Mostrando recursos 1 - 20 de 80

  1. Recursive Least Squares with Linear Constraints

    Zhu, Yunmin; Li, X. Rong
    Recursive Least Squares (RLS) algorithms have wide-spread applications in many areas, such as real-time signal processing, control and communications. This paper shows that the unique solutions to linear-equality constrained and the unconstrained LS problems, respectively, always have exactly the same recursive form. Their only difference lies in the initial values. Based on this, a recursive algorithm for the linear-inequality constrained LS problem is developed. It is shown that these RLS solutions converge to the true parameter that satisfies the constraints as the data size increases. A simple and easily implementable initialization of the RLS algorithm is proposed. Its convergence to the exact LS solution and the true parameter is...

  2. Conformal Spherical Parametrization for High Genus Surfaces

    Zeng, Wei; Li, Xin; Yau, Shing-Tung; Gu, Xianfeng
    Surface parameterization establishes bijective maps from a surface onto a topologically equivalent standard domain. It is well known that the spherical parameterization is limited to genus-zero surfaces. In this work, we design a new parameter domain, two-layered sphere, and present a framework for mapping high genus surfaces onto sphere. This setup allows us to trans- fer the existing applications based on general spherical parameterization to the field of high genus surfaces, such as remeshing, consistent parameterization, shape analysis, and so on. Our method is based on Riemann surface theory. We construct meromorphic functions on surfaces: for genus one surfaces, we apply Weierstrass $P$-functions; for high genus surfaces, we compute...

  3. When the Cramér-Rao Inequality Provides No Information

    Miller, Steven J.
    We investigate a one-parameter family of probability densities (related to the Pareto distribution, which describes many natural phenomena) where the Cramér-Rao inequality provides no information.

  4. On Asymptotic Stabilizability of Discrete-time Linear Systems with Delayed Input

    Lin, Lin
    This paper examines the asymptotic stabilizability of discrete-time linear systems with delayed input. By explicit construction of stabilizing feedback laws, it is shown that a stabilizable able and detectable linear system with an arbitrarily large delay in the input can be asymptotically stabilized by either linear state or output feedback as long as the open loop system is not exponentially unstable (i.e., all the open loop poles are on or inside the unit circle.) It is further shown that such a system, when subject to actuator saturation, is semi-globally asymptotically stabilizable by linear state or output feedback.

  5. Curve Space: Classifying Curves On Surfaces

    Li, Xin; Gu, Xianfeng; Qin, Hong
    We design signatures for curves defined on genus zero surfaces. The signature classifies curves according to the conformal geometry of the given curves and their embedded surface. Based on Teichmüller theory, our signature describes not only the curve shape but also the intrinsic relationship between the curve and its embedded surface. Furthermore, the signature metric is stable, it is close to identity between surfaces sharing similar Riemannian geometry metrics. Based on this, we propose a surface matching framework: first, with curve signatures, we match the partitioning of two surfaces defined by simple closed curves on them; second, the segmented subregions are pairwisely matched and then compared on canonical planar...

  6. Special solutions to some Kolmogorov equations arising from cubic sensor problems

    Yau, Stephen S.T.; Du, Ruxu; Jia, Lixing

  7. Active pointing control for short range free-space optical communication

    Komaee, Arash; Krishnaprasad, P.S.; Narayan, Prakash
    Maintaining optical alignment between stations of a free-space optical link requires an active pointing mechanism to persistently aim an optical beam toward the receiving station with an acceptable accuracy. This mechanism ensures delivery of maximum optical power to the receiving station in spite of the relative motion of the stations. In the active pointing scheme proposed in the present paper, the receiving station estimates the center of the incident optical beam based on the output of a position-sensitive photodetector. The transmitting station receives this estimate via an independent communication link and uses it to accurately aim at the receiving station. The...

  8. Hurst parameter estimation for epleptic seizure detection

    Osorio, Ivan; Frei, Mark G.
    Estimation of the Hurst parameter provides information about the memory range orcorrelations (long vs. short) of processes (time-series). A new application for the Hurst parameter, real-time event detection, is identified. Hurst estimates using rescaled range, dispersional and bridgedetrended scaled windowed variance analyses of seizure time-series recorded from human subjects reliably detect their onset, termination and intensity. Detection sensitivity is unaltered by signal decimation and window size increases. The high sensitivity to brain state changes, ability to operate in real time and small computational requirements make Hurst parameter estimation using any of these three methods well suited for implementation into miniature implantable devices...

  9. Modelling High-Dimensional Time Series by Generalized Linear Dynamic Factor Models: An Introductory Survey

    Deistler, Manfred; Zinner, Christiane
    Factor models are used to condense high dimensional data consisting of many vari ables into a much smaller number of factors. Here we present an introductory survey to factor models for time series, where the factors represent the comovement between the single time series. Principal component analysis, linear dynamic factor models with idiosyncratic noise and generalized linear dynamic factor models are introduced and structural properties, such as identifiability, as well as estimation are discussed.

