A survey of numerical methods for solving matrix Riccati differential equations

Choi, Chiu

doi:10.1109/secon.1990.117906

Cited by 21 publications

(16 citation statements)

References 14 publications

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“…The numerical methods for solving the matrix Riccati equation are based on the transformation of the matrix quadratic equation into a system of linear, first-order differential equations by means of the Bernoulli substitution [28][29][30][31] . The theoretical basis for this substitution is the following result: If U (R ) and V(R ) solve the ma-…”

Section: The Matrix Riccati Equationmentioning

confidence: 99%

An overview of the methods for deriving recurrence relations for T-matrix calculation

Doicu

Wriedt

Khebbache

2019

Journal of Quantitative Spectroscopy and Radiative Transfer

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In this paper, we present a consistent analysis of the methods dealing with the derivation of recurrence relations for calculation of the T-matrix. Central and forward recurrence relations are obtained in the framework of the invariant embedding T-matrix method, the matrix Riccati equation method, and the superposition T-matrix method. The accuracies and efficiencies of the central and forward recurrence schemes are analyzed, and some implementation issues related to the improvement of the numerical accuracy and to the problem of overcoming of overflow errors are discussed.

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Section: The Matrix Riccati Equationmentioning

confidence: 99%

An overview of the methods for deriving recurrence relations for T-matrix calculation

Doicu

Wriedt

Khebbache

2019

Journal of Quantitative Spectroscopy and Radiative Transfer

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“…In order to minimize the error, recently the conventional Riccati equation has been analysed using neural network approach and genetic programming approach [2][3][4][5][19][20][21]24]. A variety of numerical algorithms [14] have been developed for solving the algebraic Riccati equation.…”

Section: Introductionmentioning

confidence: 99%

Singular optimal control for stochastic linear quadratic singular system using ant colony programming

Kumaresan

Balasubramaniam

2010

International Journal of Computer Mathematics

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In this article, singular optimal control for stochastic linear singular system with quadratic performance is obtained using ant colony programming (ACP). To obtain the optimal control, the solution of matrix Riccati differential equation is computed by solving differential algebraic equation using a novel and nontraditional ACP approach. The obtained solution in this method is equivalent or very close to the exact solution of the problem. Accuracy of the solution computed by the ACP approach to the problem is qualitatively better. The solution of this novel method is compared with the traditional Runge Kutta method. An illustrative numerical example is presented for the proposed method.

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“…Using neural networks, a variety of off-line learning control algorithms have been developed for nonlinear systems [16,22]. A variety of numerical algorithms (see [10]) have been developed for solving the algebraic Riccati equation. In recent years, neural network problems have attracted considerable attention of many researchers for numerical aspects for algebraic Riccati equations (see [13,15,26]).…”

Section: Introductionmentioning

confidence: 99%

Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

Kumaresan

2010

Neural Comput & Applic

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In this paper, solution of generalized matrix Riccati differential equation (GMRDE) for indefinite stochastic linear quadratic singular fuzzy system with crossterm is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of GMRDE obtained from wellknown traditional Runge Kutta (RK) method and nontraditional neural network method. To obtain the optimal control, the solution of GMRDE is computed by feed forward neural network (FFNN). Accuracy of the solution of the neural network approach to this problem is qualitatively better. The advantage of the proposed approach is that, once the network is trained, it allows instantaneous evaluation of solution at any desired number of points spending negligible computing time and memory. The computation time of the proposed method is shorter than the traditional RK method. An illustrative numerical example is presented for the proposed method.

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A survey of numerical methods for solving matrix Riccati differential equations

Cited by 21 publications

References 14 publications

An overview of the methods for deriving recurrence relations for T-matrix calculation

An overview of the methods for deriving recurrence relations for T-matrix calculation

Singular optimal control for stochastic linear quadratic singular system using ant colony programming

Solution of generalized matrix Riccati differential equation for indefinite stochastic linear quadratic singular fuzzy system with cross-term using neural networks

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