Abstract: In this paper we study a bilinear optimal control problem for a diffusive Lotka-Volterra competition model with chemo-repulsion in a bounded domain of $\mathbb{R^N},$ $N=2,3$. This model describes the competition of two species in which one of them avoid encounters with rivals through a chemo-repulsion mechanism. We prove the existence and uniqueness of weak-strong solutions, and then we analyze the existence of a global optimal solution for a related bilinear optimal control problem, where the control is acting on the chemical signal. Posteriorly, we derive first-order optimality conditions for local optimal solutions using the Lagrange multipliers theory. Finally, we propose a discrete approximation scheme of the optimality system based on the gradient method, which is validated with some computational experiments.

Key words: Lotka-Volterra, chemo-repulsion, optimal control, optimality conditions