  The optimal control problem of connecting any two trajectories in a behavior
B with maximal persistence of that behavior is put forth and a compact solution
is obtained for a general class of behaviors. The behavior B is understood in
the context of Willems's behavioral theory and its representation is given by
the kernel of some operator. In general the solution to the problem will not
lie in the same behavior and so a maximally persistent solution is defined as
one that will be as close as possible to the behavior. A vast number of
behaviors can be treated in this framework such as stationary solutions, limit
cycles etc. The problem is linked to the ideas of controllability presented by
Willems. It draws its roots from quasi-static transitions in thermodynamics and
bears connections to morphing theory. The problem has practical applications in
finite time thermodynamics, deployment of tensigrity structures and legged
locomotion.
