All Questions
4 questions with no upvoted or accepted answers
3
votes
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Attainability of Global Optima In Optimal Control
Given a manifold $M$ and a set of smooth functions of one real variable $\mathcal{A}$ and a 'control system' type first order differential equation:
$\frac{d x(t)}{dt} = F(x,u)$
one can consider the ...
- 2,099
2
votes
0
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94
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Maximize a tricky function on $SU(n)$
Given non-zero $\xi \in \mathfrak{su}(n)$ and $G \in SU(n)$, consider the function:
$Q(U) = Tr(G^{\dagger}U)GU^{\dagger} - Tr(U^{\dagger}G) UG^{\dagger}$
(which just happens to be the gradient of $|...
2
votes
0
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115
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Are singular critical points isolated for control systems on compact semisimple Lie groups
Given a control system on $\mathrm{SU}(n)$ (or any other compact, semi-simple Lie group I suspect) of the form:
$\frac{d U_t}{dt} = (A + w(t)B)U_t$
where $A,B \in \mathfrak{su}(n)$ generate the ...
- 2,099
0
votes
0
answers
71
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Curves in $\mathfrak{su}(n)$ with specific property
Consider a curve $\gamma_s= U_s^{\dagger} b U_s$ in $\mathfrak{su}(n)$ where $U_s$ is a smooth curve on $SU(n)$ (starting at $U_0 = \mathbb{I}$) and nonzero $b\in \mathfrak{su}(n)$ and $s \in[0,T]$ ...
- 2,099