Journal of Computational and Applied Mathematics, ISSN 0377-0427, 03/2015, Volume 277, pp. 115 - 126

We consider the numerical solution of large-scale discrete-time algebraic Riccati equations. The doubling algorithm is adapted, with the iterates for A not...

Large-scale problem | Doubling algorithm | Discrete-time algebraic Riccati equation | Discrete-time algebraic | Riccati equation | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | LYAPUNOV EQUATIONS | RECIPES | KRYLOV SUBSPACE METHODS | Analysis | Algorithms

Large-scale problem | Doubling algorithm | Discrete-time algebraic Riccati equation | Discrete-time algebraic | Riccati equation | MATHEMATICS, APPLIED | NUMERICAL-SOLUTION | LYAPUNOV EQUATIONS | RECIPES | KRYLOV SUBSPACE METHODS | Analysis | Algorithms

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 04/2019, Volume 350, pp. 80 - 86

A fast iterative algorithm is proposed for numerically computing an interval matrix containing the Hermitian positive definite solution to the conjugate...

Hermitian positive definite solution | Verified numerical computation | Perron–Frobenius theory | Discrete-time algebraic Riccati equation | MATHEMATICS, APPLIED | Perron-Frobenius theory | Algorithms

Hermitian positive definite solution | Verified numerical computation | Perron–Frobenius theory | Discrete-time algebraic Riccati equation | MATHEMATICS, APPLIED | Perron-Frobenius theory | Algorithms

Journal Article

Automatica, ISSN 0005-1098, 09/2017, Volume 83, pp. 47 - 57

This paper deals with a set of S-coupled algebraic Riccati equations that arises in the study of filtering of discrete-time linear jump systems with the Markov...

Discrete-time systems | Markov models | Stochastic jump processes | Filtering problems | Riccati equations | Optimal filtering | LINEAR-SYSTEMS | NETWORKED CONTROL | STOCHASTIC-CONTROL | ENGINEERING, ELECTRICAL & ELECTRONIC | CHAIN | STABILITY ANALYSIS | GENERAL BOREL SPACE | TOLERANT CONTROL-SYSTEMS | SWITCHING PARAMETERS | ORDERED BANACH-SPACES | AUTOMATION & CONTROL SYSTEMS | LQ CONTROL | Markov processes | Analysis

Discrete-time systems | Markov models | Stochastic jump processes | Filtering problems | Riccati equations | Optimal filtering | LINEAR-SYSTEMS | NETWORKED CONTROL | STOCHASTIC-CONTROL | ENGINEERING, ELECTRICAL & ELECTRONIC | CHAIN | STABILITY ANALYSIS | GENERAL BOREL SPACE | TOLERANT CONTROL-SYSTEMS | SWITCHING PARAMETERS | ORDERED BANACH-SPACES | AUTOMATION & CONTROL SYSTEMS | LQ CONTROL | Markov processes | Analysis

Journal Article

Japan Journal of Industrial and Applied Mathematics, ISSN 0916-7005, 9/2019, Volume 36, Issue 3, pp. 763 - 776

A robust algorithm is proposed for numerically computing an interval matrix containing the stabilizing solution of a discrete-time algebraic Riccati equation....

Computational Mathematics and Numerical Analysis | 39B42 | 15A24 | 65G20 | Verified numerical computation | Perron–Frobenius theory | Mathematics | Applications of Mathematics | Stabilizing solution | Discrete-time algebraic Riccati equation | VERIFIED COMPUTATION | MATHEMATICS, APPLIED | Perron-Frobenius theory

Computational Mathematics and Numerical Analysis | 39B42 | 15A24 | 65G20 | Verified numerical computation | Perron–Frobenius theory | Mathematics | Applications of Mathematics | Stabilizing solution | Discrete-time algebraic Riccati equation | VERIFIED COMPUTATION | MATHEMATICS, APPLIED | Perron-Frobenius theory

Journal Article

Asian Journal of Control, ISSN 1561-8625, 01/2013, Volume 15, Issue 1, pp. 132 - 141

In the present paper we obtain an explicit closed‐form solution for the discrete‐time algebraic Riccati equation (DTARE) with vanishing state weight, whenever...

optimal control | Discrete‐time algebraic Riccati equation | linear systems | Discrete-time algebraic Riccati equation | NETWORKED CONTROL-SYSTEMS | FEEDBACK STABILIZATION | CLOSED-FORM SOLUTION | CHANNELS | AUTOMATION & CONTROL SYSTEMS

optimal control | Discrete‐time algebraic Riccati equation | linear systems | Discrete-time algebraic Riccati equation | NETWORKED CONTROL-SYSTEMS | FEEDBACK STABILIZATION | CLOSED-FORM SOLUTION | CHANNELS | AUTOMATION & CONTROL SYSTEMS

Journal Article

Operators and Matrices, ISSN 1846-3886, 03/2018, Volume 12, Issue 1, pp. 169 - 187

The purpose of this paper is to introduce a two-stage procedure that can be used to decompose a discrete-time algebraic Riccati equation into a trivial part, a...

