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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).

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  • $\begingroup$ do you have an idea of what your states are going to look like, or some kind of statespacemodel? $\endgroup$ – morbo Mar 31 '20 at 22:39
  • $\begingroup$ I'd recon that MPC is the better choice here, because you have so much more freedom in the formulation of constraints and cost functions, while LQR has only one cost function for which it is defined $\endgroup$ – OpticalResonator Apr 1 '20 at 8:48
  • $\begingroup$ @ morbo, the state space isn't specified, but you could imagine it's something like the position & velocity of a predator & prey agent (eg with prey under control, and the predator attracted towards the prey). But -- if there are other representations that make this easier, then so much the better. @ OpticalResonator that sounds promising, but I'd love to avoid dynamic programming, to keep it feasible that animals are using a given solution. Looks like there is a little bit on explicit MPC, but these seems to look like LQR (any recommendations would be welcome!!) $\endgroup$ – hritz Apr 1 '20 at 16:39

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