## Thesis etd-09052018-185037 |

Link copiato negli appunti

Thesis type

Tesi di laurea magistrale

Author

CORTINOVIS, ALICE

URN

etd-09052018-185037

Thesis title

Minimizing the optimality residual for algebraic Riccati equations

Department

MATEMATICA

Course of study

MATEMATICA

Supervisors

**relatore**Prof. Poloni, Federico

Keywords

- algebraic Riccati equation
- optimal control
- residual

Graduation session start date

21/09/2018

Availability

Full

Summary

The thesis is about continuous-time algebraic Riccati equations A^T X + X A + Q - X G X = 0 that can be obtained from autonomous linear quadratic optimal control problems.

To quantify the accuracy of a computed solution of an algebraic Riccati equation, we introduce the optimality residual, that is a measure of residual linked to the original optimal control problem. We obtain a way to compute this residual in terms of the approximate solution and the problem data, up to first-order corrections.

Among the methods to solve algebraic Riccati equations we focus on Schur's method, which works on finding the stable invariant subspace of a suitable Hamiltonian matrix. Scaling this matrix before finding the stable invariant subspace, i.e. applying a change of basis, can result in an improved solution of the equation. We analyze how the optimality residual changes with scaling and we propose some scaling strategies that aim at reducing this residual. Numerical experiments are done in order to compare these strategies.

To quantify the accuracy of a computed solution of an algebraic Riccati equation, we introduce the optimality residual, that is a measure of residual linked to the original optimal control problem. We obtain a way to compute this residual in terms of the approximate solution and the problem data, up to first-order corrections.

Among the methods to solve algebraic Riccati equations we focus on Schur's method, which works on finding the stable invariant subspace of a suitable Hamiltonian matrix. Scaling this matrix before finding the stable invariant subspace, i.e. applying a change of basis, can result in an improved solution of the equation. We analyze how the optimality residual changes with scaling and we propose some scaling strategies that aim at reducing this residual. Numerical experiments are done in order to compare these strategies.

File

Nome file | Dimensione |
---|---|

Tesi.pdf | 4.60 Mb |

Contatta l’autore |