Mathematics – Analysis of PDEs
Scientific paper
2012-03-23
Mathematics
Analysis of PDEs
Scientific paper
We analyse an optimal control with the following features: the dynamical system is linear, and the dependence upon the control parameter is affine. More precisely we consider $\dot x_\alpha(t) = (G + \alpha(t) F)x_\alpha(t)$, where $G$ and $F$ are $3\times 3$ matrices with some prescribed structure. In the case of constant control $\alpha(t)\equiv \alpha$, we show the existence of an optimal Perron eigenvalue with respect to varying $\alpha$ under some assumptions. Next we investigate the Floquet eigenvalue problem associated to time-periodic controls $\alpha(t)$. Finally we prove the existence of an eigenvalue (in the generalized sense) for the optimal control problem. The proof is based on the results by [Arisawa 1998, Ann. Institut Henri Poincar\'e] concerning the ergodic problem for Hamilton-Jacobi equations. We discuss the relations between the three eigenvalues. Surprisingly enough, the three eigenvalues appear to be numerically the same.
Calvez Vincent
Gabriel Pierre
No associations
LandOfFree
Optimal growth for linear processes with affine control does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Optimal growth for linear processes with affine control, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Optimal growth for linear processes with affine control will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-471794