44 Issue 1, ISSN: 0363-0129 Publisher Information: Society for Industrial & Applied Mathematics 3600 University City, Science Center, Philadelphia Pennsylvania 19104-2688, United States
Trang 1Зарубежная периодика по тематике ИПИ РАН
Выпуск № 5, октябрь 2006 г.
Материалы подготовлены лаб 13
Журнал «Управление и оптимизация» Общества промышленной и прикладной математики; 2005 год, том 44, вып 1
SIAM Journal on Control & Optimization; 2005, Vol 44 Issue 1,
ISSN: 0363-0129
Publisher Information: Society for Industrial & Applied Mathematics
3600 University City, Science Center, Philadelphia Pennsylvania 19104-2688, United States of America
Ключевые слова::BESSEL functions, BOUNDARY value problems, DIFFERENTIAL equations,
MATHEMATICAL physics, MATHEMATICS
Author-Supplied Keywords: spatially distributed control, symmetric system, boundary conditions
Abstract: We present a class of spatially interconnected systems with boundary conditions that have close links with their spatially invariant extensions In particular, well-posedness, stability, and performance of the extension imply the same characteristics for the actual, finite extent system In turn, existing synthesis methods for control of spatially invariant systems can be extended to this class The relation between the two kinds of systems is proved using ideas based on the "method of images" of partial differential equations theory and uses symmetry properties of the interconnection as a key tool [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Center for the Mathematics of Information, California Institute of Technology, 1200 E
California , Blvd., MS 136-93, Pasadena, CA 9112, 2Mechanical and Aerospace Engineering, Cornell
University, 101 Rhodes Hall, Ithaca, NY 1485, 2 Optimal Control of Ergodic Continuous-Time Markov
2 Оптимальное управление в эргодических Марковских цепях с непрерывным временем и
средней выборочной полезностью.
Optimal Control of Ergodic Continuous-Time Markov Chains with Average Sample-Path Rewards By:
Xianping Guo; Xi-Ren Cao, 3 Lp-Optimal Boundary Control for the Wave Equation By: Gugat, M.; Leugering, G.; Sklyar, G., p49, 26p
Ключевые слова::ALGORITHMS, DECISION making, DIFFUSION processes, MARKOV processes,
is based on the time discretization technique, the martingale stability theory, and the concept of potential We also provide both policy and value iteration algorithms for computing, or at least approximating, the $\epsilon$-ASPR-optimal stationary policies We illustrate with examples our main results as well as the difference
between the ASPR and the average expected reward criteria [ABSTRACT FROM AUTHOR]
Trang 2Author Affiliations: 1The School of Mathematics and Computational Science, Zhongshan University,
Guangzhou 510275, People's Republic of Chinа, 2Department of Electrical and Electronic Engineering, The Hong Kong University of Science and Technology, Hong Kong
3 Lp-оптимальное управление на границе в волновом уравнении.
Lp-Optimal Boundary Control for the Wave Equation
Ключевые слова::BOUNDARY value problems, DIFFERENTIAL equations, DIRICHLET principle, VON
Neumann algebras, WAVE equation
Author-Supplied Keywords: optimal control, boundary control, wave equation, analytic solution, distributed parameter systems, robust optimization, controllability, state constraint, sensitivity test examples
Abstract: We study problems of boundary controllability with minimal Lp norm ($p\in [2,\infty]$) for the one-dimensional wave equation, where the state is controlled at both boundaries through Dirichlet or Neumann conditions The problem is to reach a given terminal state and velocity in a given finite time, while minimizing the Lp norm of the controls We give necessary and sufficient conditions for the solvability of this problem
We show as follows how this infinite-dimensional optimization problem can be transformed into a problem which is much simpler: The feasible set of the transformed problem is described by a finite number of simple pointwise equality constraints for the control function in the Dirichlet case while, in the Neumann case, an additional integral equality constraint appears We provide explicit complete solutions of the problems for all
$p\in[2,\infty]$ in the Dirichlet case solutions for some typical examples in the Neumann case [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Lehrstuhl für angewandte Mathematik, Martensstr 3, 91058 Erlangen, Germany
2University Szczecin, Institute of Mathematics, Wielkopolska 15, 70451 Szczecin, Poland
Abstract: We develop a direct Lyapunov method for the almost sure open-loop stabilizability and
asymptotic stabilizability of controlled degenerate diffusion processes The infinitesimal decrease condition for
a Lyapunov function is a new form of Hamilton Jacobi Bellman partial differential inequality of second order
We give local and global versions of the first and second Lyapunov theorems, assuming the existence of a lowersemicontinuous Lyapunov function satisfying such an inequality in the viscosity sense An explicit formula for
a stabilizing feedback is provided for affine systems with smooth Lyapunov function Several examples
illustrate the theory [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Dipartimento di Matematica P e A., Universitàa di Padova, via Belzoni 7, 35131
Ключевые слова: APPROXIMATION theory, CALCULUS of variations, CRITICAL point theory
(Mathematical analysis), FUNCTIONAL analysis, FUNCTIONS, Entire
Author-Supplied Keywords:calculus of variations, Lavrentiev phenomenon, reparameterization
Abstract: We prove the following approximation theorem: given a function $x : [a,b] \to \mathbb{R}^N$
in the Sobolev space ${\bf W}^{\nu+1, 1}$, $\nu \geq 1$, and $\epsilon > 0$, there exists a function $x
[ABSTRACT FROM AUTHOR]
Trang 3Author Affiliations: 1Dipartimento di Matematica e Applicazioni, Universit#x00E0; degli Studi di
Milano-Bicocca,Via R Cozzi 53, 20126 Milano, Italy
6 Оптимизированный по времени синтез левоинвариантных систем управления по сериям
SO (3).
