Exploring the exact solutions to the nonlinear systems with neural networks method [PDF]
Scientific ReportsThis paper explores the use of Riccati subequation neural networks to solve nonlinear partial differential equations modeling complex biological processes like cancer, brain function, and wound healing.
Jan Muhammad +3 more
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An accelerated technique for solving one type of discrete-time algebraic Riccati equations [PDF]
Journal of Computational and Applied Mathematics, 2017 Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and $H^\infty$ control theory. In this work, we study the properties of one type of discrete-time algebraic Riccati equations.
Matthew M. Lin, Chun-Yueh Chiang
semanticscholar +4 more sources
Applied Sciences, 2021 This paper presents modeling and infinite-time suboptimal control of a quadcopter device using the state-dependent Riccati equation (SDRE) method. It establishes a solution to the control problem using SDRE and proposes a new procedure for solving the ...
Sławomir Stępień +1 more
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A subspace shift technique for nonsymmetric algebraic Riccati equations associated with an M‐matrix [PDF]
Numerical Linear Algebra with Applications, 2010 The worst situation in computing the minimal nonnegative solution of a nonsymmetric algebraic Riccati equation associated with an M‐matrix occurs when the corresponding linearizing matrix has two very small eigenvalues, one with positive and one with ...
B. Iannazzo, F. Poloni
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A reduction technique for generalised Riccati difference equations arising in linear-quadratic optimal control [PDF]
2012 IEEE 51st IEEE Conference on Decision and Control (CDC), 2012 In this paper we develop a reduction technique for the generalised Riccati difference equation arising in optimal control and optimal filtering. This technique relies on a decomposition method for the generalised Riccati difference equation that isolates its nilpotent part, which becomes constant in a number of iteration steps equal to the nilpotency ...
Lorenzo Ntogramatzidis +1 more
exaly +3 more sources
A Riccati technique for proving oscillation of a half-linear equation
Electronic Journal of Differential Equations, 2008 In this paper we study the oscillation of solutions to the half-linear differential equation $$ (r(t)|y'|^{p-1}hbox{sgn} y)'+c(t)|y|^{p-1}hbox{sgn} y=0, $$ under the assumptions $int^infty r^{1/(1-p)}(s),ds0$, $p>1$.
Pavel Rehak
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On oscillatory behaviour of third-order half-linear dynamic equations on time scales [PDF]
Opuscula Mathematica, 2022 In this work, we study the oscillation and asymptotic behaviour of third-order nonlinear dynamic equations on time scales. The findings are obtained using an integral criterion as well as a comparison theorem with the oscillatory properties of a first ...
Said R. Grace, Gokula Nanda Chhatria
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Nonoscillation of damped linear differential equations with a proportional derivative controller and its application to Whittaker-Hill-type and Mathieu-type equations [PDF]
Opuscula Mathematica, 2022 The proportional derivative (PD) controller of a differential operator is commonly referred to as the conformable derivative. In this paper, we derive a nonoscillation theorem for damped linear differential equations with a differential operator using ...
Kazuki Ishibashi
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Riccati technique for oscillation of half-linear/Emden-Fowler neutral dynamic equations
Journal of Mathematics and Computer Science, 2022 By using the Riccati technique, which reduces the higher order dynamic equations to a Riccati dynamic inequality, we will establish some new sufficient conditions for the oscillation of half-linear/Emden-Fowler neutral dynamic equation of the ...
S. Saker +3 more
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Approximate solution for quadratic Riccati differential equation
Journal of Taibah University for Science, 2017 The quadratic Riccati differential equations are a class of nonlinear differential equations of much importance, and play a significant role in many fields of applied science.
Fateme Ghomanjani, Esmaile Khorram
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