I'm interested in using linear quadratic regulators (LQR) to model prey avoidance behaviors. I want to adapt the LQR algorithm to incorporate dynamics and state costs that maximize the distance from a fixed point (instead of minimize the distance; 'repulsion' instead of 'attraction'), eg like the prey maximizing the distance from a predator or the predator predicting the trajectory of the prey.
This might only work in a subset of cases (eg with something like trace(Q) > 0; or with some kind of state-dependent trajectory tracking). I'm interested in whether LQR can do this at all, or whether I'll have to add non-linearities (and the tractability of these non-linearities).