Numerical solution of the symmetric riccati equation through riccati iteration
Copyright policy )Numerical solution of the symmetric riccati equation through riccati iteration
AbstractThis paper presents a new method for solving the symmetric algebraic Riccati equation from optimal control. The new method employs ‘Riccati iteration’ as used for time‐scale decoupling in structural vibration problems. The rate of convergence of the algorithm is governed by the relative separation of small and large eigenvalues in the shifted Hamiltonian equations. If this ratio of eigenvalues is less than one, the algorithm is globally convergent. Riccati iteration is demonstrated for a set of 8th‐order linear‐quadratic regulator problems, and preliminary timing and accuracy comparisons are presented.
- Virginia Tech United States
- University of Arkansas United States
- University of Arkansas at Fayetteville United States
Numerical computation of eigenvalues and eigenvectors of matrices, Linear systems in control theory, numerical Riccati iteration, Numerical computation of solutions to systems of equations, Matrix equations and identities, algebraic Riccati equation, Computational methods in systems theory, Control/observation systems governed by ordinary differential equations
Numerical computation of eigenvalues and eigenvectors of matrices, Linear systems in control theory, numerical Riccati iteration, Numerical computation of solutions to systems of equations, Matrix equations and identities, algebraic Riccati equation, Computational methods in systems theory, Control/observation systems governed by ordinary differential equations
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