Time-Optimal Synthesis for Left-Invariant Control Systems on series SO (3) By: Boscain, Ugo; Chitour, Yacine.p111, 29p;
Ключевые слова: DIFFERENTIAL equations, Partial Numerical solutions, MAXIMUM entropy method,
MAXIMUM principles (Mathematics), VECTOR analysis, VECTOR fields
Author-Supplied Keywords: optimal control,optimal synthesis, minimum time, SO(3)
Abstract:Consider the control system $(\Sigma)$ given by $\dot x=x(f+ug)$, where $x\in SO(3)$, $|u|\leq 1$,
and $f,g\in so(3)$ define two perpendicular left-invariant vector fields normalized so that $\|f\|=\cos(\al)$ and
$\|g\|=\sin(\al)$, $\al\in ]0,\pi/4[$ In this paper, we provide an upper bound and a lower bound for $N(\alpha)$, the maximum number of switchings for time-optimal trajectories of $(\Sigma)$ More precisely, we show that
$N [ABSTRACT FROM AUTHOR]
Author Affiliations: 1SISSA-ISAS, Via Beirut 2-4, 34014 Trieste, Italy
2Université Paris XI, Laboratoiré des signaux et systèmes (L2S) Supélec, 3 rue Joliot-Cure, 91190 Yvette, France
Gif-sur-7 Контролируемость точного значения глобальной границы в классе квазилинейных
гиперболических систем по Законодательству об охране природы II.
Global Exact Boundary Controllability of a Class of Quasilinear Hyperbolic Systems of Conservation Laws II By: De-Xing Kong; Hui Yao.p140, 19p;
Ключевые слова: BOUNDARY value problems, DIFFERENTIAL equations, DIFFERENTIAL equations,
Nonlinear Numerical solutions, EXPONENTIAL functions, QUASILINEARIZATION
Author-Supplied Keywords: quasilinear hyperbolic system, conservation laws, global exact boundary, controllability, Cauchy problem, Goursat problem, classical discontinuous solution, contact discontinuity, optimal control time
Abstract: In this paper, by a new constructive method, the authors reprove the global exact boundary controllability of a class of quasilinear hyperbolic systems of conservation laws with linearly degenerate
characteristics It is shown that the system with nonlinear boundary conditions is globally exactly boundary controllable in the class of piecewise C1 functions In particular, the authors give the optimal control time of thesystem Finally, a new example belonging to this kind of system is also provided [ABSTRACT FROM
AUTHOR]
Author Affiliations: 1Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China
2Department of Mathematics, City University of Hong Kong, Kowloon, Hong Kong
8 Об обратном стохастическом уравнении Риккати в бесконечномерном измерении.
On the Backward Stochastic Riccati Equation in Infinite Dimensions By: Guatteri, Giuseppina; Tessitore, Gianmario.p159, 36p;
Ключевые слова: DIFFERENTIAL equations, DIFFERENTIAL equations, Partial, HILBERT space,
RICCATI equation, WAVE equation
Author-Supplied Keywords: backward stochastic differential equation, Riccati equation, linear
quadratic optimal control, Hilbert spaces, stochastic coefficients
Abstract: We study backward stochastic Riccati equations (BSREs) arising in quadratic optimal control problems with infinite dimensional stochastic differential state equations We allow the coefficients, both in the state equation and in the cost, to be random In such a context BSREs are backward stochastic differential equations existing in a non-Hilbert space and involving quadratic nonlinearities We propose two different notions of solutions to BSREs and prove, for both of them, existence and uniqueness results We also show that such solutions allow us to perform the synthesis of the optimal control Finally we apply our results to the
Trang 4optimal control of a delay equation and of a wave equation with random damping [ABSTRACT FROM
AUTHOR]
Author Affiliations: 1Dipartimento di Matematica, Politecnico di Milano, piazza Leonardo da Vinci 32, 20133
Milano, Itali2Dipartimento di Matematica, Universitá di Parma, via D'Azeglio 85, 43100 Parma, Italia
9 Релаксация проблемы оптимального проектирования с помощью целочисленных
ограничений.
