A computational solution for a Matrix Riccati differential equation

Razzaghi, Mohsen

doi:10.1007/bf01397001

Cited by 23 publications

(11 citation statements)

References 9 publications

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“…By using this approach, the solution of MRDE is obtained by partitioning the transition matrix of the associated Hamiltonian system [11]. Another class of methods is based on transforming MRDE into a linear matrix differential equation and then solving MRDE analytically or computationally [12,13,14]. However, the method in [15] is restricted for cases when certain coefficients of MRDE are non-singular.…”

Section: Introductionmentioning

confidence: 98%

Optimal control for fuzzy linear partial differential algebraic equations using Simulink

Kumaresan

Ratnavelu

Wong

2011

2011 International Conference on Recent Trends in Information Technology (ICRTIT)

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In this paper, optimal control for fuzzy linear partial differential algebraic equations (FPDAE) with quadratic performance is obtained using Simulink. By using the method of lines, the FPDAE is transformed into a fuzzy differential algebraic equations (FDAE). Hence, the optimal control of FPDAE can be found out by finding the optimal control of the corresponding FDAE. The goal is to provide optimal control with reduced calculus effort by the solutions of the matrix Riccati differential equation (MRDE) obtained from Simulink. Accuracy of the solution of the Simulink approach to the problem is qualitatively better. The advantage of the proposed approach is that, once the Simulink model is constructed, it allows to evaluate the solution at any desired number of points spending negligible computing time and memory and the solution curves can be obtained from the model without writing any code. An illustrative numerical example is presented for the proposed method.

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Section: Introductionmentioning

confidence: 98%

Optimal control for fuzzy linear partial differential algebraic equations using Simulink

Kumaresan

Ratnavelu

Wong

2011

2011 International Conference on Recent Trends in Information Technology (ICRTIT)

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“…These equations are solved analytically or computationally . In , an analytic procedure of solving the D R E of the linear quadratic control problem for homing systems is presented, a solution K ( t ) of the D R E is obtained by using K ( t ) = P ( t )/ f ( t ), where f ( t ) and P ( t ) are solutions of certain first‐order ordinary linear differential equations. However, the technique given in is restricted to single input.…”

Section: Introductionmentioning

confidence: 99%

Existence of Solution for Generalized Coupled Differential Riccati Equation

Ren

Liu

2018

Asian Journal of Control

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“…By using this approach, the solution of MRDE is obtained by partitioning the transition matrix of the associated Hamiltonian system [35]. Another class of method is based on transforming MRDE into a linear matrix differential equation and then solving MRDE analytically or computationally [20,31,32]. However, the method in [30] is restricted for cases when certain coefficients of MRDE are nonsingular.…”

Section: Introductionmentioning

confidence: 99%

Solution of matrix Riccati differential equation for nonlinear singular system using neural networks

Samath¹,

Selvaraju²

2010

IJCA

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In this paper, the solution of the matrix Riccati differential equation(MRDE) for nonlinear singular system is obtained using neural networks. The goal is to provide optimal control with reduced calculus effort by comparing the solutions of the MRDE obtained from well known traditional Runge Kutta(RK)method and nontraditional neural network method. Accuracy of the neural solution to the 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 computational solution for a Matrix Riccati differential equation

Cited by 23 publications

References 9 publications

Optimal control for fuzzy linear partial differential algebraic equations using Simulink

Optimal control for fuzzy linear partial differential algebraic equations using Simulink

Existence of Solution for Generalized Coupled Differential Riccati Equation

Solution of matrix Riccati differential equation for nonlinear singular system using neural networks

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