suitable also for input output data obtained from closed loop experiments

technical communique all doubly coprime factorizations of a general rational matrix for a general rational matrix function possibly polynomial or improper we give state space formulas for the class of all doubly coprime factorizations over an arbitrary fixed set in the closed complex plane the main result is expressed in terms of a special type of realization called centered that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the proper case in particular the formulas can be specialized to get the parametrization of all proper polynomial or proper and stable doubly coprime factorizations of an arbitrary descriptor system en route we provide a closed state space formula for the inverse of an invertible general rational matrix

comments on an algorithm for real time failure detection in kalman filters in the above mentioned paper by zolghadri ibid vol 41 1996 the commenter objects to claims made of providing simpler implementation complexity or computational burden without an explicit mechanization for obtaining a solution ever actually being offered and operations counts being tallied

bounded error parameter estimation a sequential analytic center approach a sequential analytic center approach for bounded error parameter estimation is proposed the authors show that the analytic center minimizes the logarithmic average output error among all the estimates within the membership set and is a maximum likelihood estimator for a class of noise density functions which include parabolic densities and approximations of truncated gaussian they also show that the analytic center is easily computable for both offline and online problems with a sequential algorithm the convergence proof of this sequential algorithm is obtained and moreover it is shown that the complexity in terms of the maximum number of newton iterations is linear in the number of observed data points

an algorithm for real time failure detection in kalman filters an algorithm is presented for solving the problem of real time failure detection in dynamic systems using kalman filters we give a geometric solution to derive a test decision based on the overlap between the confidence regions associated with two estimates one obtained using on line measurements and the other based on a priori information the implementation of a necessary and sufficient condition is shown to result in a scalar test the advantage compared to standard techniques is a significantly lower computational burden

market equilibrium under separable piecewise linear concave utilities we consider fisher and arrow debreu markets under additively separable piecewise linear concave utility functions and obtain the following results for both market models if an equilibrium exists there is one that is rational and can be written using polynomially many bits there is no simple necessary and sufficient condition for the existence of an equilibrium the problem of checking for existence of an equilibrium is np complete for both market models the same holds for existence of an e approximate equilibrium for e e o n 5 under standard mild sufficient conditions the problem of finding an exact equilibrium is in ppad for both market models finally building on the techniques of chen et al 2009a we prove that under these sufficient conditions finding an equilibrium for fisher markets is ppad hard

a combinatorial polynomial algorithm for the linear arrow debreu market we present the first combinatorial polynomial time algorithm for computing the equilibrium of the arrow debreu market model with linear utilities our algorithm views the allocation of money as flows and iteratively improves the balanced flow as in 11 for fisher s model we develop new methods to carefully deal with the flows and surpluses during price adjustments our algorithm performs o n 6 log n u maximum flow computations where n is the number of agents and u is the maximum integer utility the flows have to be presented as numbers of bitlength o n log n u to guarantee an exact solution previously 22 29 have given polynomial time algorithms for this problem which are based on solving convex programs using the ellipsoid algorithm and the interior point method respectively

a generalized least absolute deviation method for parameter estimation of autoregressive signals this paper proposes a generalized least absolute deviation glad method for parameter estimation of autoregressive ar signals under non gaussian noise environments the proposed glad method can improve the accuracy of the estimation of the conventional least absolute deviation lad method by minimizing a new cost function with parameter variables and noise error variables compared with second and high order statistical methods the proposed glad method can obtain robustly an optimal ar parameter estimation without requiring the measurement noise to be gaussian moreover the proposed glad method can be implemented by a cooperative neural network nn which is shown to converge globally to the optimal ar parameter estimation within a finite time simulation results show that the proposed glad method can obtain more accurate estimates than several well known estimation methods in the presence of different noise distributions

on the value of information in system identification bounded noise case assuming instantaneous bounds on the noise system parameter identification is formulated as membership set estimation problem sequential algorithms are constructed to estimate the membership sets of the parameters which are consistent with the measurements and the noise constraints the important new feature of the proposed algorithms is their ability to ignore redundant data the efficient data extraction property of the new algorithms is achieved with small computational effort and with improved performance when compared to the least square algorithm the convergence properties and the notion of identifiability in the set theoretic context are also studied

new results on doubly coprime fractional representations of generalized dynamical systems this note first points out that the main results by wang and balas regarding the doubly coprime fractional representations for generalized dynamical systems have severe limitation in their applications that is the doubly coprime factorization obtained by wang and balas cannot characterize the parameterization of all properly stabilizing controllers when a system is singular therefore truly generalized to remedy those results two new doubly coprime factorizations have been developed that will parameterize all properly stabilizing controllers for single input or single output cases in addition the new results can characterize the parameterization of all corresponding causal properly stabilizing controllers finally the extension to the multiple input multiple output case is presented

