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Adaptive critic learning with fuzzy utility

Adaptive critic learning with fuzzy utility

NAFIPS 2004 - Annual Meeting of the North American Fuzzy Information Processing Society: Fuzzy Sets in the Heart of the Canadian Rockies

作者： Matzner, Shari A. Shannon, Thaddeus T. NW Computational Intelligence Lab. Systems Science Ph.D. Program Portland State University P.O. Box 751 Portland OR 97207 United States

Adaptive Critic methods, which approximate dynamic programming, have been used successfully for solving optimal control problems. The Adaptive Critic learning algorithm optimizes a secondary utility function that is the sum of the present and an future primary utility. The primary utility function measures the instantaneous cost incurred for the last action taken and the resulting state. The motivation for using a fuzzy primary utility function comes from the set of control problems for which there is only a qualitative definition of performance - for example, success or failure. Previous work in applying Adaptive Critic methods to this type of problem showed that a crisp definition of success resulted in solutions that met the control objective, but in an undesirable manner. An appropriate fuzzy utility function, on the other hand, is able to generate the optimal solution. Another motivation for incorporating fuzzy techniques into the utility function is to overcome measurement noise. Measurement noise has a significant adverse effect on the reliability and speed of Adaptive Critic learning;by incorporating fuzzy sets into the utility function, the effect of the noise can be mitigated.

关键词： Fuzzy sets

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Linguistic Adaptive Critics for tuning fuzzy controllers

Linguistic Adaptive Critics for tuning fuzzy controllers

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Conference of the North American Fuzzy Information Processing Society - NAFIPS

作者： T.T. Shannon NW Computational Intelligence Laboratory Systems Science Program Portland State University Portland OR USA

In this paper we demonstrate the use of Linguistic Adaptive Critics (LACs) for the design of fuzzy control systems. This technique is related to Adaptive Critic based Approximate Dynamic programming as developed and applied in the neurocontrol context. We have previously shown how such techniques can be conveniently generalized to fuzzy controllers or neuro-fuzzy hybrids. We demonstrate LACs by designing a temperature controller for a simple water bath system.

关键词： programmable control Adaptive control Fuzzy control Dynamic programming Control systems Los Angeles Council Temperature control Communication system control computational intelligence Laboratories

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Dynamical model of birdsong maintenance and control

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Physical Review E 2004年第5期70卷 051911-051911页

作者： Henry D. I. Abarbanel Sachin S. Talathi Gabriel Mindlin Misha Rabinovich Leif Gibb Graduate Program in Computational Neurobiology and Institute for Nonlinear Science Division of Biological Sciences University of California–San Diego La Jolla California 92093-0402 USA

The neuroethology of song learning, production, and maintenance in songbirds presents interesting similarities to human speech. We have developed a biophysical model of the manner in which song could be maintained in adult songbirds. This model may inform us about the human counterpart to these processes. In songbirds, signals generated in nucleus High Vocal center (HVc) follow a direct route along a premotor pathway to the robust nucleus of the archistriatum (RA) as well as an indirect route to RA through the anterior forebrain pathway (AFP): the neurons of RA are innervated from both sources. HVc expresses very sparse bursts of spikes having interspike intervals of about 2ms. The expressions of these bursts arrive at the RA with a time difference ΔT≈50±10ms between the two pathways. The observed combination of AMPA and NMDA receptors at RA projection neurons suggests that long-term potentiation and long-term depression can both be induced by spike timing plasticity through the pairing of the HVc and AFP signals. We present a dynamical model that stabilizes this synaptic plasticity through a feedback from the RA to the AFP using known connections. The stabilization occurs dynamically and is absent when the RA→AFP connection is removed. This requires a dynamical selection of ΔT. The model does this, and ΔT lies within the observed range. Our model represents an illustration of a functional consequence of activity-dependent plasticity directly connected with neuroethological observations. Within the model the parameters of the AFP, and thus the magnitude of ΔT, can also be tuned to an unstable regime. This means that destabilization might be induced by neuromodulation of the AFP.

