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International Journal of Mathematics and Mathematical Sciences, 1987 In this paper we find closed form solutions of some Riccati equations. Attention is restricted to the scalar as opposed to the matrix case. However, the ones considered have important applications to mathematics and the sciences, mostly in the form of ...
Lloyd K. Williams
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RADI: a low-rank ADI-type algorithm for large scale algebraic Riccati equations. [PDF]
Numer Math (Heidelb), 2018 This paper introduces a new algorithm for solving large-scale continuous-time algebraic Riccati equations (CARE). The advantage of the new algorithm is in its immediate and efficient low-rank formulation, which is a generalization of the Cholesky ...
Benner P +3 more
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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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Nonlinear Engineering, 2018 In this paper, the fractional derivatives in the sense of modified Riemann–Liouville and the Riccati-Bernoulli Sub-ODE method are used to construct exact solutions for some nonlinear partial fractional differential equations via the nonlinear fractional ...
Abdelrahman Mahmoud A.E.
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Gradient-augmented Supervised Learning of Optimal Feedback Laws Using State-Dependent Riccati Equations [PDF]
IEEE Control Systems Letters, 2021 A supervised learning approach for the solution of large-scale nonlinear stabilization problems is presented. A stabilizing feedback law is trained from a dataset generated from State-dependent Riccati Equation solvers.
G. Albi, Sara Bicego, D. Kalise
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Solving of some nonlinear ordinary differential equations in the form of power series
Физико-химические аспекты изучения кластеров, наноструктур и наноматериалов, 2022 In the current scientific literature, a variety of nonlinear ordinary differential equations are widely and successfully used to describe real processes in various fields of natural sciences: optics, elasticity theory, molecular physics, etc. For example,
I.N. Belyaeva +2 more
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Numerical solution of nonlinear fractional Riccati differential equations using compact finite difference method [PDF]
Iranian Journal of Numerical Analysis and Optimization, 2022 This paper aims to apply and investigate the compact finite difference methods for solving integer-order and fractional-order Riccati differential equations. The fractional derivative in the fractional case is described in the Caputo sense.
H. Porki, M. Arabameri, R. Gharechahi
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About one problem of optimal control synthesis [PDF]
E-Journal of Analysis and Applied Mathematics, 2023 This paper tackles the problem of characterizing the natural class, or Riccati rule space, of solutions to a specific e quation. Despite the significant theoretical and practical implications, there is limited research exploring the application of ...
Muhametberdy Rakhimov
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Integral Operator Riccati Equations Arising in Stochastic Volterra Control Problems [PDF]
SIAM Journal of Control and Optimization, 2019 We establish existence and uniqueness for infinite dimensional Riccati equations taking values in the Banach space L 1 ($\mu$ $\otimes$ $\mu$) for certain signed matrix measures $\mu$ which are not necessarily finite.
E. A. Jaber, Enzo Miller, H. Pham
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A Numerical Comparison of Different Solvers for Large-Scale, Continuous-Time Algebraic Riccati Equations and LQR Problems [PDF]
SIAM Journal on Scientific Computing, 2018 In this paper, we discuss numerical methods for solving large-scale continuous-time algebraic Riccati equations.
P. Benner +3 more
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