CHARACTERIZATION OF EXPONENTIAL DIVERGENCE OF THE KALMAN FILTER FOR TIME-VARYING SYSTEMS

This paper studies semistability of the recursive Kalman filter in the context of linear time-varying (LTV), possibly nondetectable systems with incorrect noise information. Semistability is a key property, as it ensures that the actual estimation error does not diverge exponentially. We explore structural properties of the filter to obtain a necessary and sufficient condition for the filter to be semistable. The condition does not involve limiting gains nor the solution of Riccati equations, as they can be difficult to obtain numerically and may not exist. We also compare semistability with the notions of stability and stability w.r.t. the initial error covariance, and we show that semistability in a sense makes no distinction between persistent and nonpersistent incorrect noise models, as opposed to stability. In the linear time invariant scenario we obtain algebraic, easy to test conditions for semistability and stability, which complement results available in the context of detectable systems. Illustrative examples are included.

Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise Systems

In this paper we consider the existence of the maximal and mean square stabilizing solutions for a set of generalized coupled algebraic Riccati equations (GCARE for short) associated to the infinite-horizon stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a sufficient condition, based only on some positive semi-definite and kernel restrictions on some matrices, under which there exists the maximal solution and a necessary and sufficient condition under which there exists the mean square stabilizing solution fir the GCARE. We also present a solution for the discounted and long run average cost problems when the performance criterion is assumed be composed by a linear combination of an indefinite quadratic part and a linear part in the state and control variables. The paper is concluded with a numerical example for pension fund with regime switching.

On state representations of time-varying nonlinear systems

This work considers a nonlinear time-varying system described by a state representation, with input u and state x. A given set of functions v, which is not necessarily the original input u of the system, is the (new) input candidate. The main result provides necessary and sufficient conditions for the existence of a local classical state space representation with input v. These conditions rely on integrability tests that are based on a derived flag. As a byproduct, one obtains a sufficient condition of differential flatness of nonlinear systems. (C) 2009 Elsevier Ltd. All rights reserved.

On the dominance of roots of characteristic equations for neutral functional differential equations

We present a sufficient condition for a zero of a function that arises typically as the characteristic equation of a linear functional differential equations of neutral type, to be simple and dominant. This knowledge is useful in order to derive the asymptotic behaviour of solutions of such equations. A simple characteristic equation, arisen from the study of delay equations with small delay, is analyzed in greater detail. (C) 2009 Elsevier Inc. All rights reserved.

Benders, metric and cutset inequalities for multicommodity capacitated network design

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.

Towards a maximal extension of Pelczynski`s decomposition method in Banach spaces

l Suppose that X, Y. A and B are Banach spaces such that X is isomorphic to Y E) A and Y is isomorphic to X circle plus B. Are X and Y necessarily isomorphic? In this generality. the answer is no, as proved by W.T. Cowers in 1996. In the present paper, we provide a very simple necessary and sufficient condition on the 10-tuples (k, l, m, n. p, q, r, s, u, v) in N with p+q+u >= 3, r+s+v >= 3, uv >= 1, (p,q)$(0,0), (r,s)not equal(0,0) and u=1 or v=1 or (p. q) = (1, 0) or (r, s) = (0, 1), which guarantees that X is isomorphic to Y whenever these Banach spaces satisfy X(u) similar to X(p)circle plus Y(q), Y(u) similar to X(r)circle plus Y(s), and A(k) circle plus B(l) similar to A(m) circle plus B(n). Namely, delta = +/- 1 or lozenge not equal 0, gcd(lozenge, delta (p + q - u)) divides p + q - u and gcd(lozenge, delta(r + s - v)) divides r + s - v, where 3 = k - I - in + n is the characteristic number of the 4-tuple (k, l, m, n) and lozenge = (p - u)(s - v) - rq is the discriminant of the 6-tuple (p, q, r, s, U, v). We conjecture that this result is in some sense a maximal extension of the classical Pelczynski`s decomposition method in Banach spaces: the case (1, 0. 1, 0, 2. 0, 0, 2. 1. 1). (C) 2009 Elsevier Inc. All rights reserved.