Symplectic pencil | Discrete-time algebraic Riccati equations | MATHEMATICS | ORDER REDUCTION | FILTERS | symplectic pencil | CLOSED-LOOP MATRIX | SYSTEMS | CONVERGENCE | TIME | STOCHASTIC-CONTROL

Symplectic pencil | Discrete-time algebraic Riccati equations | MATHEMATICS | ORDER REDUCTION | FILTERS | symplectic pencil | CLOSED-LOOP MATRIX | SYSTEMS | CONVERGENCE | TIME | STOCHASTIC-CONTROL

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 03/2019, Volume 64, Issue 3, pp. 1125 - 1136

This paper will investigate the stabilization and optimal linear quadratic (LQ) control problems for infinite horizon discrete-time mean-field systems. Unlike...

Algebraic Riccati equation (ARE) | Symmetric matrices | Stochastic systems | stabilizing controller | Riccati equations | Optimal control | Cost function | mean-field LQ (linear quadratic) control | Observability | Standards | optimal controller | Mean-field LQ control | algebraic Riccati equation | DIFFERENTIAL-EQUATIONS | LIMIT | QUADRATIC OPTIMAL-CONTROL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Observability (systems) | Controllers | Stabilization | Discrete time systems | Riccati equation | Linear quadratic

Algebraic Riccati equation (ARE) | Symmetric matrices | Stochastic systems | stabilizing controller | Riccati equations | Optimal control | Cost function | mean-field LQ (linear quadratic) control | Observability | Standards | optimal controller | Mean-field LQ control | algebraic Riccati equation | DIFFERENTIAL-EQUATIONS | LIMIT | QUADRATIC OPTIMAL-CONTROL | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Observability (systems) | Controllers | Stabilization | Discrete time systems | Riccati equation | Linear quadratic

Journal Article

Discrete Dynamics in Nature and Society, ISSN 1026-0226, 2015, Volume 2015, pp. 1 - 11

We provide necessary and sufficient conditions for the existence of stabilizing solutions for a class of modified algebraic discrete-time Riccati equations...

LINEAR-SYSTEMS | HILBERT-SPACES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | MULTIDISCIPLINARY SCIENCES | ORDERED BANACH-SPACES | Discrete-time systems | Research | Riccati equation | Mathematical research | Linear systems | Operators | Algebra | Mathematical analysis | Markov processes | Banach space | Linear quadratic

LINEAR-SYSTEMS | HILBERT-SPACES | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | OPERATORS | MULTIDISCIPLINARY SCIENCES | ORDERED BANACH-SPACES | Discrete-time systems | Research | Riccati equation | Mathematical research | Linear systems | Operators | Algebra | Mathematical analysis | Markov processes | Banach space | Linear quadratic

Journal Article

Applied Numerical Mathematics, ISSN 0168-9274, 06/2020, Volume 152, pp. 499 - 510

We apply the Krylov subspace methods to large-scale discrete-time algebraic Riccati equations. The solvability of the projected algebraic Riccati equation is...

Inheritance property | Krylov subspace | LQR optimal control | Projection methods | Discrete-time algebraic Riccati equation

Inheritance property | Krylov subspace | LQR optimal control | Projection methods | Discrete-time algebraic Riccati equation

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 04/2019, Volume 64, Issue 4, pp. 1603 - 1610

We study distributed Kalman filtering over the wireless sensor network, where each sensor node is required to locally estimate the state of a linear...

