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The role of parameter constraints in EE and OE methods for optimal identification of continuous LTI models

Witold Byrski, Jedrzej Byrski (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents two methods used for the identification of Continuous-time Linear Time Invariant (CLTI) systems. In both methods the idea of using modulating functions and a convolution filter is exploited. It enables the proper transformation of a differential equation to an algebraic equation with the same parameters. Possible different normalizations of the model are strictly connected with different parameter constraints which have to be assumed for the nontrivial solution of the optimal...

The strongest t-norm for fuzzy metric spaces

Dong Qiu, Weiquan Zhang (2013)

Kybernetika

In this paper, we prove that for a given positive continuous t-norm there is a fuzzy metric space in the sense of George and Veeramani, for which the given t-norm is the strongest one. For the opposite problem, we obtain that there is a fuzzy metric space for which there is no strongest t-norm. As an application of the main results, it is shown that there are infinite non-isometric fuzzy metrics on an infinite set.

The UD RLS algorithm for training feedforward neural networks

Jarosław Bilski (2005)

International Journal of Applied Mathematics and Computer Science

A new algorithm for training feedforward multilayer neural networks is proposed. It is based on recursive least squares procedures and U-D factorization, which is a well-known technique in filter theory. It will be shown that due to the U-D factorization method, our algorithm requires fewer computations than the classical RLS applied to feedforward multilayer neural network training.

The value function in ergodic control of diffusion processes with partial observations II

Vivek Borkar (2000)

Applicationes Mathematicae

The problem of minimizing the ergodic or time-averaged cost for a controlled diffusion with partial observations can be recast as an equivalent control problem for the associated nonlinear filter. In analogy with the completely observed case, one may seek the value function for this problem as the vanishing discount limit of value functions for the associated discounted cost problems. This passage is justified here for the scalar case under a stability hypothesis, leading in particular to a "martingale"...

Time-varying Markov decision processes with state-action-dependent discount factors and unbounded costs

Beatris A. Escobedo-Trujillo, Carmen G. Higuera-Chan (2019)

Kybernetika

In this paper we are concerned with a class of time-varying discounted Markov decision models ℳ n with unbounded costs c n and state-action dependent discount factors. Specifically we study controlled systems whose state process evolves according to the equation x n + 1 = G n ( x n , a n , ξ n ) , n = 0 , 1 , ... , with state-action dependent discount factors of the form α n ( x n , a n ) , where a n and ξ n are the control and the random disturbance at time n , respectively. Assuming that the sequences of functions { α n } , { c n } and { G n } converge, in certain sense, to α ∞ , c ∞ and G ∞ , our...

Topological dual of B ∞ ( I , ₁ ( X , Y ) ) with application to stochastic systems on Hilbert space

N.U. Ahmed (2009)

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

In this paper, we prove that the topological dual of the Banach space of bounded measurable functions with values in the space of nuclear operators, furnished with the natural topology, is isometrically isomorphic to the space of finitely additive linear operator-valued measures having bounded variation in a Banach space containing the space of bounded linear operators. This is then applied to a stochastic structural control problem. An optimal operator-valued measure, considered as the structural...

Trajectory tracking for a mobile robot with skid-slip compensation in the Vector-Field-Orientation control system

Maciej Michałek, Piotr Dutkiewicz, Marcin Kiełczewski, Dariusz Pazderski (2009)

International Journal of Applied Mathematics and Computer Science

The article is devoted to a motion control problem for a differentially driven mobile robot in the task of trajectory tracking in the presence of skid-slip effects. The kinematic control concept presented in the paper is the Vector Field Orientation (VFO) feedback approach with a nonlinear feed-forward skid-slip influence compensation scheme. The VFO control law guarantees asymptotic convergence of the position tracking error to zero in spite of the disturbing influence of skid-slip phenomena. The...

Transformée en paquets d'ondelettes des signaux stationnaires: comportement asymptotique des densités spectrales.

Loïc Hervé (1996)

Revista Matemática Iberoamericana

We consider quadrature mirror filters, and the associated wavelet packet transform. Let X = {Xn}n∈Z be a stationary signal which has a continuous spectral density f. We prove that the 2n signals obtained from X by n iterations of the transform converge to white noises when n → +∞. If f is holderian, the convergence rate is exponential.

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