Cantor-Bernstein Sextuples for Banach Spaces

Let X and Y be Banach spaces isomorphic to complemented subspaces of each other with supplements A and B. In 1996, W. T. Gowers solved the Schroeder-Bernstein (or Cantor-Bernstein) problem for Banach spaces by showing that X is not necessarily isomorphic to Y. In this paper, we obtain a necessary and sufficient condition on the sextuples (p, q, r, s, u, v) in N with p + q >= 1, r + s >= 1 and u, v is an element of N*, to provide that X is isomorphic to Y, whenever these spaces satisfy the following decomposition scheme A(u) similar to X(P) circle plus Y(q) B(v) similar to X(r) circle plus Y(s). Namely, Phi = (p - u)(s - v) - (q + u)(r + v) is different from zero and Phi divides p + q and r + s. These sextuples are called Cantor-Bernstein sextuples for Banach spaces. The simplest case (1, 0, 0, 1, 1, 1) indicates the well-known Pelczynski`s decomposition method in Banach space. On the other hand, by interchanging some Banach spaces in the above decomposition scheme, refinements of the Schroeder-Bernstein problem become evident.

The disk-percolation model on graphs

We study a long-range percolation model whose dynamics describe the spreading of an infection on an infinite graph. We obtain a sufficient condition for phase transition and prove all upper bound for the critical parameter of spherically symmetric trees. (C) 2008 Elsevier B.V. All rights reserved.

On Approximate KKT Condition and its Extension to Continuous Variational Inequalities

In this work, we introduce a necessary sequential Approximate-Karush-Kuhn-Tucker (AKKT) condition for a point to be a solution of a continuous variational inequality, and we prove its relation with the Approximate Gradient Projection condition (AGP) of Garciga-Otero and Svaiter. We also prove that a slight variation of the AKKT condition is sufficient for a convex problem, either for variational inequalities or optimization. Sequential necessary conditions are more suitable to iterative methods than usual punctual conditions relying on constraint qualifications. The AKKT property holds at a solution independently of the fulfillment of a constraint qualification, but when a weak one holds, we can guarantee the validity of the KKT conditions.

Intercepting moving targets: does memory from practice in a specific condition of target displacement affect movement timing?

This investigation aimed at assessing the extent to which memory from practice in a specific condition of target displacement modulates temporal errors and movement timing of interceptive movements. We compared two groups practicing with certainty of future target velocity either in unchanged target velocity or in target velocity decrease. Following practice, both experimental groups were probed in the situations of unchanged target velocity and target velocity decrease either under the context of certainty or uncertainty about target velocity. Results from practice showed similar improvement of temporal accuracy between groups, revealing that target velocity decrease did not disturb temporal movement organization when fully predictable. Analysis of temporal errors in the probing trials indicated that both groups had higher timing accuracy in velocity decrease in comparison with unchanged velocity. Effect of practice was detected by increased temporal accuracy of the velocity decrease group in situations of decreased velocity; a trend consistent with the expected effect of practice was observed for temporal errors in the unchanged velocity group and in movement initiation at a descriptive level. An additional point of theoretical interest was the fast adaptation in both groups to a target velocity pattern different from that practiced. These points are discussed under the perspective of integration of vision and motor control by means of an internal forward model of external motion.

Number of options in a movement sequence affects learners' behavior in a self-controlled practice condition

Self controlling practice implies a process of decision making which suggests that the options in a self controlled practice condition could affect learners The number of task components with no fixed position in a movement sequence may affect the (Nay learners self control their practice A 200 cm coincident timing track with 90 light emitting diodes (LEDs)-the first and the last LEDs being the warning and the target lights respectively was set so that the apparent speed of the light along the track was 1 33 m/sec Participants were required to touch six sensors sequentially the last one coincidently with the lighting of the tar get light (timing task) Group 1 (n=55) had only one constraint and were instructed to touch the sensors in any order except for the last sensor which had to be the one positioned close to the target light Group 2 (n=53) had three constraints the first two and the last sensor to be touched Both groups practiced the task until timing error was less than 30 msec on three consecutive trials There were no statistically significant differences between groups in the number of trials needed to reach the performance criterion but (a) participants in Group 2 created fewer sequences corn pared to Group 1 and (b) were more likely to use the same sequence throughout the learning process The number of options for a movement sequence affected the way learners self-controlled their practice but had no effect on the amount of practice to reach criterion performance.