Wireless sensor networks | Protocols | Heuristic algorithms | Data packet drops | Distributed databases | Estimation | wireless sensor network | Steady-state | modified algebraic Riccati equation (MARE) | Kalman filters | distributed Kalman filtering | Kalman consensus filter (KCF) | data packet drops | Kalman consensus filter | modified algebraic Riccati equation | Distributed Kalman filtering | STABILIZATION | CONSENSUS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | STATE ESTIMATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Remote sensors | TCP (protocol) | Wireless networks | Mathematical analysis | Discrete time systems | Error detection | Linear matrix inequalities | Sensors | Riccati equation | Matrix methods

Wireless sensor networks | Protocols | Heuristic algorithms | Data packet drops | Distributed databases | Estimation | wireless sensor network | Steady-state | modified algebraic Riccati equation (MARE) | Kalman filters | distributed Kalman filtering | Kalman consensus filter (KCF) | data packet drops | Kalman consensus filter | modified algebraic Riccati equation | Distributed Kalman filtering | STABILIZATION | CONSENSUS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | STATE ESTIMATION | ENGINEERING, ELECTRICAL & ELECTRONIC | Remote sensors | TCP (protocol) | Wireless networks | Mathematical analysis | Discrete time systems | Error detection | Linear matrix inequalities | Sensors | Riccati equation | Matrix methods

Journal Article

SIAM Journal on Matrix Analysis and Applications, ISSN 0895-4798, 2009, Volume 31, Issue 3, pp. 1257 - 1278

A discrete-time nonsymmetric algebraic Riccati system which incorporates as special cases of various discrete-time nonsymmetric algebraic Riccati equations is...

Discrete-time nonsymmetric algebraic riccati equations | Matrix pencil | Deflating subspaces | Game theory | IMPROVED ALGORITHM | MATHEMATICS, APPLIED | discrete-time nonsymmetric algebraic Riccati equations | game theory | matrix pencil | PARAMETRIZATION | COMPUTATION | deflating subspaces | Studies | Matrix | Engineering Sciences | Automatic

Discrete-time nonsymmetric algebraic riccati equations | Matrix pencil | Deflating subspaces | Game theory | IMPROVED ALGORITHM | MATHEMATICS, APPLIED | discrete-time nonsymmetric algebraic Riccati equations | game theory | matrix pencil | PARAMETRIZATION | COMPUTATION | deflating subspaces | Studies | Matrix | Engineering Sciences | Automatic

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 2008, Volume 206, Issue 1, pp. 34 - 41

We consider a set of discrete-time coupled algebraic Riccati equations that arise in quadratic optimal control. Two iterations for computing a symmetric...

Stein equation | Positive definite solution | Jump systems | A set of discrete-time Riccati equations | MATHEMATICS, APPLIED | JUMP LINEAR-SYSTEMS | LYAPUNOV ITERATIONS | Analysis | Methods | Algorithms

Stein equation | Positive definite solution | Jump systems | A set of discrete-time Riccati equations | MATHEMATICS, APPLIED | JUMP LINEAR-SYSTEMS | LYAPUNOV ITERATIONS | Analysis | Methods | Algorithms

Journal Article

Advances in Computational Mathematics, ISSN 1019-7168, 11/2011, Volume 35, Issue 2, pp. 119 - 147

We discuss the numerical solution of large-scale discrete-time algebraic Riccati equations (DAREs) as they arise, e.g., in fully discretized linear-quadratic...

Numeric Computing | Large | Newton’s method | Theory of Computation | Smith iteration | Algebraic Riccati equation | Algebra | Discrete-time control | 15A24 | Calculus of Variations and Optimal Control; Optimization | 93C05 | Low-rank factor | 65F30 | Computer Science | Mathematics, general | Sparse | 49M15 | Riccati equation | 93C20 | ADI iteration | Newton's method | MATHEMATICS, APPLIED | ALGORITHM | LYAPUNOV EQUATIONS | CONSTANT | AXB(T)+CXD(T)=E | EIGENPROBLEM | REGULATOR | RANK SMITH METHOD | SYSTEMS | ITERATIVE METHODS | MATRIX EQUATIONS | Control systems | Usage | Algorithms | Analysis | Approximation | Nodular iron | Partial differential equations | Computation | Mathematical analysis | Mathematical models | Iterative methods

Numeric Computing | Large | Newton’s method | Theory of Computation | Smith iteration | Algebraic Riccati equation | Algebra | Discrete-time control | 15A24 | Calculus of Variations and Optimal Control; Optimization | 93C05 | Low-rank factor | 65F30 | Computer Science | Mathematics, general | Sparse | 49M15 | Riccati equation | 93C20 | ADI iteration | Newton's method | MATHEMATICS, APPLIED | ALGORITHM | LYAPUNOV EQUATIONS | CONSTANT | AXB(T)+CXD(T)=E | EIGENPROBLEM | REGULATOR | RANK SMITH METHOD | SYSTEMS | ITERATIVE METHODS | MATRIX EQUATIONS | Control systems | Usage | Algorithms | Analysis | Approximation | Nodular iron | Partial differential equations | Computation | Mathematical analysis | Mathematical models | Iterative methods

Journal Article

Automatica, ISSN 0005-1098, 01/2018, Volume 87, pp. 383 - 388

This paper proposes a novel lifting method which converts the standard discrete-time linear periodic system to an augmented linear time-invariant system. The...

