0
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0answers
17 views

What about the HUM for a finite-dimensional system?

We consider the finite-dimensional system \begin{equation}\begin{cases}y'(t)=Ay(t)+Bv,\ t\in (0,T)\\ y(0)=y^0\end{cases}\end{equation} Where $v$ is the control, $A\in Mat(N\times N); B\in Mat(N\times ...
4
votes
1answer
36 views

Reference request: “initial” PDE control

I'm somewhat familiar with the ideas of boundary and internal (source) control for PDE (in particular, for wave equations) but am wondering if the following type of problem is classified/studied; if ...
1
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0answers
41 views

improving fluid analysis on queuing problems

Discrete-queuing models are hard to solve computationally and can become easily intractable with an increased number of state-action pairs. Markov decision processes can be employed to come up with ...
1
vote
0answers
79 views

optimal control -Taylor expansion - PDE problem

I am trying to follow perturbation analysis in this paper (Optimal control of fluid limits of queuing networks and stochasticity corrections) and I am stuck at one point. For the given control ...
0
votes
1answer
75 views

Nonlinear Systems- L2 stability analysis

I hope you are having a good day. I am working on a homework and I was looking for some help. Can anyone please help me with the next step to prove whether the L-2 stability of the system and the ...
2
votes
1answer
83 views

A control problem for the wave equation solved by the HUM

My question is about an article by J.L. Lions 1, where he introduced the "Hilbert Uniqueness Method" (HUM) for finding a boundary control function (dirichlet action) to bring the system to rest within ...
2
votes
1answer
215 views

The yacht race problem from L.C.Evans's PDE book 2nd edition chapter 10

There is one yacht starting at $(x_1,0)$ when $t=0$, which is sailing toward positive direction of $x$-axis with a constant velocity $b_1$, another yacht is starting at $(0,x_2)$ when $t=0$, and is ...