Systems & Control Letters, ISSN 0167-6911, 05/2019, Volume 127, pp. 35 - 38

We consider Homogeneous Algebraic Riccati Equations in the general situation when the matrix of the dynamics can be . We show that in this case the equation...

Invariant subspaces | Homogeneous algebraic Riccati equation | Symmetric matrices

Invariant subspaces | Homogeneous algebraic Riccati equation | Symmetric matrices

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 12/2019, Volume 361, pp. 130 - 143

We consider the numerical solution of large-scale algebraic Riccati equations with high-rank constant terms. The solutions are not numerically low-rank, so the...

Algebraic Riccati equation | Feedback gain | High-rank constant term | Large-scale problem | LQR optimal control | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | PARAMETER-ESTIMATION | SYSTEMS | MATRIX EQUATIONS | DOUBLING-ALGORITHM | Algorithms

Algebraic Riccati equation | Feedback gain | High-rank constant term | Large-scale problem | LQR optimal control | MATHEMATICS, APPLIED | ITERATIVE SOLUTIONS | PARAMETER-ESTIMATION | SYSTEMS | MATRIX EQUATIONS | DOUBLING-ALGORITHM | Algorithms

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 11/2019

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 06/2020, Volume 371, p. 112685

Journal Article

IEEE Transactions on Information Theory, ISSN 0018-9448, 03/2015, Volume 61, Issue 3, pp. 1351 - 1372

This paper studies the convergence of the estimation error process and the characterization of the corresponding invariant measure in distributed Kalman...

large deviations | Protocols | Heuristic algorithms | Estimation | Kalman filter | Sensor systems | Covariance matrices | consensus | Distributed signal processing | random algebraic Riccati equation | random dynamical systems | massive data sets | gossip | Kalman filters | TOPOLOGY | GOSSIP ALGORITHMS | COMPUTER SCIENCE, INFORMATION SYSTEMS | NETWORKS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYSTEMS | Wireless sensor networks | Usage | Innovations | Markov processes | Error-correcting codes | Kalman filtering | Distribution (Probability theory) | Riccati equation

large deviations | Protocols | Heuristic algorithms | Estimation | Kalman filter | Sensor systems | Covariance matrices | consensus | Distributed signal processing | random algebraic Riccati equation | random dynamical systems | massive data sets | gossip | Kalman filters | TOPOLOGY | GOSSIP ALGORITHMS | COMPUTER SCIENCE, INFORMATION SYSTEMS | NETWORKS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYSTEMS | Wireless sensor networks | Usage | Innovations | Markov processes | Error-correcting codes | Kalman filtering | Distribution (Probability theory) | Riccati equation

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2020, Volume 368, p. 112567

In this paper, based on the study of fluid flow models modulated by a Markov chain, we propose a new class of complex nonsymmetric algebraic Riccati equations...

Extremal solution | Newton’s method | Basic fixed-point iterative method | Doubling algorithm | Preprocessing technique | H-matrix algebraic Riccati equation (HARE)

Extremal solution | Newton’s method | Basic fixed-point iterative method | Doubling algorithm | Preprocessing technique | H-matrix algebraic Riccati equation (HARE)

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 08/2017, Volume 527, pp. 184 - 215

We give a rank characterization of the solution set of discrete algebraic Riccati equations (DAREs) involving real matrices. Our characterization involves the...

Discrete Lyapunov equation | Difference Riccati equation | Discrete algebraic Riccati equation | Non-symmetric algebraic Riccati equation | Schur complement | BERNOULLI EQUATIONS | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | PARAMETRIZATION | Electrical engineering | Electric properties

Discrete Lyapunov equation | Difference Riccati equation | Discrete algebraic Riccati equation | Non-symmetric algebraic Riccati equation | Schur complement | BERNOULLI EQUATIONS | MATHEMATICS | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | PARAMETRIZATION | Electrical engineering | Electric properties

Journal Article

Linear Algebra and its Applications, ISSN 0024-3795, 08/2017, Volume 527, p. 184

We give a rank characterization of the solution set of discrete algebraic Riccati equations (DAREs) involving real matrices. Our characterization involves the...

Matrix | Algebra | Mathematical analysis | Integral equations | Integrals | Algebraic group theory | Subspaces | Riccati equation | Invariants

Matrix | Algebra | Mathematical analysis | Integral equations | Integrals | Algebraic group theory | Subspaces | Riccati equation | Invariants

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 04/2019, Volume 347, pp. 442 - 448

Research on the theories and efficient numerical methods of M-matrix algebraic Riccati equation (MARE) has become a hot topic in recent years. In this paper,...

Minimal nonnegative solution | ALI iteration method | M-matrix algebraic Riccati equation | Newton method | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | PRESERVING DOUBLING-ALGORITHM

Minimal nonnegative solution | ALI iteration method | M-matrix algebraic Riccati equation | Newton method | MATHEMATICS, APPLIED | WIENER-HOPF FACTORIZATION | PRESERVING DOUBLING-ALGORITHM

Journal Article

10.
Full Text
An accelerated technique for solving one type of discrete-time algebraic Riccati equations

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2018, Volume 338, pp. 91 - 110

Algebraic Riccati equations are encountered in many applications of control and engineering problems, e.g., LQG problems and control theory. In this work, we...