Relaxation of an Optimal Design Problem With an Integral-Type Constraint By: Aranda, Ernesto; Bellido, JoséC., p195, 15p;
Ключевые слова: EXPERIMENTAL design, HEAT equation, MATHEMATICS, OPTIMAL designs
(Statistics), VECTOR fields
Author-Supplied Keywords:optimal design, relaxation, constrained quasiconvexification
Abstract: We study a new relaxation for a two-dimensional optimal design problem in conductivity
consisting of determining how to mix two given conducting materials in order to minimize the amount of one
of them, subject to a constraint on the efficiency of the conducting properties of the mixture Our approach here
is different from that obtained in [R V Kohn and G Strang, Comm Pure Appl Math., 39 (1986), pp 113 137,139 182, 353 377], and is based on a local reformulation of the optimal design problem by means of the introduction of new potentials The concept of constrained quasiconvexification is used in an important way [ABSTRACT FROM AUTHOR]
Author Affiliations: 1E.T.S.I Industriales, Universidad de Castilla-La Mancha, Campus Universitario s/n,
13071-Ciudad Real, Spain
2Mathematical Institute, University of Oxford, OX1 3LB, Oxford, UK
10 Обратная теорема Ляпунова для вариации линейных параметров и линейных систем коммутации
A Converse Lyapunov Theorem for Linear Parameter-Varying and Linear Switching Systems By: Wirth, Fabian., p210, 30p;
Ключевые слова: DIFFERENTIAL equations, Linear, EXPONENTIAL functions, LINEAR systems,
LYAPUNOV functions, SYSTEM theory
Author-Supplied Keywords: converse Lyapunov theorem, linear parameter-varying systems, linear switching systems, linear flows on vector bundles, Gelfand formula, periodic systems
Abstract: We study families of linear time-varying systems, where time variations have to satisfy
restrictions on the dwell time, that is, on the minimum distance between discontinuities, as well as on the derivative in between discontinuities Such classes of systems may be formulated as linear flows on vector bundles The main objective of this paper is to construct parameter-dependent Lyapunov functions, which characterize the exponential growth rate This is possible in the generic irreducible case As an application the Gelfand formula is generalized to the class of systems studied here In other words, the maximal exponential growth rate may be approximated by only considering the periodic systems in the family of time-varying systems A perspective on the question of continuous dependence of the exponential growth rate on the data is given [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Hamilton Institute, NUI Maynooth, Maynooth, Co Kildare, Ireland
11 Вычисление факторизации без потерь (J, J') для матриц общего вида с рациональными элементами.
Computation of the (J, J')-Lossless Factorization for General Rational Matrices By: Delin Chu; Ho, Daniel W C., p240, 28p;
Ключевые слова:ALGORITHMS, EIGENVALUES, FACTORIZATION (Mathematics), FACTORIZATION
of operators, MATHEMATICS
Author-Supplied Keywords:J, J'-lossless factorization, rational matrix, eigenfactorization orthogonal
transformation, J'-lossless factorization, J
Trang 5Abstract: J, J'-lossless factorization plays a central role in $H [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, National University of Singapore, 2 Science Drive 2,
Singapore 117543, 2Department of Mathematics, City University of Hong Kong, Hong Kong
Abstract: An optimal control problem for the thermistor system is considered First, the precise
mathematical problem is established and the proof of existence of the optimal solution is given with appropriatefunction spaces Then, Gâteaux differentiability is shown for the thermistor system, with respect to control, and the optimality system is obtained [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, Ajou University, Suwon 442-749, South Korea
2V A Steklov Institute of Mathematics, St Petersburg Department, Fontanka 27, 191011 St Petersburg, Russia
13 Устойчивость стохастической аппроксимации при контролируемых условиях.
Stability of Stochastic Approximation under Verifiable Conditions By: Andrieu, Christophe; Moulines, Eric; Priouret, Pierre p283, 30p;
Ключевые слова:APPROXIMATION theory, BOUNDARY value problems, DIFFERENTIAL equations,
STOCHASTIC approximation, STOCHASTIC processes
Author-Supplied Keywords: stochastic approximation, state-dependent noise, randomly varying
truncation, adaptive Markov chain Monte Carlo
Abstract: In this paper we address the problem of the stability and convergence of the stochastic
approximation procedure \[ \theta [ABSTRACT FROM AUTHOR]
Author Affiliations: 1University of Bristol, School of Mathematics, University Walk, BS8 1TW, UK
2école Nationale Supérieure des Télécommunications, URA CNRS 820, 46, rue Barrault, F 75634 Paris 13, France, 3Université Pierre & Marie Curie, Laboratoire de Probabilités et Modélisation Aléatoire, URA CNRS
Ключевые слова: DIGITAL control system, EIGENVALUES, EXPONENTIAL functions, OPERATOR
theory, TRANSFER operators
Author-Supplied Keywords: sampled-data system, spectral analysis, robust stability
L2-stability, exponential stability
Abstract: This paper begins by studying some spectral properties of the transfer operators of sampled-data systems described by applying the lifting technique Through a "nonasymptotic" characterization of the transfer operator, its spectrum is determined in terms of finite-dimensional eigenvalue problems Then, it is shown that aclose connection with such eigenvalue problems and the exponential stability condition can be exploited to study the robust internal (exponential) stability problem of sampled-data systems Since the transfer operator is relevant to input-output characteristics, the relationship between input-output stability and internal stability is also discussed in the context of sampled-data systems [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Electrical Engineering, Kyoto University, Kyotodaigaku-Katsura,
Nishikyo-ku, Kyoto 615-8510, Japan
Trang 615 Стохастическая аппроксимация и дифференциальное включение.