Spacecraft attitude control | Magnetic torque | Linear periodic discrete-time system | Periodic algebraic Riccati equation | LQR | SPACECRAFT ATTITUDE | NUMERICAL-SOLUTION | ALGEBRAIC RICCATI-EQUATIONS | ALGORITHMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Space vehicles | Space ships | Algorithms | Analysis | Methods | Mathematics - Optimization and Control

Spacecraft attitude control | Magnetic torque | Linear periodic discrete-time system | Periodic algebraic Riccati equation | LQR | SPACECRAFT ATTITUDE | NUMERICAL-SOLUTION | ALGEBRAIC RICCATI-EQUATIONS | ALGORITHMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Space vehicles | Space ships | Algorithms | Analysis | Methods | Mathematics - Optimization and Control

Journal Article

International Journal of Robust and Nonlinear Control, ISSN 1049-8923, 11/2017, Volume 27, Issue 16, pp. 2921 - 2936

Summary This paper deals with the leader‐following consensus of discrete‐time multi‐agent systems subject to both position and rate saturation. Each agent is...

consensus | saturation | leader‐following | low‐gain feedback | modified algebraic Riccati equation | leader-following | low-gain feedback | MATHEMATICS, APPLIED | DELAYS | NETWORKS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | INPUT SATURATION | AGENTS | AUTOMATION & CONTROL SYSTEMS | FLOCKING | Actuators | State feedback | Multiagent systems | Stability | Discrete time systems | Actuator position | Design modifications | Saturation | Feedback control | Riccati equation | Output feedback

consensus | saturation | leader‐following | low‐gain feedback | modified algebraic Riccati equation | leader-following | low-gain feedback | MATHEMATICS, APPLIED | DELAYS | NETWORKS | ENGINEERING, ELECTRICAL & ELECTRONIC | SYNCHRONIZATION | INPUT SATURATION | AGENTS | AUTOMATION & CONTROL SYSTEMS | FLOCKING | Actuators | State feedback | Multiagent systems | Stability | Discrete time systems | Actuator position | Design modifications | Saturation | Feedback control | Riccati equation | Output feedback

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 11/2004, Volume 49, Issue 11, pp. 2049 - 2054

The classical discrete-time algebraic Riccati equation (DARE) is considered in the case when the corresponding closed-loop matrix is singular. It is shown that...

Linear systems | order reduction | Symmetric matrices | Target tracking | Control systems | Algebraic Riccati equation (ARE) | Riccati equations | Optimal control | Automatic control | Controllability | closed-loop matrix | symplectic pencils | Observability | discrete-time linear quadratic (LQ) optimal control | Arithmetic | Discrete-time linear quadratic (LQ) optimal control | Symplectic pencils | Order reduction | Closed-loop matrix | algebraic Riccati equation (ARE) | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Parametrization | Algebra | Algorithms | Computation | Eigenvalues | Mathematical models | Riccati equation

Linear systems | order reduction | Symmetric matrices | Target tracking | Control systems | Algebraic Riccati equation (ARE) | Riccati equations | Optimal control | Automatic control | Controllability | closed-loop matrix | symplectic pencils | Observability | discrete-time linear quadratic (LQ) optimal control | Arithmetic | Discrete-time linear quadratic (LQ) optimal control | Symplectic pencils | Order reduction | Closed-loop matrix | algebraic Riccati equation (ARE) | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Parametrization | Algebra | Algorithms | Computation | Eigenvalues | Mathematical models | Riccati equation

Journal Article

17.
Full Text
Exact Discretization of a Matrix Differential Riccati Equation With Constant Coefficients

IEEE Transactions on Automatic Control, ISSN 0018-9286, 05/2009, Volume 54, Issue 5, pp. 1065 - 1068

An exact method is presented for discretizing a constant-coefficient, non-square, matrix differential Riccati equation, whose solution is assumed to exist. The...