Expert system for the assessment of power transformer insulation condition based on type-2 fuzzy logic systems

An efficient expert system for the power transformer condition assessment is presented in this paper. Through the application of Duval`s triangle and the method of the gas ratios a first assessment of the transformer condition is obtained in the form of a dissolved gas analysis (DGA) diagnosis according IEC 60599. As a second step, a knowledge mining procedure is performed, by conducting surveys whose results are fed into a first Type-2 Fuzzy Logic System (T2-FLS), in order to initially evaluate the condition of the equipment taking only the results of dissolved gas analysis into account. The output of this first T2-FLS is used as the input of a second T2-FLS, which additionally weighs up the condition of the paper-oil system. The output of this last T2-FLS is given in terms of words easily understandable by the maintenance personnel. The proposed assessing methodology has been validated for several cases of transformers in service. (C) 2010 Elsevier Ltd. All rights reserved.

Effect of precracking method on K(Ic) results for medium-density polyethylene tested under cryogenic condition

The effect of different precracking methods on the results of linear elastic K(Ic) fracture toughness testing with medium-density polyethylene (MDPE) was investigated. Cryogenic conditions were imposed in order to obtain valid K(Ic) values from specimens of suitable size. Most conservative K(Ic) values were obtained by slow pressing a fresh razor blade at the notch root of the specimen. Due to the low deformation level imposed on the crack tip region, the slow pressing razor blade technique also produced less scatter in fracture toughness results. It has been shown that the slow stable crack growth preceding catastrophic brittle failure during K(Ic) tests in MOPE under cryogenic conditions should not be disregarded as it has relevant physical meaning and may affect the fracture toughness results. (C) 2010 Elsevier Ltd. All rights reserved.

THE VANISHING DISCOUNT APPROACH FOR THE AVERAGE CONTINUOUS CONTROL OF PIECEWISE DETERMINISTIC MARKOV PROCESSES

This work is concerned with the existence of an optimal control strategy for the long-run average continuous control problem of piecewise-deterministic Markov processes (PDMPs). In Costa and Dufour (2008), sufficient conditions were derived to ensure the existence of an optimal control by using the vanishing discount approach. These conditions were mainly expressed in terms of the relative difference of the alpha-discount value functions. The main goal of this paper is to derive tractable conditions directly related to the primitive data of the PDMP to ensure the existence of an optimal control. The present work can be seen as a continuation of the results derived in Costa and Dufour (2008). Our main assumptions are written in terms of some integro-differential inequalities related to the so-called expected growth condition, and geometric convergence of the post-jump location kernel associated to the PDMP. An example based on the capacity expansion problem is presented, illustrating the possible applications of the results developed in the paper.

Some remarks on static-feedback linearization for time-varying systems

This work summarizes some results about static state feedback linearization for time-varying systems. Three different necessary and sufficient conditions are stated in this paper. The first condition is the one by [Sluis, W. M. (1993). A necessary condition for dynamic feedback linearization. Systems & Control Letters, 21, 277-283]. The second and the third are the generalizations of known results due respectively to [Aranda-Bricaire, E., Moog, C. H., Pomet, J. B. (1995). A linear algebraic framework for dynamic feedback linearization. IEEE Transactions on Automatic Control, 40, 127-132] and to [Jakubczyk, B., Respondek, W. (1980). On linearization of control systems. Bulletin del` Academie Polonaise des Sciences. Serie des Sciences Mathematiques, 28, 517-522]. The proofs of the second and third conditions are established by showing the equivalence between these three conditions. The results are re-stated in the infinite dimensional geometric approach of [Fliess, M., Levine J., Martin, P., Rouchon, P. (1999). A Lie-Backlund approach to equivalence and flatness of nonlinear systems. IEEE Transactions on Automatic Control, 44(5), 922-937]. (C) 2008 Elsevier Ltd. All rights reserved.