Annabell Del Real Tamariz

Sequential and parallel algebraic Riccati equations solutions via ESST on the Schur method

A method for solving the discrete/continuous algebraic Riccati equation in sequential and parallel and distributed forms, that modifies and proposes a parallelization for the Schur method of Laub (1979) is presented. To transform the symplectic/Hamiltonian matrix in a simple form, elementary stabilized similarity transformations (ESSTs) are utilized. A sequential implementation of the proposed algorithm for dense matrices is made and a parallel implementation on a distributed memory system with an asynchronous parallelization strategy over a workstations network is proposed.

Discrete-time systems neuro-Riccati equation solution

In this article proposal for solving the discrete-time algebraic Riccati equation (DARE) using a multilayer recurrent neural network (RNN) approach is presented. Systems of coupled matricial nonlinear differential equations are derived describing the neural dynamics of the Neuro-riccati equation. By solving these coupled matrix equations using recurrent neural networks a symmetric and positive definite solution is obtained. Several examples demonstrate the effectiveness of this proposal and respective implementation.

Discrete-time algebraic Riccati inequation neuro-LMI solution

In this article we present a proposal for solving the discrete-time algebraic Riccati inequation (DARI). This associate linear matrix inequality (LMI) is solved using a multilayer recurrent neural network (RNN) approach. Systems of coupled matricial nonlinear differential equations are derived describing the neural dynamics of the neuro-LMI. By solving these coupled matrix equations using recurrent neural networks, our approach is capable of obtaining a symmetric and positive definite solution for this problem. Examples demonstrate the effectiveness of this proposal and respective implementation, for different learning rates.

Parallel and distributed computational multivariate time series modeling in the state space

In this paper a parallel and distributed computational procedure using a subspace method developed by Aoki (1990) for state space modeling of multivariate time series is proposed and implemented. The parallel solution of the Riccati equation due to the large computational effort it requires receives a special attention. For model evaluation, short time predictions, where a central role is played by a Kalman filtering approach are tested and some results are presented.

Parallel and distributed computational data modeling via Verhaegen and Dewilde's subspace method

Computational data modelling and state-space realization theory for linear discrete time systems are closely related. Verhaegen and Dewildes identification algorithm is an efficient subspace data modelling method. For increasing its computational performance, we propose a parallelization structure for such an algorithm, and present some results for an experiment made on a benchmark we developed.