Topic
Riccati equation
About: Riccati equation is a research topic. Over the lifetime, 10428 publications have been published within this topic receiving 210015 citations. The topic is also known as: Riccati's differential equation.
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TL;DR: In this article, the authors consider the matrix equation X = Q + NX −1 N∗, where the Hermitian solutions are parametrized in terms of the generalized Lagrangian eigenspaces of a certain matrix pencil.
125 citations
TL;DR: In this article, a parametric Lyapunov differential equation approach is proposed to solve the constrained regulation problem of the Tschauner-Hempel equations, and the authors prove that the proposed linear periodic controller can be made as small as desired by tuning some free parameters in the feedback laws.
Abstract: and energy. A parametric Lyapunov differential equation approach is proposed in this paper to solve this constrained regulation problem. After establishing the fact that the Tschauner-Hempel equations are both null controllable with controls of bounded magnitude and energy, this paper proves that the proposed linear periodic controllersemigloballystabilizesthesystem.Equivalently,forany fixedinitialconditions,themagnitudeandenergy of the control can be made as small as desired by tuning some free parameters in the feedback laws. In comparison with the existing quadratic-regulation-based approach, which requires solutions to nonlinear Riccati differential equations,thenewapproachrequiresonlythesolutionoflinearperiodicLyapunovdifferentialequations,whichare investigated inthepaperbyusingtheperiodicgenerator approach.Numericalsimulationsofthe nonlinearmodelof the spacecraft rendezvous instead of a linearized one show that both the magnitude and energy of the control can be reduced to an arbitrarily small level by reducing the values of some parameters in the controller and that the rendezvous mission can be accomplished satisfactorily.
124 citations
TL;DR: In this paper, a monotoneity result and an inertia theorem on the location of the eigenvalues of W and B + CW are proved for the matrix equation A + WB + BTW + WCW = 0.
Abstract: In this note the matrix equation A + WB + BTW + WCW = 0 is considered. A monotoneity result and an inertia theorem on the location of the eigenvalues of W and B + CW are proved.
124 citations
TL;DR: In this article, the problem of selecting an initial covariance matrix for the Kalman filter to ensure that the closed-loop filter at every subsequent time instant is exponentially asymptotically stable as a time-invariant filter is considered.
123 citations
TL;DR: In this paper, the existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riemannian equation.
Abstract: The existence of a Lagrangian description for the second-order Riccati equation is analyzed and the results are applied to the study of two different nonlinear systems both related with the generalized Riccati equation. The Lagrangians are non-natural and the forces are not derivable from a potential. The constant value E of a preserved energy function can be used as an appropriate parameter for characterizing the behavior of the solutions of these two systems. In the second part the existence of two-dimensional versions endowed with superintegrability is proved. The explicit expressions of the additional integrals are obtained in both cases. Finally it is proved that the orbits of the second system, that represents a nonlinear oscillator, can be considered as nonlinear Lissajous figures
123 citations