parametrization of ω stabilizing controllers and closed loop transfer matrices of a singular system abstract for a completely general singular system whose transfer matrix may be improper or even polynomial and an arbitrary set in the closed complex plane we give a state space parametrization of all controllers that achieve closed loop transfer matrices having all poles in and of the respective closed loop transfer matrices the main result is expressed in terms of a special type of state space realization called centered that exhibits the same attractive features and allows for formulas that bear essentially the same elegant simplicity of the standard proper case in particular the formulas can be specialized to get the parametrization of all controllers that achieve proper polynomial or proper and stable closed loop transfer matrices for a singular system

adaptive control of arma plants using worst case design by semi infinite optimization this paper presents a new approach to on line control system tuning based on worst case design using semi infinite optimlzation together with a plant uncertainty identification scheme which this approach requires

false alarm and correct detection probabilities over a time interval for restricted classes of failure detection algorithms the statistical analysis of failure detection decisions in terms of the instantaneous probabilities of false alarm and correct detection for a specified failure magnitude at each check time have previously been performed for several different failure detection techniques that utilize a kalman filter by performing a discrete time specialization of a result of gallager and helstrom on a tightened upper bound for continuous time level crossing probabilities upper bounds on the probabilities of false alarm and correct detection over a time interval have been obtained for the specific technique of cr2 tailnre detection to allow an accounting for the effect of time correlations of the filter estimates when these upper bounds are optimized to be as tight as possible to the desired probabilities the resulting optimization problem for discrete time is a collection of quadratic programming qp problems which may easily be solved exactly without recourse to approximate solutions as were resorted to in the continuous time formulation this technique for evaluating tightened upper bounds on the false alarm and correct detection probabilities may be of general interest since it can be applied to any failure detection technique or signal detection technique that can relate an exceeding of the deterministic decision threshold by the test statistic directly to a deterministic level being exceeded by a scalar gaussian random process

bounded error identification for closed loop systems this paper presents a scheme for the identification of a system which operates in closed loop and in the presence of bounded output disturbances two algorithms are proposed to solve this identification problem the first algorithm is an optimal bounding ellipsoid obe type algorithm this first algorithm is analyzed and sufficient conditions for stability and convergence are established relaxation of these conditions leads to a second identification algorithm the implementation of that second algorithm is realized in an iterative scheme a numerical example is provided to show the efficiency of the scheme

robust filtering and feedforward control based on probabilistic descriptions of model errors abstract a new approach to robust estimation of signals prediction of time series and robust feedforward control is considered modelling errors are parametrized by random variables with known covariances a robust design is obtained by minimizing the squared estimation error averaged both with respect to model errors and the noise a polynomial equations approach based on averaged spectral factorizations and averaged diophantine equations is derived mild solvability conditions guarantee the existence of stable optimal filters and feedforward regulators the robust design turns out to be no more complicated than the design of an ordinary wiener filter or lqg regulator the proposed approach avoids two drawbacks of minimax design first probabilistic descriptions of model uncertainties may have soft bounds these are more readily obtainable in a noisy environment than the hard bounds required for minimax design furthermore not only the range of uncertainties but also their likelihood is taken into account common model deviations will have a greater impact on an estimator design than do very rare worst cases the conservativeness is thus reduced

hard frequency domain model error bounds from least squares like identification techniques the problem of deriving so called hard error bounds for estimated transfer functions is addressed a hard bound is one that is sure to be satisfied i e the true system nyquist plot will be confined with certainty to a given region provided that the underlying assumptions are satisfied by blending a priori knowledge and information obtained from measured data it is shown how the uncertainty of transfer function estimates can be quantified the emphasis is on errors due to model mismatch the effects of unmodeled dynamics can be considered as bounded disturbances hence techniques from set membership identification can be applied to this problem the approach taken corresponds to weighted least squares estimation and provides hard frequency domain transfer function error bounds the main assumptions used in the current contribution are that the measurement errors are bounded that the true system is indeed linear with a certain degree of stability and that there is some knowledge about the shape of the true frequency response

market equilibria with hybrid linear leontief utilities we introduce a new family of utility functions for exchange markets this family provides a natural and continuous hybridization of the traditional linear and leontief utilities and might be useful in understanding the complexity of computing approximating market equilibria although computing an equilibrium in a market with this family of utility functions this is ppad hard in general in this paper we present an algorithm for finding an approximate arrow debreu equilibrium when the leontief components of the market are grouped finite and well conditioned

brief paper an algorithm for bounded error identification of nonlinear systems based on dc functions this paper presents a guaranteed method for the parameter estimation of nonlinear models in a bounded error context this method is based on functions which consists of the difference of two convex functions called dc functions the method considers dc representations of the functional form of the dynamic system to obtain an outer bound of the set of parameters that are consistent with the measurements the system and the considered bounded error at each iteration the proposed algorithm solves several convex optimization problems to discard from the initial search region subregions that are proved not consistent this operation is repeated while the obtained solution is improved four examples are provided to clarify the proposed identification algorithm