[formula omitted]-superlinear with order [formula omitted] | Doubling algorithm | Sherman morrison woodbury formula | Algebraic Riccati equations | Semigroup property | Positive definite solution | r-superlinear with order r | MATHEMATICS, APPLIED | POSITIVE-DEFINITE SOLUTIONS | CONVERGENCE | COMPUTATION | DOUBLING-ALGORITHM

[formula omitted]-superlinear with order [formula omitted] | Doubling algorithm | Sherman morrison woodbury formula | Algebraic Riccati equations | Semigroup property | Positive definite solution | r-superlinear with order r | MATHEMATICS, APPLIED | POSITIVE-DEFINITE SOLUTIONS | CONVERGENCE | COMPUTATION | DOUBLING-ALGORITHM

Journal Article

Computers and Mathematics with Applications, ISSN 0898-1221, 07/2018, Volume 76, Issue 1, pp. 187 - 203

In this paper we consider a family of high-order iterative methods which is more efficient than the Newton method to approximate a solution of symmetric...

High order iterative schemes | Algebraic Riccati equations | Local convergence | Lyapunov equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | EFFICIENCY

High order iterative schemes | Algebraic Riccati equations | Local convergence | Lyapunov equations | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | EFFICIENCY

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 10/2016, Volume 507, pp. 356 - 372

We give a new characterization of the solution set of non-symmetric algebraic Riccati equations involving real matrices. Our characterization involves the use...

Poset | Non-symmetric algebraic Riccati equation | Sylvester equation | M-MATRICES | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | Electrical engineering | Electric properties

Poset | Non-symmetric algebraic Riccati equation | Sylvester equation | M-MATRICES | MATHEMATICS | MATHEMATICS, APPLIED | FACTORIZATION | Electrical engineering | Electric properties

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 08/2017, Volume 319, pp. 352 - 364

Fast iterative algorithms for computing interval matrices containing solutions of discrete-time algebraic Riccati equations are proposed. These algorithms...

Algebraic Riccati equations | Stabilizing solution | Verified computation | MATHEMATICS, APPLIED | Algorithms

Algebraic Riccati equations | Stabilizing solution | Verified computation | MATHEMATICS, APPLIED | Algorithms

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 12/2017, Volume 314, pp. 80 - 97

This paper is devoted to a structured perturbation analysis of the symmetric algebraic Riccati equations by exploiting the symmetry structure. Based on the...

Condition number | Statistical condition estimation | Symmetric algebraic Riccati equation | Perturbation analysis | MATHEMATICS, APPLIED | LINEAR LEAST-SQUARES | COMPONENTWISE CONDITION NUMBERS | SYSTEMS | Statistics | Analysis | Algorithms

Condition number | Statistical condition estimation | Symmetric algebraic Riccati equation | Perturbation analysis | MATHEMATICS, APPLIED | LINEAR LEAST-SQUARES | COMPONENTWISE CONDITION NUMBERS | SYSTEMS | Statistics | Analysis | Algorithms

Journal Article

15.
Full Text
Methods for verified stabilizing solutions to continuous-time algebraic Riccati equations

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2017, Volume 313, pp. 515 - 535

We describe a procedure based on the Krawczyk method to compute a verified enclosure for the stabilizing solution of a continuous-time algebraic Riccati...

Algebraic Riccati equation | Stabilizing solution | Verified computation | Krawczyk’s method | Interval arithmetic | Krawczyk's method | MATHEMATICS, APPLIED | ENCLOSURES | COMPUTATION | Applications of mathematics | State of the art | Algebra | Mathematical analysis | Benchmarking | Mathematical models | Riccati equation | Standards

Algebraic Riccati equation | Stabilizing solution | Verified computation | Krawczyk’s method | Interval arithmetic | Krawczyk's method | MATHEMATICS, APPLIED | ENCLOSURES | COMPUTATION | Applications of mathematics | State of the art | Algebra | Mathematical analysis | Benchmarking | Mathematical models | Riccati equation | Standards

Journal Article

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, ISSN 1292-8119, 01/2018, Volume 24, Issue 1, pp. 129 - 151

The algebraic Riccati equation (ARE) is a matrix valued quadratic equation with many important applications in the field of control theory, such as feedback...