Stochastic Approximations and Differential Inclusions By: Benạm, Michel; Hofbauer, Josef; Sorin, Sylvain p328, 21p;
Ключевые слова:APPROXIMATION theory, BESSEL functions, DIFFERENTIAL equations,
STOCHASTIC approximation, STOCHASTIC processes
Author-Supplied Keywords: stochastic approximation, differential inclusions, set-valued dynamical, systems, chain recurrence, approachability, fictitious play
Abstract: The dynamical systems approach to stochastic approximation is generalized to the case where the mean differential equation is replaced by a differential inclusion The limit set theorem of Benạm and Hirsch is extended to this situation Internally chain transitive sets and attractors are studied in detail for set-valued dynamical systems Applications to game theory are given, in particular to Blackwell's approachability theorem and the convergence of fictitious play [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Institut de Mathematiques, Université de Neuchâtel, Rue Emile-Argand 11, Neuchâtel,
Switzerland, 2Department of Mathematics, University College London, London WC1E 6BT, UK, and Institut fur Mathematik, Universität Wien, , Nordbergstrasse 15, 1090 Wien, Austria
3Laboratoire d'Econométrie, Ecole Polytechnique, 1 rue Descartes, 75005 Paris, France, and Equipe
Combinatoire et Optimisation, UFR 929, Université P et M Curie - Paris 6, 175 Rue du Chevaleret, 75013 Paris, France
Author-Supplied Keywords:damped wave equation, optimal location, spillover, stabilization
Abstract: In this paper, we are interested in finding the optimal location and shape of the actuators in a stabilization problem Namely, we consider the one-dimensional wave equation damped by an internal feedbacksupported on a subdomain $\omega$ of given length The criterion we want to optimize represents the rate of decay of the total energy of the system It theoretically involves all the eigenmodes of the operator From an engineering point of view, it seems more realistic to consider only a finite number of modes, say the N first ones In that context, we are able to prove existence and uniqueness of an optimal domain $\omega
[ABSTRACT FROM AUTHOR]
Author Affiliations: 1Dassault Systems and Institut Élie Cartan Nancy UMR 7502 UHP-CNRS-INRIA 54506
Vandoeuvre-les-Nancy, France, 2Ecole des Mines de Nancy-INPL, Institut Élie Cartan Nancy UMR 7502 CNRS-INRIA 54506 Vandoeuvre-les-Nancy, France
UHP-17 Вырожденные проблемы стохастического управления при экспоненциальной стоимости и слабой двухсторонней динамике Определение значений вязкости и принцип максимума.
Degenerate Stochastic Control Problems with Exponential Costs and Weakly Coupled Dynamics: Viscosity Solutions and a Maximum Principle By: Huang, Minyi; Caines, Peter E.; Malhamé, Roland P p367, 21p;
Ключевые слова: CALCULUS of variations, HAMILTON-Jacobi equations, MATHEMATICA,
optimization, VISCOSITY solutions, WIRELESS communication systems
Author-Supplied Keywords: degenerate stochastic control, power control, HJB equations, dynamic programming, viscosity solutions
Abstract: This paper considers a class of optimization problems arising in wireless communication
systems We analyze the optimal control and the associated Hamilton Jacobi Bellman (HJB) equations It turns out that the value function is a unique viscosity solution of the HJB equation in a certain function class Todeal with the fast growth condition of the value function in establishing uniqueness, we construct particular semiconvex/semiconcave approximations for the viscosity sub/supersolutions, and obtain a maximum principle
on unbounded domains The localized envelope function technique introduced in this paper permits an analysis
Trang 7of the uniqueness of viscosity solutions defined on unbounded domains in cases with very general growth conditions when combined with appropriate system dynamics The optimization problem with state constraints
is also considered [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Electrical and Electronic Engineering, University of Melbourne, Victoria
3010, Australia
2Department of Electrical and Computer Engineering, McGill University, 3480 University Street, Montreal, QCH3A 2A7, Canada, 3Department of Electrical Engineering, École Polytechnique de Montréal, 2900 Boul Édouard Montpetit, Montreal, QC H3C 3A7,Canada
Журнал «Управление и оптимизация» Общества промышленной и прикладной математики; 2005 год, том 44, вып 2
SIAM Journal on Control & Optimization; 2005, Vol 44 Issue 2,
ISSN: 0363-0129
Publisher Information: Society for Industrial & Applied Mathematics
3600 University City, Science Center, Philadelphia Pennsylvania 19104-2688, United States of America
http://www.siam.org
СТАТЬИ
1 Ограниченная вариация проблемы управления для процессов диффузии.
A Bounded Variation Control Problem for Diffusion Processes By: Weerasinghe, Ananda p389, 29p;
Ключевые слова : MATHEMATICAL analysis, MATHEMATICS, STOCHASTIC analysis, STOCHASTIC
processes
Author-Supplied Keywords: stochastic optimal control, optimal stopping, local-time processes,
diffusions with reflections
Abstract: We consider an infinite horizon discounted cost minimization problem for a one-dimensional stochastic differential equation model The available control is an added bounded variation process The cost structure involves a running cost function and a proportional cost for the use of the control process The runningcost function is not necessarily convex We obtain sufficient conditions to guarantee the optimality of the zero control Also, for unbounded cost functions, we provide sufficient conditions which make our optimal state process a reflecting diffusion on a compact interval In both cases, the value function is a C2 function For bounded cost functions, under additional assumptions, we obtain a complex optimal strategy which turned out
to be a mixture of jumps and local-time-type processes In this case, we show that the value function is only a C1 function and that it fails to be a C2 function We also discuss a related variance control problem
[ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, 400 Carver Hall, Iowa State University, Ames, IA 50011
2 Топологии графов, метрики лакун и робастная устойчивость в нелинейных системах.
