A lower bound for the solution of the algebraic Riccati equation of optimal control and a geometric convergence rate for the Kleinman algorithm

DOI10.1109/TAC.1980.1102412zbMath0447.49023OpenAlexW2066429540MaRDI QIDQ3892852

Publication date: 1980

Published in: IEEE Transactions on Automatic Control (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1109/tac.1980.1102412

zbMATH Keywords

state feedback Lyapunov equation algebraic Riccati equation quadratic performance index

Mathematics Subject Classification ID

Numerical methods based on necessary conditions (49M05) Linear systems in control theory (93C05) Existence theories for optimal control problems involving ordinary differential equations (49J15) Control/observation systems governed by ordinary differential equations (93C15) Model systems in control theory (93C99)

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Bounds for the eigenvalues of the solution matrix of the algebraic Riccati equation ⋮ Output‐feedback robust control of systems with uncertain dynamics via data‐driven policy learning ⋮ New matrix bounds, an existence uniqueness and a fixed-point iterative algorithm for the solution of the unified coupled algebraic Riccati equation ⋮ A brief summary of the bounds on the solution of the algebraic matrix equations in control theory ⋮ New estimates of upper bounds for the solutions of the continuous algebraic Riccati equation and the redundant control inputs problems ⋮ Lower bounds on the solution of coupled algebraic Riccati equation ⋮ Solution bounds for the discrete Riccati equation and its applications

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