Abstract
This note deals with solving scalar coupled algebraic Riccati equations. These equations arise in finding linear feedback Nash equilibria of the scalar N-player affine quadratic differential game. A numerical procedure is provided to compute all the stabilizing solutions. The main idea is to reformulate the Riccati equations into an extended eigenvalue-eigenvector problem for a specific parametrized matrix U ∈ ℝ2N ×2N. Since the size of U increases exponentially on N, the algorithm only applies for games where the number of players is not too large.
| Original language | English |
|---|---|
| Pages (from-to) | 3101-3106 |
| Number of pages | 6 |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 60 |
| Issue number | 11 |
| DOIs | |
| Publication status | Published - 2015 |
Keywords
- Riccati equations
- differential games
- eigenvalues and eigenfunctions
- feedback
- linear systems
- matrix algebra