关键词： Neurophysiology

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Adaptive critic learning with fuzzy utility

Adaptive critic learning with fuzzy utility

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Conference of the North American Fuzzy Information Processing Society - NAFIPS

作者： S.A. Matzner T.T. Shannon NW Computational Intelligence Laboratory Systems Science Ph.D. Program Portland State University Portland OR USA

Adaptive critic methods, which approximate dynamic programming, have been used successfully for solving optimal control problems. The adaptive critic learning algorithm optimizes a secondary utility function that is the sum of the present and all future primary utility. The primary utility function measures the instantaneous cost incurred for the last action taken and the resulting state. The motivation for using a fuzzy primary utility function comes from the set of control problems for which there is only a qualitative definition of performance - for example, success or failure. Previous work in applying adaptive critic methods to this type of problem showed that a crisp definition of success resulted in solutions that met the control objective, but in an undesirable manner. An appropriate fuzzy utility function, on the other hand, is able to generate the optimal solution. Another motivation for incorporating fuzzy techniques into the utility function is to overcome measurement noise. Measurement noise has a significant adverse effect on the reliability and speed of adaptive critic learning; by incorporating fuzzy sets into the utility function, the effect of the noise can be mitigated.

关键词： Dynamic programming Optimal control programmable control Adaptive control Cost function Control systems computational intelligence Fuzzy sets Noise measurement Neural networks

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Finite Size Effects on Thermal Denaturation of Globular Proteins

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Physical Review Letters 2004年第26期93卷 268107-268107页

作者： Mai Suan Li Dmitri K. Klimov D. Thirumalai Institute of Physics Polish Academy of Sciences Al. Lotnikow 32/46 02-668 Warsaw Poland Institute for Physical Science and Technology University of Maryland College Park Maryland 20742 USA Bioinformatics and Computational Biology Program School of Computational Sciences George Mason University Manassas Virginia 20110 USA

Finite size effects on the cooperative thermal denaturation of proteins are considered. A dimensionless measure of cooperativity, Ωc, scales as Nζ, where N is the number of amino acids. Surprisingly, we find that ζ is universal with ζ=1+γ, where the exponent γ characterizes the divergence of the susceptibility for a self-avoiding walk. Our lattice model simulations and experimental data are consistent with the theory. Our finding rationalizes the marginal stability of proteins and substantiates the earlier predictions that the efficient folding of two-state proteins requires TF≈Tθ, where Tθ and TF are the collapse and folding transition temperatures, respectively.

关键词： .stability Transitions PRL ending susceptibility experimental data Thermal denaturation folding transition exponent unfolded native state Globular Proteins cooperativity two-state NBA

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LARGE SCALE DYNAMICS OF PRECIPITATION FRONTS IN THE TROPICAL ATMOSPHERE: A NOVEL RELAXATION LIMIT ¤

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Communications in Mathematical sciences 2004年第4期2卷 591-626页

作者： Frierson, Dargan M. W. Majda, Andrew J. Pauluis, Olivier M. Program in Applied and Computational Mathematics Princeton University Fine HallWashington Rd Princeton 08544 NJ United States Department of Mathematics and Center for Atmosphere Ocean Science Courant Institute of Mathematical Sciences New York University 251 Mercer St New York 10012 NY United States Center for Atmosphere Ocean Science Courant Institute of Mathematical Sciences New York University 251 Mercer St. New York 10012 NY United States

A simplified set of equations is derived systematically below for the interaction of large scale flow fields and precipitation in the tropical atmosphere. These equations, the Tropical Climate Model, have the form of a shallow water equation and an equation for moisture coupled through a strongly nonlinear source term. This source term, the precipitation, is of relaxation type in one region of state space for the temperature and moisture, and vanishes identically elsewhere in the state space of these variables. In addition, the equations are coupled nonlinearly to the equations for barotropic incompressible flow. Several mathematical features of this system are developed below including energy principles for solutions and their first derivatives independent of relaxation time. With these estimates, the formal infinitely fast relaxation limit converges to a novel hyperbolic free boundary problem for the motion of precipitation fronts from a large scale dynamical perspective. Elementary exact solutions of the limiting dynamics involving precipitation fronts are developed below and include three families of waves: fast drying fronts as well as slow and fast moistening fronts. The last two families of waves violate Lax's Shock Inequalities;nevertheless, numerical experiments presented below confirm their robust realizability with realistic finite relaxation times. From the viewpoint of tropical atmospheric dynamics, the theory developed here provides a new perspective on the fashion in which the prominent large scale regions of moisture in the tropics associated with deep convection can move and interact with large scale dynamics in the quasi-equilibrium approximation. © 2004 International Press

