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Backward state trajectories given by a continuous backward flow: mathematical definition
$begingroup$
Consider the following nonlinear system described by:
$$dot{x}(t)=f(x(t),u(t)),$$
subjected to a constant input that we can describe as:
$$dot{u}(t)=0.$$
It is stated as hypothesis that the system above is assumed to have well-defined backward state trajectories, given by a continuous backward flow.
Now, apart from the intuitive meaning of the previous statement, I was wondering which could be a formal mathematical definition. Any suggestions?
ordinary-differential-equations dynamical-systems nonlinear-system
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
$endgroup$
add a comment |
$begingroup$
Consider the following nonlinear system described by:
$$dot{x}(t)=f(x(t),u(t)),$$
subjected to a constant input that we can describe as:
$$dot{u}(t)=0.$$
It is stated as hypothesis that the system above is assumed to have well-defined backward state trajectories, given by a continuous backward flow.
Now, apart from the intuitive meaning of the previous statement, I was wondering which could be a formal mathematical definition. Any suggestions?
ordinary-differential-equations dynamical-systems nonlinear-system
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
$endgroup$
2
$begingroup$
Consider the solution of $dot y=-f(y,u_0)$ such that $y(0)=x_0$.
$endgroup$
– Did
Jan 28 at 21:28
add a comment |
$begingroup$
Consider the following nonlinear system described by:
$$dot{x}(t)=f(x(t),u(t)),$$
subjected to a constant input that we can describe as:
$$dot{u}(t)=0.$$
It is stated as hypothesis that the system above is assumed to have well-defined backward state trajectories, given by a continuous backward flow.
Now, apart from the intuitive meaning of the previous statement, I was wondering which could be a formal mathematical definition. Any suggestions?
ordinary-differential-equations dynamical-systems nonlinear-system
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
$endgroup$
Consider the following nonlinear system described by:
$$dot{x}(t)=f(x(t),u(t)),$$
subjected to a constant input that we can describe as:
$$dot{u}(t)=0.$$
It is stated as hypothesis that the system above is assumed to have well-defined backward state trajectories, given by a continuous backward flow.
Now, apart from the intuitive meaning of the previous statement, I was wondering which could be a formal mathematical definition. Any suggestions?
ordinary-differential-equations dynamical-systems nonlinear-system
ordinary-differential-equations dynamical-systems nonlinear-system
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
asked Jan 24 at 8:28
giovanni_13giovanni_13
757
757
2
$begingroup$
Consider the solution of $dot y=-f(y,u_0)$ such that $y(0)=x_0$.
$endgroup$
– Did
Jan 28 at 21:28
add a comment |
2
$begingroup$
Consider the solution of $dot y=-f(y,u_0)$ such that $y(0)=x_0$.
$endgroup$
– Did
Jan 28 at 21:28
2
2
$begingroup$
Consider the solution of $dot y=-f(y,u_0)$ such that $y(0)=x_0$.
$endgroup$
– Did
Jan 28 at 21:28
$begingroup$
Consider the solution of $dot y=-f(y,u_0)$ such that $y(0)=x_0$.
$endgroup$
– Did
Jan 28 at 21:28
add a comment |
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$begingroup$
Consider the solution of $dot y=-f(y,u_0)$ such that $y(0)=x_0$.
$endgroup$
– Did
Jan 28 at 21:28