Linear systems | discrete time Riccati equations | Nonlinear equations | exact discretization | Terrorism | Riccati equations | Differential algebraic equations | Differential equations | exact linearization | Systems engineering and theory | Nonlinear systems | Differential Riccati equations | Exact discretization | Discrete time Riccati equations | Exact linearization | nonlinear systems | DISCRETE-TIME MODELS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Evaluation | Linearization (Electronics) | Chaos theory | Design and construction | Riccati equation | Methods | Intervals | Discretization | Mathematical analysis | Automatic control | Mathematical models | Transformations

Linear systems | discrete time Riccati equations | Nonlinear equations | exact discretization | Terrorism | Riccati equations | Differential algebraic equations | Differential equations | exact linearization | Systems engineering and theory | Nonlinear systems | Differential Riccati equations | Exact discretization | Discrete time Riccati equations | Exact linearization | nonlinear systems | DISCRETE-TIME MODELS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Evaluation | Linearization (Electronics) | Chaos theory | Design and construction | Riccati equation | Methods | Intervals | Discretization | Mathematical analysis | Automatic control | Mathematical models | Transformations

Journal Article

IEEE Transactions on Signal Processing, ISSN 1053-587X, 05/2015, Volume 63, Issue 10, pp. 2559 - 2571

This paper considers the problem of estimating and tracking channels in a distributed transmission system with N t transmit nodes and N r receive nodes. Since...

oscillator dynamics | Riccati equations | distributed communication systems | discrete-time algebraic Riccati equation | MIMO | channel prediction | Steady-state | coherent transmission | Kalman filters | Synchronization | Asymptotic analysis | Oscillators | SYNCHRONIZATION | PHASE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Research | Riccati equation | Analysis of covariance | MIMO communications

oscillator dynamics | Riccati equations | distributed communication systems | discrete-time algebraic Riccati equation | MIMO | channel prediction | Steady-state | coherent transmission | Kalman filters | Synchronization | Asymptotic analysis | Oscillators | SYNCHRONIZATION | PHASE | ENGINEERING, ELECTRICAL & ELECTRONIC | Usage | Research | Riccati equation | Analysis of covariance | MIMO communications

Journal Article

Linear Algebra and Its Applications, ISSN 0024-3795, 2006, Volume 416, Issue 2, pp. 1060 - 1082

This paper is concerned with a characterization of all symmetric solutions to the discrete-time algebraic Riccati equation (DARE). Dissipation theory and...

Dissipativesystem | Quadraticdifferenceforms | Discrete-timealgebraicRiccatiequation | Storage function | Behavioral approach | Spectral factorization | behavioral approach | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | dissipative system | discrete-time algebraic Riccati equation | SYSTEMS | spectral factorization | quadratic difference forms | storage function | STATE FUNCTION | Universities and colleges

Dissipativesystem | Quadraticdifferenceforms | Discrete-timealgebraicRiccatiequation | Storage function | Behavioral approach | Spectral factorization | behavioral approach | EXISTENCE | MATHEMATICS | MATHEMATICS, APPLIED | dissipative system | discrete-time algebraic Riccati equation | SYSTEMS | spectral factorization | quadratic difference forms | storage function | STATE FUNCTION | Universities and colleges

Journal Article

IEEE Transactions on Automatic Control, ISSN 0018-9286, 07/2017, Volume 62, Issue 7, pp. 3262 - 3276

In this paper, we obtain a general characterization of discrete-time all-pass rational matrix functions from state-space representations. We establish a...

Symmetric matrices | Riccati equations | Stochastic processes | Transfer functions | Eigenvalues and eigenfunctions | Reduced order systems | Kernel | ALGEBRAIC RICCATI EQUATION | INFINITY-ERROR-BOUNDS | HANKEL-NORM APPROXIMATIONS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | UNMIXED SOLUTIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Usage | Matrices

Symmetric matrices | Riccati equations | Stochastic processes | Transfer functions | Eigenvalues and eigenfunctions | Reduced order systems | Kernel | ALGEBRAIC RICCATI EQUATION | INFINITY-ERROR-BOUNDS | HANKEL-NORM APPROXIMATIONS | SYSTEMS | AUTOMATION & CONTROL SYSTEMS | UNMIXED SOLUTIONS | ENGINEERING, ELECTRICAL & ELECTRONIC | Discrete-time systems | Usage | Matrices

Journal Article

No results were found for your search.

Cannot display more than 1000 results, please narrow the terms of your search.