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- Algebraic_Riccati_equation abstract "An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. In such a problem, one cares about the value of some variable of interest arbitrarily far into the future, and one must optimally choose a value of a controlled variable right now, knowing that one will also behave optimally at all times in the future. The optimal current values of the problem's control variables at any time can be found using the solution of the Riccati equation and the current observations on evolving state variables. With multiple state variables and multiple control variables, the Riccati equation will be a matrix equation.A typical algebraic Riccati equation is similar to one of the following:the continuous time algebraic Riccati equation (CARE): or the discrete time algebraic Riccati equation (DARE): X is the unknown n by n symmetric matrix and A, B, Q, R are known real coefficient matrices.The name Riccati is given to the CARE equation by analogy to the Riccati differential equation: the unknown elements of X appear linearly and in quadratic terms (but no higher-order terms). The DARE arises in place of the CARE when studying discrete time systems; it is not obviously related to the differential equation studied by Riccati.The algebraic Riccati equation determines the solution of the infinite-horizon time-invariant Linear-Quadratic Regulator problem (LQR) as well as that of the infinite horizon time-invariant Linear-Quadratic-Gaussian control problem (LQG). These are two of the most fundamental problems in control theory.A solution to the algebraic Riccati equation can be obtained by matrix factorizations or by iterating on the Riccati equation. One type of iteration can be obtained in the discrete time case by using the dynamic Riccati equation that arises in the finite-horizon problem: in the latter type of problem each iteration of the value of the matrix is relevant for optimal choice at each period that is a finite distance in time from a final time period, and if it is iterated infinitely far back in time it converges to the specific matrix that is relevant for optimal choice an infinite length of time prior to a final period—that is, for when there is an infinite horizon.".
- Algebraic_Riccati_equation wikiPageExternalLink solve-riccati-equation.
- Algebraic_Riccati_equation wikiPageExternalLink R-0859-05666488.pdf;jsessionid=8CCF9A002524048AFD0F91D1F15EB6AE?sequence=1.
- Algebraic_Riccati_equation wikiPageExternalLink DiscreteRiccatiSolve.html.
- Algebraic_Riccati_equation wikiPageExternalLink RiccatiSolve.html.
- Algebraic_Riccati_equation wikiPageExternalLink care.html.
- Algebraic_Riccati_equation wikiPageExternalLink dare.html.
- Algebraic_Riccati_equation wikiPageID "16684054".
- Algebraic_Riccati_equation wikiPageRevisionID "572492621".
- Algebraic_Riccati_equation hasPhotoCollection Algebraic_Riccati_equation.
- Algebraic_Riccati_equation subject Category:Equations.
- Algebraic_Riccati_equation subject Category:Matrices.
- Algebraic_Riccati_equation subject Category:Optimal_control.
- Algebraic_Riccati_equation type Abstraction100002137.
- Algebraic_Riccati_equation type Arrangement107938773.
- Algebraic_Riccati_equation type Array107939382.
- Algebraic_Riccati_equation type Communication100033020.
- Algebraic_Riccati_equation type Equation106669864.
- Algebraic_Riccati_equation type Equations.
- Algebraic_Riccati_equation type Group100031264.
- Algebraic_Riccati_equation type MathematicalStatement106732169.
- Algebraic_Riccati_equation type Matrices.
- Algebraic_Riccati_equation type Matrix108267640.
- Algebraic_Riccati_equation type Message106598915.
- Algebraic_Riccati_equation type Statement106722453.
- Algebraic_Riccati_equation comment "An algebraic Riccati equation is a type of nonlinear equation that arises in the context of infinite-horizon optimal control problems in continuous time or discrete time. In such a problem, one cares about the value of some variable of interest arbitrarily far into the future, and one must optimally choose a value of a controlled variable right now, knowing that one will also behave optimally at all times in the future.".
- Algebraic_Riccati_equation label "Algebraic Riccati equation".
- Algebraic_Riccati_equation label "Algebraiczne równanie Riccatiego".
- Algebraic_Riccati_equation sameAs Algebraiczne_równanie_Riccatiego.
- Algebraic_Riccati_equation sameAs m.03ymnvl.
- Algebraic_Riccati_equation sameAs Q4723989.
- Algebraic_Riccati_equation sameAs Q4723989.
- Algebraic_Riccati_equation sameAs Algebraic_Riccati_equation.
- Algebraic_Riccati_equation wasDerivedFrom Algebraic_Riccati_equation?oldid=572492621.
- Algebraic_Riccati_equation isPrimaryTopicOf Algebraic_Riccati_equation.