Graph Topologies, Gap Metrics, and Robust Stability for Nonlinear Systems By: Bian, W.; French, M.p418, 26p;
Ключевые слова : GRAPHIC methods, NONLINEAR systems, SCIENCE, SYSTEM theory
Author-Supplied Keywords: gap metric, graph metric, graph topology, robust stability, nonlinear systems
Abstract: Graph topologies for nonlinear operators which admit coprime factorizations are defined w.r.t a gain , function notion of stability in a general normed signal space setting Several metrics are also defined and their relationship to the graph topologies are examined In particular, relationships between nonlinear
generalizations of the gap and graph metrics, Georgiou-type formulae, and the graph topologies are established.Closed loop robustness results are given w.r.t the graph topology, where the role of a coercivity condition on the nominal plant is emphasized [ABSTRACT FROM AUTHOR]
Author Affiliations: 1School of Electronics and Computer Science, University of Southampton, Southampton
SO17 1BJ, United Kingdom
Trang 8processes Employing Tanaka's formula, optimal control and optimal cost are explicitly obtained via solutions
to two extended stochastic Riccati equations (ESREs) The ESREs, introduced for the first time in this paper, are highly nonlinear backward stochastic differential equations (BSDEs), whose solvability is proved based on
a truncation function technique and Kobylanski's results The general results obtained are then applied to a mean-variance portfolio selection problem for a financial market with random appreciation and volatility rates, and with short-selling prohibited Feasibility of the problem is characterized, and efficient portfolios and
efficient frontier are presented in closed forms [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Institut de Recherche Mathématique de Rennes, Université de Rennes 1, Campus de
Beaulieu, 35042 Rennes Cedex, France, 2Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong
4 Одновременное решение прямой и двойственной задач активного нахождения стратегии
управления с оптимальными границами для нелинейных систем реактивной диффузии.
A Primal-Dual Active Set Strategy for Optimal Boundary Control of a Nonlinear Reaction-Diffusion System By: Griesse,R.; Volkwein, S.p467, 28p;
Ключевые слова :BURGERS equation, DIFFUSION, NONLINEAR systems, SYSTEM theory
Author-Supplied Keywords: reaction-diffusion equations, optimal boundary control, bilateral and integral control constraints, primal-dual active set strategy, semismooth Newton methods
Abstract: This paper is concerned with optimal boundary control of an instationary reaction-diffusion system in three spatial dimensions This problem involves a coupled nonlinear system of parabolic differential equations with bilateral as well as integral control constraints We include the integral constraint in the cost by apenalty term whereas the bilateral control constraints are handled explicitly First- and second-order conditions for the optimization problem are analyzed A primal-dual active set strategy is utilized to compute optimal solutions numerically The algorithm is compared to a semismooth Newton method [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Karl-Franzens-Universität Graz, Institut für Mathematik, Heinrichstrasse 36, A-8010
Graz, Austria, 2Johann Radon Institute for Computational and Applied Mathematics (RICAM),
Altenbergerstrasse 69, A-4040 Linz, Austria
5 Алгоритм индивидуального обучения в играх нормальной формы
Individual Q-Learning in Normal Form Games By: Leslie, David S.; Collins, E J.p495, 20p;
Ключевые слова : COMPREHENSION, EDUCATION, EXTENSION (Logic), LEARNING
Author-Supplied Keywords: reinforcement learning, normal form games, stochastic approximationmulti-agent learning, player-dependent learning rates
Abstract: The single-agent multi-armed bandit problem can be solved by an agent that learns the values of each action using reinforcement learning However, the multi-agent version of the problem, the iterated normal form game, presents a more complex challenge, since the rewards available to each agent depend on the
strategies of the others We consider the behavior of value-based learning agents in this situation, and show that such agents cannot generally play at a Nash equilibrium, although if smooth best responses are used, a Nash
Trang 9distribution can be reached We introduce a particular value-based learning algorithm, which we call individual Q-learning, and use stochastic approximation to study the asymptotic behavior, showing that strategies will converge to Nash distribution almost surely in 2-player zero-sum games and 2-player partnership games Player-dependent learning rates are then considered, and it is shown that this extension converges in some games for which many algorithms, including the basic algorithm initially considered, fail to converge
[ABSTRACT FROM AUTHOR]
Author Affiliations: 1School of Economics, The University of New South Wales, Sydney, NSW 2052,
Australia, 2Department of Mathematics, University Walk, Bristol BS8 1TW, UK
6 Процедура проектирования фильтрации, использующая метрику H2 and H(infinity) для установления неопределенности.
H2 and H(infinity) Filtering Design Subject to Implementation Uncertainty By: de Oliveira, Maurício C.; Geromel, José C.p515, 16p
Ключевые слова : CONTROL theory, LINEAR systems, MATRIX inequalities, SYSTEM analysis,
SYSTEM theory
Author-Supplied Keywords: robust filtering, implementation uncertainty, fragility
linear matrix inequalities
Abstract: This paper presents new filtering design procedures for discrete-time linear systems It provides asolution to the problem of linear filtering design, assuming that the filter is subject to parametric uncertainty The problem is relevant, since the proposed filter design incorporates real world implementation constraints that are always present in practice The transfer function and the state space realization of the filter are
simultaneously computed The design procedure can also handle plant parametric uncertainty In this case, the plant parameters are assumed not to be exactly known but belonging to a given convex and closed polyhedron Robust performance is measured by the H2 and H$ [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mechanical and Aerospace Engineering, University of California, San
Diego, La Jolla, CA 92093-041 2DSCE, School of Electrical and Computer Engineering, UNICAMP, CP 6101, 13083-970, Campinas, SP, Brazil
7 Формулы пространства состояний в проблеме Нехари-Такаджи для устойчивых бесконечномерных систем.
