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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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Journal ArticleDOI
TL;DR: Linear, null controllable systems, for which an arbitrary initial state can be transferred to the origin with arbitrarily small energy, are characterized and Ornstein--Uhlenbeck operators for which the Liouville theorem about bounded harmonic functions holds are determined.
Abstract: Linear, null controllable systems, for which an arbitrary initial state can be transferred to the origin with arbitrarily small energy, are characterized. Theorems are stated in terms of an associated algebraic Riccati equation and in terms of the spectrum of the linear part of the system. The results so obtained allow us to determine Ornstein--Uhlenbeck operators for which the Liouville theorem about bounded harmonic functions holds.

55 citations

Journal ArticleDOI
TL;DR: In this paper, the authors considered the regulator problem for a parabolic equation (generally unstable), defined on an open, bounded domain Ω, with control function acting in the Dirichlet boundary condition: minimize the quadratic functional which penalizes the L 2 (0, ∞; L 2(Ω))-norm of the solutiony and the L 1.2(0, ε) norm of the controlu.
Abstract: This paper considers the regulator problem for a parabolic equation (generally unstable), defined on an open, bounded domain Ω, with control functionu acting in the Dirichlet boundary condition: minimize the quadratic functional which penalizes theL 2(0, ∞; L2(Ω))-norm of the solutiony and theL 2(0, ∞; L2(Γ))-norm of the Dirichlet controlu. The paper is divided in two parts. Part I derives, in a constructive way, the algebraic Riccati equation satisfied by the candidate Riccati operator solution (unique in our case) and, moreover, studies the regularity properties of the optimal pairu 0, y0. Part II studies a Galerkin approximation of the regulator problem. It shows first the uniform analyticity and the uniform exponential stability of the underlying discrete (approximating) semigroups. Then it establishes the desired convergence properties, in particular, pointwise Riccati operators convergence and, as a final goal, convergence of the original dynamics acted upon by the discrete feedbacks.

55 citations

01 Mar 1990
TL;DR: In this paper, two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane.
Abstract: Two linear quadratic regulators are developed for placing the closed-loop poles of linear multivariable continuous-time systems within the common region of an open sector, bounded by lines inclined at +/- pi/2k (for a specified integer k not less than 1) from the negative real axis, and the left-hand side of a line parallel to the imaginary axis in the complex s-plane, and simultaneously minimizing a quadratic performance index. The design procedure mainly involves the solution of either Liapunov equations or Riccati equations. The general expression for finding the lower bound of a constant gain gamma is also developed.

55 citations

Journal ArticleDOI
TL;DR: It is shown that this computation can be done via computing only the minimal positive solution of a vector equation, which is derived from the special form of solutions of the Riccati equation.
Abstract: We are interested in computing the minimal positive solution of a nonsymmetric algebraic Riccati equation arising in transport theory. We show that this computation can be done via computing only the minimal positive solution of a vector equation, which is derived from the special form of solutions of the Riccati equation. A simple iterative method is presented for solving the vector equation. The simple iteration is much more efficient than the Gauss--Jacobi method presented by Juang in [Linear Algebra Appl., 230 (1995), pp. 89--100] for the Riccati equation. The symmetric case and bounds of the minimal positive solution are also considered. Numerical experiments are given.

55 citations

Proceedings ArticleDOI
11 Aug 2003
TL;DR: This paper is an initial report on flight experiments with a small, unmanned helicopter using a state dependent Riccati Equation (SDRE) controller for autonomous, agile maneuvering.
Abstract: This paper is an initial report on flight experiments with a small, unmanned helicopter using a state dependent Riccati Equation (SDRE) controller for autonomous, agile maneuvering. The control design is based upon a full, 6-DoF, analytic nonlinear dynamic model, which is manipulated into a pseudo-linear form in which system matrices are given explicitly as a function of the current state. A standard Riccati equation is then solved numerically in each frame of a 50 Hz. control loop to design the state feedback control law on-line. Several flights have been flown with the helicopter to evaluate the accuracy of tracking under SDRE control in comparison with simulation results.

55 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023153
2022335
2021203
2020240
2019223
2018231