Lyapunov–schmidt Reduction for Optimal Control Problems

LYAPACK - A MATLAB Toolbox for Large Lyapunov and Riccati Equations, Model Reduction Problems, and Linear-Quadratic Optimal Control Problems - Users' Guide (Version 1.0)

Optimal integrated passive/active design of the suspension system using iteration on the Lyapunov equations

In this paper, an iterative technique is proposed to solve linear integrated active/passive design problems. The optimality of active and passive parts leads to the nonlinear algebraic Riccati equation due to the active parameters and some associated additional Lyapunov equations due to the passive parameters. Rather than the solution of the nonlinear algebraic Riccati equation, it is proposed ...

Model Reduction by Balanced Truncation for Systems with Nuclear Hankel Operators

We prove the H-infinity error bounds for Lyapunov balanced truncation and for optimal Hankel norm approximation under the assumption that the Hankel operator is nuclear. This is an improvement of the result from Glover, Curtain, and Partington [SIAM J. Control Optim., 26 (1998), pp. 863–898], where additional assumptions were made. The proof is based on convergence of the Schmidt pairs of the H...

Proper Orthogonal Decomposition for Linear-Quadratic Optimal Control

Optimal control problems for partial differential equation are often hard to tackle numerically because their discretization leads to very large scale optimization problems. Therefore, different techniques of model reduction were developed to approximate these problems by smaller ones that are tractable with less effort. Balanced truncation [2, 66, 81] is one well studied model reduction techni...

Generalized Lyapunov{schmidt Reduction for Parametrized Equations at near Singular Points

The Lyapunov-Schmidt reduction is generalized to the case of imperfect singularities. The results presented neither need very precise information about the location of the (near) singularities nor a precise knowledge of (near) null spaces.