неэкспоненциально-State-Space Formulas for the Nehari Takagi Problem for Nonexponentially Stable Infinite-Dimensional
Systems By: Ball, Joseph A.; Mikkola, Kalle M.; Sasane, Amol J.p531, 33p;
Ключевые слова : FACTORIZATION (Mathematics), FACTORIZATION of operators, MATHEMATICS,
TECHNOLOGY
Author-Supplied Keywords: Nehari Takagi problem, infinite-dimensional systems, state-space
formulas, Nehari-Takagi problem
Abstract: We obtain state-space formulas for the solution of the Nehari Takagi/suboptimal Hankel norm approximation problem for infinite-dimensional systems with a nonexponentially stable generator, via the method of J-spectral factorization We make key use of a purely frequency-domain solution of the problem [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, 460 McBryde, Virginia Polytechnic Institute and State
University, Blacksburg, VA 24061-0123
2Institute of Mathematics, Box 1100, FIN-02015 Helsinki University of Technology, Helsinki, Finland
3Department of Mathematics, London School of Economics, Houghton St., London WC2A 2AE, UK
Trang 10Author-Supplied Keywords: networked control systems, finite data rate, communication constraints, stabilizability
Abstract: The paper addresses a feedback stabilization problem involving bit-rate communication capacity constraints A discrete-time partially observed linear system is studied Unlike classic theory, the signals from multiple sensors are transmitted to the controller over separate finite capacity communication channels The sensors do not have constant access to the channels, and the channels are not perfect: the messages incur time-varying transmission delays and may be corrupted or lost However, we suppose that the time-average number
of bits per sample period that can be successfully transmitted over the channel during a time interval converges
to a certain limit as the length of the interval becomes large Necessary and sufficient conditions for
stabilizability are established They give the tightest lower bounds on the channel capacities for which
stabilization is possible An algorithm for stabilization is also presented [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics and Mechanics, Saint Petersburg University, Universitetskii
pr 28, Petrodvoretz, St Petersburg, 198504, Russia
2School of Electrical Engineering and Telecommunications, The University of New South Wales, Sydney,
Ключевые слова :LINEAR operators, LINEAR systems, MATHEMATICS, SYSTEM theory
Author-Supplied Keywords: continuous-time periodic system, Nyquist criterion, determinant of
Hilbert Schmidt operators, convergence, determinant of Hilbert-Schmidt operators
Abstract: First, by using the 2-regularized determinant technique for Hilbert Schmidt operators, the computation formula, infinite-product convergence, and analyticity of the 2-regularized determinant of the modified harmonic state operator in finite-dimensional linear continuous-time periodic (FDLCP) systems are derived in this paper Second, based on these results, a 2-regularized Nyquist criterion is established for
asymptotic stability analysis of a class of FDLCP systems for the first time Third, a numeric implementation algorithm for the 2-regularized Nyquist criterion is also proposed via the staircase truncation on the harmonic transfer operator of the FDLCP system concerned Finally, to illustrate the results of this paper, asymptotic stability of the lossy Mathieu differential equation is investigated [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Electrical Engineering, Kyoto University, Kyotodaigaku-Katsura,
Nishikyo-ku, Kyoto 615-8510, Japan
10 Производящий ряд для взаимосвязанных аналитических нелинейных систем.
Generating Series for Interconnected Analytic Nonlinear Systems By: Gray, W Steven; Yaqin Li.p646, 27p;
Ключевые слова :MATHEMATICS, NONLINEAR operators, NONLINEAR systems, SYSTEM theory,
connection, and feedback connection In each case, the corresponding generating series is produced and
conditions for the convergence of the corresponding Fliess operator are given In the process, an existing notion
of a composition product for formal power series has its set of known properties significantly expanded In addition, the notion of a feedback product for formal power series is shown to be well defined in a broad
context, and its basic properties are characterized [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Electrical and Computer Engineering, Old Dominion University,
Trang 11Ключевые слова : DYNAMIC programming, MATHEMATICAL optimization, PROGRAMMING
(Mathematics), SYSTEMS engineering
Author-Supplied Keywords: differential inclusions, nondegenerate maximum principle, dynamic programming, generalized derivatives, state constraints, variational inclusions
Abstract: We consider the Mayer optimal control problem with dynamics given by a nonconvex
differential inclusion, whose trajectories are constrained to a closed set and obtain necessary optimality
conditions in the form of the maximum principle together with a relation between the costate and the value function This additional relation is applied in turn to show that the maximum principle is nondegenerate We also provide a sufficient condition for the normality of the maximum\break principle To derive these results weuse convex linearizations of differential inclusions and convex linearizations of constraints along optimal trajectories Then duality theory of convex analysis is applied to derive necessary conditions for optimality In this way we extend the known relations between the maximum principle and dynamic programming from the unconstrained problems to the constrained case [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Faculty of Mathematics and Informatics, University of Bucharest, Academiei 14,
010014 Bucharest, Romania, 2CNRS, CREA, École Polytechnique, 1, rue Descartes, 75005 Paris, France
12 Устойчивость типа «вход-состояние» в биохимических сетях с регулируемой скоростью обмена.
