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International Conference on control, Decision and Information Technologies (CoDIT)

作者： Bhaya, Amit Pazos, Fernando A. Univ Fed Rio de Janeiro Dept Elect Engn PEE COPPE UFRJ BR-21945970 Rio De Janeiro RJ Brazil

ISBN: (纸本)9781467355476;9781467355490

""This paper revisits a class of recently proposed so-called invariant manifold methods for zero finding, showing that this class of homotopy methods can be designed in a natural manner from the control liapunov function (CLF) approach proposed earlier by the authors. Moreover, the CLF approach clarifies the interplay between the homotopy parameter, which can be interpreted as a learning parameter and the choice of descent direction, which is the control vector and guides the choice of both. From this viewpoint, maintaining manifold invariance is equivalent to ensuring that the CLF satisfies a certain ordinary differential equation, involving the learning parameter, that allows an estimate of rate of convergence. In order to illustrate this approach, algorithms recently proposed using the invariant manifold approach, are rederived, via CLFs, in a unified manner.""

关键词： Homotopy methods continuation methods learning control liapunov functions

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Design of second order neural networks as dynamical control systems that aim to minimize nonconvex scalar functions

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NEUROCOMPUTING 2012年 97卷 174-191页

作者： Pazos, Fernando A. Bhaya, Amit Kaszkurewicz, Eugenius Univ Fed Rio de Janeiro Dept Elect Engn PEE COPPE UFRJ BR-21945970 Rio De Janeiro Brazil

This paper presents a unified way to design neural networks characterized as second order ordinary differential equations (ODEs) that aim to find the global minimum of nonconvex scalar functions. These neural networks, alternatively referred to as continuous time algorithms, are interpreted as dynamical closed loop control systems. The design is based on the control liapunov function (CLF) method. For nonconvex scalar functions, the goal of these algorithms is to produce trajectories, starting from an arbitrarily chosen initial guess, that do not get stuck in local minima, thereby increasing the chances of converging to the global minimum. (C) 2012 Elsevier B.V. All rights reserved.

关键词： Neural networks control liapunov functions Second order continuous time control systems

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control liapunov function design of neural networks that solve convex optimization and variational inequality problems

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NEUROCOMPUTING 2009年第16-18期72卷 3863-3872页

作者： Pazos, Fernando A. Bhaya, Amit Univ Fed Rio de Janeiro Dept Elect Engn PEE COPPE BR-21945970 Rio De Janeiro Brazil

This paper presents two neural networks to find the optimal point in convex optimization problems and variational inequality problems, respectively. The domain of the functions that define the problems is a convex set, which is determined by convex inequality constraints and affine equality constraints. The neural networks are based on gradient descent and exact penalization and the convergence analysis is based on a control liapunov function analysis, since the dynamical system corresponding to each neural network may be viewed as a so-called variable structure closed loop control system. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Variable structure control systems control liapunov functions Convex optimization Variational inequalities

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Comparative Study of the CG and HBF ODEs Used in the Global Minimization of Nonconvex functions

Comparative Study of the CG and HBF ODEs Used in the Global ...

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19th International Conference on Artificial Neural Networks (ICANN 2009)

作者： Bhaya, Amit Pazos, Fernando A. Kaszkurewicz, Eugenius Univ Fed Rio de Janeiro COPPE Dept Elect Engn BR-21945970 Rio de Janeiro Brazil

ISBN: (纸本)9783642042737

This paper presents a unified control liapunov function (CLF) approach to the design of heavy ball with friction (HBF) and conjugate gradient (CG) neural networks that aim to minimize scalar nonconvex functions that have continuous first- and second-order derivatives and a unique global minimum. This approach leads naturally to the design of second-order differential equations which are the mathematical models of the corresponding implementations as neural networks. Preliminary numerical simulations indicate that, on a small suite of benchmark test problems, a continuous version of the well known conjugate gradient algorithm, designed by the proposed CLF method, has better performance than its HBF competitor.

关键词： control liapunov functions Nonconvex functions Global Minimization Second Order ODEs

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