  10. An improved bound for the exponential stability of predictive filters of hidden Markov models

    Gerencser, László; Michaletzky, György; Molnár-Sáska, Gábor
    We consider hidden Markov processes in discrete time with a finite state space $X$ and a general observation or read-out space $Y$, which is assumed to be a Polish space. It is well-known that in the statistical analysis of HMMs the so-called predictive filter plays a fundamental role. A useful result establishing the exponential stability of the predictive filter with respect to perturbations of its initial condition was given in "Exponential forgetting and geometric ergodicity in hidden Markov models" (F. LeGland, L. Mevel, Mathematics of control, signals and systems, 13(2000), pp. 63-93) in the case, when the assumed transition probability...

  11. Using stochastic optimization methods for stock selling decision making and option pricing: numerics and bias and variance dependent convergence rates

    Bao, J.; Belu, A.; Gershon, Y.; Liu, Y.J.; Yin, G.; Zhang, Q.
    This paper is concerned with using stochastic approximation and optimization methods for stock liquidation decision making and option pricing. For stock liquidation problem, we present a class of stochastic recursive algorithms, and make comparisons of performances using stochastic approximation methods and that of certain commonly used heuristic methods, such as moving averaging method and moving maximum method. Stocks listed in NASDAQ are used for making the comparisons. For option pricing, we design stochastic optimization algorithms and present numerical experiments using data derived from Berkeley Options Data Base. An important problem in these studies concerns the rate of convergence taking into...

  12. Selling a large stock position: a stochastic control approach with state constraints

    Pemy, M.; Zhang, Q.; Yin, G.
    A common practice for stock-selling decision making is often concerned with liquidation of the security in a short duration. This is feasible when a relative smaller number of shares of a stock is treated. Selling a large position during a short period of time in the market frequently depresses the market, resulting in poor filling prices. In this work, liquidation strategies are considered for selling much smaller number of shares over a longer period of time. By using a fluid model in which the number of shares are treated as fluid, and the corresponding liquidation is dictated by the rate of...

  13. A survey of some simulation-based algorithms for Markov decision processes

    Chang, Hyeong Soo; Fu, Michael C.; Hu, Jiaqiao; Marcus, Steven I.
    Many problems modeled by Markov decision processes (MDPs) have very large state and/or action spaces, leading to the well-known curse of dimensionality that makes solution of the resulting models intractable. In other cases, the system of interest is complex enough that it is not feasible to explicitly specify some of the MDP model parameters, but simulated sample paths can be readily generated (e.g., for random state transitions and rewards), albeit at a non-trivial computational cost. For these settings, we have developed various sampling and population-based numerical algorithms to overcome the computational difficulties of computing an optimal solution in terms of a policy and/or...

  14. Maximization of the portfolio growth rate under fixed and proportional transaction costs

    Palczewski, Jan; Stettner, Lukasz
    This paper considers a discrete-time Markovian model of asset prices with economic factors and transaction costs with proportional and fixed terms. Existence of optimal strategies maximizing average growth rate of portfolio is proved in the case of complete and partial observation of the process modelling the economic factors. The proof is based on a modification of the vanishing discount approach. The main difficulty is the discontinuity of the controlled transition operator of the underlying Markov process.

  15. Regularity of renormalized self-intersection local time for fractional Brownian motion

    Hu, Yaozhong; Nualart, David

  16. Parameter estimates for linear partial differential equations with fractional boundary noise

    Maslowski, Bohdan; Pospíšil, Jan
    Parameter-dependent linear evolution equations with a fractional noise in the boundary conditions are studied. Ergodic-type theorems for stationary and non-stationary solutions are verified and used to prove the strong consistency of a suitably defined family of estimators.

  17. A maximum principle for stochastic optimal control with terminal state constraints, and its applications

    Ji, Shaolin; Zhou, Xun Yu
    This paper is concerned with a stochastic optimal control problem where the controlled system is described by a forward–backward stochastic differential equation (FBSDE), while the forward state is constrained in a convex set at the terminal time. An equivalent backward control problem is introduced. By using Ekeland’s variational principle, a stochastic maximum principle is obtained. Applications to state constrained stochastic linear–quadratic control models and a recursive utility optimization problem are investigated.

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    Bittanti, S.; Campi, M.C.
    Over the last three decades, the certainty equivalence principle has been the fundamental paradigm in the design of adaptive control laws. It is well known, however, that for general control criterions the performance achieved through its use is strictly suboptimal. In order to overcome this difficulty, two different approaches have been proposed: i) the use of cost-biased parameter estimators; and ii) the injection of probing signals into the system so as to enforce consistency in the parameter estimate. This paper presents an overview of the cost-biased approach. New insight is achieved in this paper by the formalization of a general cost-biased principle...

  19. A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems

    Li, Chanying; Xie, Liang-Liang; Guo, Lei
    In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyzes of the stabizability condition, which is determined by the growth rates of the system nonlinear dynamics only.

  20. Recursive system identification by stochastic approximation

    Chen, Han-Fu
    The convergence theorems for the stochastic approximation (SA) algorithm with expanding truncations are first presented, which the system identification methods discussed in the paper are essentially based on. Then, the recursive identification algorithms are respectively defined for the multivariate errors-in-variables systems, Hammerstein systems, and Wiener systems. All es- timates given in the paper are strongly consistent.

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