Input-to-State Stability of Rate-Controlled Biochemical Networks By: Chaves, Madalena.p704, 24p;
Ключевые слова : MATHEMATICAL optimization, MATHEMATICS, NONLINEAR systems,
OPERATIONS research, SYSTEM theory
Author-Supplied Keywords: stability, robustness, biochemical networks
Abstract: In this paper, the study of the class of biochemical systems known as zero deficiency networks isextended to the case of time-varying kinetic parameters We show that the resulting class of nonlinear systems with inputs satisfies a notion of input-to-state stability uniformly over a set of parameters In particular, the input-to-state stability estimates allow us to characterize the robustness of zero deficiency networks with respect to perturbations in the parameters as well as study their stability when the reaction rates are controlled
by an independent process [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, Rutgers University, 110 Frelinghuysen Rd., Piscataway, NJ
08854
13 Оптимальный оптический поток.
An Optimal Optical Flow By: Ito, Kazufumi p728, 15p;
Ключевые слова :CONTROL theory, MATHEMATICAL optimization, MATHEMATICS, SYSTEM
analysis, SYSTEM theory
Author-Supplied Keywords: optical flow, feedback solution
Abstract: The problem of determining optical flow for the image registration problem is discussed
Feedback solutions are proposed, and it is shown that they are optimal for certain optimal control formulations
of the problem Well-posedness of the proposed feedback solutions is analyzed, and numerical findings are presented [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Center for Research in Scientific Computation, North Carolina State University,
Raleigh, NC 27695-8205
14 Проблемы оптимизации изогнутых механических структур.
Optimization Problems for Curved Mechanical Structures By: Arnăutu, Viorel; Sprekels, Jürgen; Tiba,
Dan.p743, 33p;
Ключевые слова :CONTROL theory, GEOMETRY, MATHEMATICAL optimization, MATHEMATICS,
SYSTEM analysis, SYSTEM theory
Author-Supplied Keywords: shells and curved rods, minimal regularity, optimal design
Trang 12Abstract: We study optimal design problems for three-dimensional curved rods and for shells under
minimal regularity assumptions for the geometry The results that we establish concern the existence of optimal shapes and the sensitivity analysis We also compute some numerical examples for the optimization of curve rods The models used have been investigated in our previous works [A Ignat, J Sprekels, and D Tiba, Math Methods Appl Sci., 25 (2002), pp 835 854], [J Sprekels and D Tiba, Adv Math Sci Appl., 12 (2002), pp 175 190] A complete study of Kirchhoff Love arches and of related minimization questions has been
performed in [A Ignat, J Sprekels, and D Tiba, SIAM J Control Optim., 40 (2001), pp 1107 1133]
[ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, University "Al I Cuza," RO-6600 Iaşi, Romania
2Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstrasse 39, D-10117 Berlin, Germany3Institute of Mathematics, Romanian Academy, P O Box 1-764, RO-70700 Bucharest, Romania
Обзоры Общества промышленной и прикладной математики, том 47,
вып 3, 2005 год
SIAM Review, 2005, Vol 47 Issue 3,
Society for Industrial and Applied Mathematics
3600 University City Science Center | Philadelphia, PA 19104 USA
Canonical Forms for Hermitian Matrix Pairs under Strict Equivalence and Congruence By: Lancaster, Peter; Rodman, Leiba p407
Ключевые слова :ALGEBRA, Universal, DIOPHANTINE analysis, MATRICES, NUMBER theory,
NUMBERS, Complex, PERMUTATIONS
Author-Supplied Keywords: canonical forms, matrix pairs, strict equivalence, congruence
Abstract: After a brief historical review and an account of the canonical forms attributed to Jordan and Kronecker, a systematic development is made of the simultaneous reduction of pairs of quadratic forms over thecomplex numbers and over the reals These reductions are by strict equivalence and by congruence, and
essentially complete proofs are presented Some closely related results which can be derived from the canonicalforms are also included They concern simultaneous diagonalization, a new criterion for the existence of
positive definite linear combinations of a pair of Hermitian matrices, and the canonical structures of matrices which are self-adjoint in an indefinite inner product [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics and Statistics, University of Calgary, Calgary, AB, T2N
1N4, Canada, 2Department of Mathematics, College of William and Mary, Williamsburg, VA
Trang 134 Быстрое и устойчивое решение проблемы переноса излучения.
A Fast and Stable Solution Method for the Radiative Transfer Problem By: Edström, Per p447-468, 22p;
Ключевые слова : DIFFERENTIAL equations, Partial, EUCLID'S Elements, GEOMETRY, RADIATIVE
transfer, SCATTERING (Mathematics), SPEED
Author-Supplied Keywords: radiative transfer, discrete ordinates, solution method, numerical stability, speed Abstract: Radiative transfer theory considers radiation in turbid media and is used in a wide range of applications This paper outlines a problem formulation and a solution method for the radiative transfer problem
in multilayer scattering and absorbing media using discrete ordinate model geometry A selection of different steps is brought together The main contribution here is the synthesis of these steps, all of which have been used
in different areas, but never all together in one method First, all necessary steps to get a numerically stable solution procedure are treated, and then methods are introduced to increase the speed by a factor of several thousand This includes methods for handling strongly forward-scattering media The method is shown to be unconditionally stable, though the problem was previously considered numerically intractable [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Engineering, Physics and Mathematics, Mid Sweden University,
Gånsviksvägen 2, 87188 Härnösand, Sweden
5 Усовершенствование метода частных решений.