market equilibrium under piecewise leontief concave utilities abstract leontief is one of the most widely used and extensively studied function in economic modeling for both production and preferences however it lacks the desirable property of diminishing returns in this paper we consider piecewise leontief concave p leontief utility function which consists of a set of leontief type segments with decreasing returns and an upper limit on the utility on each segment and study complexity of computing equilibria in both fisher and exchange market models leontief is a special case of p leontief with exactly one segment with no upper limit while it is well known that equilibrium computation in fisher markets with leontief utilities is polynomial time in case of p leontief even with two segments we show that the problem is ppad hard on the other hand for the case when coefficients across segments are scaled versions of each other we give a polynomial time algorithm as a corollary we obtain a non trivial new class of exchange markets with leontief utilities where an equilibrium can be computed in a polynomial time whereas the general problem is known to be ppad hard for p leontief exchange markets with pairing economy we show that equilibria are rational and we obtain a simplex like algorithm to compute one using the classic lemke howson scheme thereby extending the results of ye tcs 2007 and codenotti saberi varadarajan and ye soda 2006 for leontief to p leontief utilities

brief infinite horizon predictive control of constrained continuous time linear systems this paper considers receding horizon control strategies for constrained linear systems continuous time predictions of input output responses on an infinite horizon allow exploitation of the full range of plant behaviour in addition an infinite prediction horizon ensures the nominal stability of the receding horizon control law the problem of optimizing predictions subject to constraints is made tractable through the use of a finite dimensional prediction class and by minimizing prediction costs at discrete instants necessary and sufficient conditions on the prediction class are derived using input output stability theory and the controller structure further refined on the basis of a criterion for ensuring feasibility in a receding horizon sense constrained optimization is performed using quadratic programming

identification of nonlinear systems in the presence of unknown but bounded disturbances this paper deals with recursive parameter estimation of nonlinear systems in the presence of unknown but bounded disturbances the proposed technique is performed by the use of a modified extended least squares algorithm so that the estimated parameters are consistent with the measurements and the noise constraints while local asymptotic convergence under very general conditions is assured one of the main features is to show from the stability analysis connection between some arbitrary factors and basin of attraction high performances from the design and implementation point of view will be shown through a numerical example under severe conditions

a fptas for computing a symmetric leontief competitive economy equilibrium in this paper we consider a linear complementarity problem lcp arisen from the nash and arrow debreu competitive economy equilibria where the lcp coefficient matrix is symmetric we prove that the decision problem to decide whether or not there exists a complementary solution is np complete under certain conditions an lcp solution is guaranteed to exist and we present a fully polynomial time approximation scheme fptas for approximating a complementary solution although the lcp solution set can be non convex or non connected our method is based on approximating a quadratic social utility optimization problem qp and showing that a certain kkt point of the qp problem is an lcp solution then we further show that such a kkt point can be approximated with a new improved running time complexity o frac n 4 epsilon log log frac 1 epsilon arithmetic operation in accuracy epsilon in 0 1 we also report preliminary computational results which show that the method is highly effective applications in competitive market model problems with other utility functions are also presented including global trading and dynamic spectrum management problems

doubly coprime fractional representations of generalized dynamical systems explicit formulas for doubly coprime fractional representations of the transfer matrix of a generalized dynamical system are given in terms of a stabilizable and detectable state space realization of the transfer matrix these formulas establish a possible way to use the fractional representation approach in the synthesis of generalized dynamical systems

ellipsoids and ellipsoid shaped fuzzy sets as natural multi variate generalization of intervals and fuzzy numbers how to elicit them from users and how to use them in data processing in this paper we show that ellipsoids are natural multi variate generalization of intervals and ellipsoid shaped fuzzy sets are a natural generalization of fuzzy numbers we explain how to elicit them from users and how to use them in data processing

approximate linear algebra is intractable abstract it is shown that the problem of computing the optimal solutions of several versions of imprecise linear systems of equations is np hard an imprecise linear system is a linear system ax b where a a 0 p a b b 0 qv b v with unknown coefficients p qv constrained by one of the five relations p q p 2 q p q 2 p q 2 where p q is a vector formed by all values p and qv given such a system we would like to find its optimal solution i e the largest possible x j and the smallest possible x j values of xj our main result is that this problem is np hard in any of the five versions this holds even when the a b v 0 v 0 are restricted to have only a single nonzero entry each in disjoint positions and even if instead of the exact values x j x j we want to compute their approximations for a given accuracy 0 so unless np p algorithms that find the optimal solution of imprecise linear systems require in the worst case exponential time

brief a convex approach to the characterization of the frequency response of ellipsoidal plants this paper deals with the frequency domain properties of an ellipsoidal family of rational functions i e a family of rational functions whose coefficients depend affinely on an ellipsoidal parameter set the considered problems are relevant to several recently developed techniques in the identification for control research area a complete characterization of the frequency plots of such a family is provided and an efficient algorithm for computing the envelope of the bode plots is devised in particular it is shown that the extremal values of the magnitude and phase of the family frequency response which in general involve non convex optimization problems can be computed via a sequence of simple algebraic tests