MATHEMATICS, APPLIED | low rank approximation | ALGORITHM | LYAPUNOV EQUATIONS | SENSITIVITY | algebraic riccati equation | POSTERIORI ERROR ESTIMATION | KRYLOV SUBSPACE METHODS | REFINEMENT | NUMERICAL-SOLUTION | REDUCTION | BOUNDS | optimal feedback control | Reduced basis method | AUTOMATION & CONTROL SYSTEMS | Quadratic equations | Error analysis | Parameters | Partial differential equations | Feedback control | Linear quadratic | Complexity | Robust control | Algebra | Robustness (mathematics) | Computation | Control theory | Riccati equation | State estimation

MATHEMATICS, APPLIED | low rank approximation | ALGORITHM | LYAPUNOV EQUATIONS | SENSITIVITY | algebraic riccati equation | POSTERIORI ERROR ESTIMATION | KRYLOV SUBSPACE METHODS | REFINEMENT | NUMERICAL-SOLUTION | REDUCTION | BOUNDS | optimal feedback control | Reduced basis method | AUTOMATION & CONTROL SYSTEMS | Quadratic equations | Error analysis | Parameters | Partial differential equations | Feedback control | Linear quadratic | Complexity | Robust control | Algebra | Robustness (mathematics) | Computation | Control theory | Riccati equation | State estimation

Journal Article

Mediterranean Journal of Mathematics, ISSN 1660-5446, 12/2016, Volume 13, Issue 6, pp. 4961 - 4973

In this paper, we consider the nonsymmetric algebraic Riccati equation whose four coefficient matrices form an M-matrix K. When K is a regular M-matrix, the...

regular M -matrix | numerical iteration methods | Mathematics, general | minimal nonnegative solution | Mathematics | 65H10 | reducible singular M -matrix | Nonsymmetric algebraic Riccati equation | reducible singular M-matrix | regular M-matrix | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | ITERATIVE SOLUTION | DOUBLING-ALGORITHM | MATRIX EQUATIONS | Computer science

regular M -matrix | numerical iteration methods | Mathematics, general | minimal nonnegative solution | Mathematics | 65H10 | reducible singular M -matrix | Nonsymmetric algebraic Riccati equation | reducible singular M-matrix | regular M-matrix | MATHEMATICS | MATHEMATICS, APPLIED | CONVERGENCE ANALYSIS | ITERATIVE SOLUTION | DOUBLING-ALGORITHM | MATRIX EQUATIONS | Computer science

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 01/2013, Volume 237, Issue 1, pp. 373 - 383

We consider the solution of large-scale algebraic Riccati equations with numerically low-ranked solutions. For the discrete-time case, the structure-preserving...

Doubling algorithm | Krylov subspace | Large-scale problem | Continuous-time algebraic Riccati equation | MATHEMATICS, APPLIED | ALGORITHMS | Algorithms | Algebra | Computation | Mathematical analysis | Mathematical models | Riccati equation | Iterative methods | Matlab

Doubling algorithm | Krylov subspace | Large-scale problem | Continuous-time algebraic Riccati equation | MATHEMATICS, APPLIED | ALGORITHMS | Algorithms | Algebra | Computation | Mathematical analysis | Mathematical models | Riccati equation | Iterative methods | Matlab

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 01/2016, Volume 488, pp. 430 - 459

This article discusses an approach to solving large-scale algebraic Riccati equations (AREs) by computing a low-dimensional stable invariant subspace of the...

Hamiltonian matrices | Invariant subspaces | Matrix equations | Krylov subspaces | Algebraic Riccati equations | ADI iteration | MATHEMATICS, APPLIED | FACTORIZATIONS | LYAPUNOV EQUATIONS | RANK | MATHEMATICS | KRYLOV SUBSPACE | SINGULAR-VALUES | Algorithms

Hamiltonian matrices | Invariant subspaces | Matrix equations | Krylov subspaces | Algebraic Riccati equations | ADI iteration | MATHEMATICS, APPLIED | FACTORIZATIONS | LYAPUNOV EQUATIONS | RANK | MATHEMATICS | KRYLOV SUBSPACE | SINGULAR-VALUES | Algorithms

Journal Article

SIAM Journal on Scientific Computing, ISSN 1064-8275, 2015, Volume 37, Issue 1, pp. B103 - B125

We consider the numerical solution of the rational algebraic Riccati equations in R-n, arising from stochastic optimal control in continuous and discrete time....

Rational algebraic Riccati equation | Stochastic algebraic Riccati equation | Generalized Stein equation | Stochastic optional control | Generalized lyapunov equation | generalized Stein equation | STEIN | MATHEMATICS, APPLIED | ITERATIONS | stochastic algebraic Riccati equation | DIFFERENTIAL-EQUATIONS | rational algebraic Riccati equation | generalized lyapunov equation | KRYLOV SUBSPACE METHODS | stochastic optional control | GENERALIZED LYAPUNOV EQUATIONS | DOUBLING-ALGORITHM | Algebra | Computation | Mathematical analysis | Optimal control | Differential equations | Mathematical models | Stochasticity | Riccati equation

Rational algebraic Riccati equation | Stochastic algebraic Riccati equation | Generalized Stein equation | Stochastic optional control | Generalized lyapunov equation | generalized Stein equation | STEIN | MATHEMATICS, APPLIED | ITERATIONS | stochastic algebraic Riccati equation | DIFFERENTIAL-EQUATIONS | rational algebraic Riccati equation | generalized lyapunov equation | KRYLOV SUBSPACE METHODS | stochastic optional control | GENERALIZED LYAPUNOV EQUATIONS | DOUBLING-ALGORITHM | Algebra | Computation | Mathematical analysis | Optimal control | Differential equations | Mathematical models | Stochasticity | Riccati equation

Journal Article

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