Reviving the Method of Particular Solutions By: Betcke, Timo; Trefethen, Lloyd N.p469-491, 23p, 4 diagrams,
13 graphs, 1c;
Ключевые слова : ALGORITHMS, DIFFERENTIAL equations, Partial, EIGENVALUES, LAPLACIAN
operator, MATRICES, POLYGONS, POLYNOMIALS
Author-Supplied Keywords: eigenvalues, method of particular solutions, subspace angles
Abstract: Fox, Henrici, and Moler made famous a "method of particular solutions" for computing
eigenvalues and eigenmodes of the Laplacian in planar regions such as polygons We explain why their
formulation of this method breaks down when applied to regions that are insufficiently simple and propose a modification that avoids these difficulties The crucial changes are to introduce points in the interior of the region as well as on the boundary and to minimize a subspace angle rather than just a singular value or a
determinant Similar methods may be used to improve other "mesh-free" algorithms for a variety of
computational problems [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Computing Laboratory, Oxford University, Wolfson Building, Parks Road, Oxford OX1
3QD, UK
6 Сходимость полиномиального перезапуска метода Крылова для вычисления собственных значений.
Convergence of Polynomial Restart Krylov Methods for Eigenvalue Computations By: Beattie, Christopher A.;Embree, Mark; Sorensen, D C.p492-515, 24p, 1 diagram, 9 graphs;
Ключевые слова : ALGEBRA, Universal, CONVERGENCE, EIGENVALUES, FUNCTIONAL analysis,
HERMITIAN forms, MATRICES, POLYNOMIALS
Author-Supplied Keywords: Krylov subspaces, Arnoldi algorithm, Lanczos algorithm, eigenvalue
computations, containment gap, pseudospectra
Abstract: Krylov subspace methods have led to reliable and effective tools for resolving large-scale, Hermitian eigenvalue problems Since practical considerations often limit the dimension of the approximating Krylov subspace, modern algorithms attempt to identify and condense significant components from the current subspace, encode them into a polynomial filter, and then restart the Krylov process with a suitably refined starting vector In effect, polynomial filters dynamically steer low-dimensional Krylov spaces toward a desired invariant subspace through their action on the starting vector The spectral complexity of nonnormal matrices makes convergence of these methods difficult to analyze, and these effects are further complicated by the polynomial filter process The principal object of study in this paper is the angle an approximating Krylov subspace forms with a desired invariant subspace Convergence analysis is posed in a geometric framework that
non-is robust to eigenvalue ill-conditioning, yet remains relatively uncluttered The bounds described here suggest
Trang 14that the sensitivity of desired eigenvalues exerts little influence on convergence, provided the associated
invariant subspace is well-conditioned; ill-conditioning of unwanted eigenvalues plays an essential role This framework also gives insight into the design of effective polynomial filters Numerical examples illustrate the subtleties that arise when restarting non-Hermitian iterations [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mathematics, Virginia Polytechnic Institute and State University,
Blacksburg, VA 24061-012 2Department of Computational and Applied Mathematics, Rice University, 6100 Main Street MS 134, Houston, TX 77005-1892
7 Обзор направления, представляемого серией статей по математическому моделированию.
SIGEST - Introduction p517-517, 1p;
Ключевые слова : MATHEMATICAL models, MATHEMATICS
Abstract: Introduces a series of articles on mathematical modeling
Abstract: The spring-loaded inverted pendulum (SLIP), or monopedal hopper, is an archetypal model for
running in numerous animal species Although locomotion is generally considered a complex task requiring sophisticated control strategies to account for coordination and stability, we show that stable gaits can be found
in the SLIP with both linear and "air" springs, controlled by a simple fixed-leg reset policy We first derive touchdown-to-touchdown Poincaré maps under the common assumption of negligible gravitational effects during the stance phase We subsequently include and assess these effects and briefly consider coupling to pitching motions We investigate the domains of attraction of symmetric periodic gaits and bifurcations from the branches of stable gaits in terms of nondimensional parameters [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Mechanical and Aerospace Engineering, Princeton University, Princeton,
NJ 0854 2Department of Electrical Engineering and Computer Science, University of Michigan, Ann Arbor, MI
4810 3Department of Mechanical and Aerospace Engineering, Program in Applied and Computational
Mathematics, Princeton University, Princeton, NJ 08544
4Department of Electrical and Systems Engineering, University of Pennsylvania, Philadelphia, PA 19104
9 Знакомство с содержанием серии статей в области асимптотической теории математики.
Education - Introduction By: Bernoff, Andrew J.p551-551, 1p;
Ключевые слова : ASYMPTOTIC distribution (Probability theory), MATHEMATICS
Abstract: Introduces a series of articles on asymptotic theory in mathematics
10 Hyperasymptotics and the Linear Boundary Layer Problem: Why Asymptotic Series Diverge By: Boyd,John P.p553-575, 23p, 2 charts, 8 graphs;
Ключевые слова : APPROXIMATION theory, BOUNDARY layer, FLUID dynamics, FUNCTIONAL
analysis, HYDRODYNAMICS, PERTURBATION (Mathematics)
Author-Supplied Keywords: perturbation methods, asymptotic, hyperasymptotic, exponential smallnessbeyond-all-orders perturbation theory
Abstract: The simplest problem with boundary layers, ε²u<sub>xx</sub> - u = -f(x) is used to illustrate (i)
why the perturbation series in powers of ε is asymptotic but divergent, (ii) why the optimally truncated
expansion is "superasymptotic" in the sense that that error is proportional to exp(-[constant]/ε), and (iii) how to obtain an improved "hyperasymptotic" approximation [ABSTRACT FROM AUTHOR]
Author Affiliations: 1Department of Atmospheric, Oceanic and Space Science, University of Michigan, 2455
Hayward Avenue, Ann Arbor, MI 48109