Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 fr all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right).

Find a control function u(t) : [0, infinity) -> R such that (1) l u(t) l smaller than or equal to 2 fr all t in [0, infinity) and (2) u steers \begin{pmatrix}1\\ 1\end{pmatrix} to \begin{pmatrix}0\\ 0\end{pmatrix} where the control system is given by \begin{pmatrix}x\\ y\end{pmatrix}^'=\begin{pmatrix}0&1\\ -1&0\end{pmatrix}\begin{pmatrix}x\\ y\end{pmatrix}+\begin{pmatrix}0\\ 1\end{pmatrix}u\left(t\right).

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter9: Multivariable Calculus

Section9.2: Partial Derivatives

Problem 25E

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