关键词： Equatorial waves Hyperbolic free boundary problems Hyperbolic pde Moisture Nonlinear relaxation equations Tropical atmospheric dynamics Tropical convection

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Weighted Eigenvalue Problem Approach To The Critical Value Determination Of Screened Coulomb Potential Systems

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 80626 İstanbul Turkey

In this work, the radial time-independent Schrödinger equation of a screened Coulomb potential system at the zero energy limit is first converted to a weighted eigenvalue problem of an ordinary differential operator. Then, by using an appropriate coordinate transformation, the differential equation is transformed into a form whose first and second order derivative related terms become same as the Extended Jacobi Polynomials' differential equation's corresponding terms. Only difference is the appearance of a multiplicative operator which can be considered as an effective potential. Work focuses on the point whether the solution is obtained easily depending on the structure of this potential. In this direction a screened Coulomb potential with a specific rational screening function is considered. The analytical solutions for the critical values of the screening parameter and the form of the wave function at the threshold of the continous spectrum are obtained. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Screened Coulomb Potentials Extended Jacobi Polynomials Energy Spectrum

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High Dimensional Model Representation Approximation of an Evolution Operator with a First Order Partial Differential Operator Argument

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： İrem Yaman Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

In this work, a novel approximation scheme based on a recently developed representation, called the High Dimensional Model Representation (HDMR), is proposed to approximate evolution operators. The approximation is not developed at the operator level, instead the effect of the operator on an arbitrary function is approximated. The purpose of the work is to investigate how HDMR can be applied for the approximation of evolution operator and its efficiency. Although the approximation can be constructed for any order of multivariance, only the constant and univariate components of HDMR are considered in this work. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Lie algebraic exponential operator High Dimensional Model Representation

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Optimally Controlled Dynamics of One Dimensional Harmonic Oscillator: Linear Dipole Function and Quadratic Penalty

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： Burcu Tunga Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

This work deals with the optimal control of one dimensional quantum harmonic oscillator under an external field characterized by a linear dipole function. The penalty term is taken as kinetic energy. The objective operator whose expectation value is desired to get a prescribed target value is taken as the square of the position operator. The dipole function hypothesis in the external field is valid only for weak fields otherwise hyperpolarizability terms which contain powers of the field amplitude higher than 1 should be considered. The weak field assumption enables us to develop a first order perturbation approach to get approximate solutions to the wave and costate equations. These solutions contain the field amplitude and another unknown, so-called deviation constant, through some certain integrals. By inserting these expressions into the connection equation which functionally relates the field amplitude to the wave and costate function it is possible to produce an integral equation. Same manipulations on the objective equation results in an algebraic equation to determine the deviation parameter. The algebraic deviation equation produces incompatibility which can be relaxed by including second order perturbative term of wave function. The integral and algebraic equations mentioned above are asymptotically solved. Their global solutions are left to future works since the main purpose of this work is to obtain the so-called field and deviation equations. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： Optimal control quantum mechanics harmonic oscillator weak field interaction perturbation

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A Parametric Sensitivity Analysis for the Solution of Extrema Evaluation Problems via a Dimensionality Reducing Approximation Method

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Applied Numerical Analysis & computational Mathematics 2004年第1期1卷

作者： Tülin Kaman Metin Demiralp Computational Science and Engineering Program Informatics Institute İstanbul Technical University Maslak 34469 İstanbul Turkey Phone: +90 212 285 70 82 Fax: +90 212 285 70 73

This work aims to apply High Dimensional Model Representation (HDMR) to the sensitivity coefficient determination of the solutions of a multivariate extrema problem. The derivations are made for general functional structure and the illustrative applications are related to structures where the resulting extrema equations are matrix eigenvalue problems. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

关键词： High Dimensional Model Representation Extrema Finding Matrix Inversion Matrix Eigenvalue

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