A dynamic game approximation for a linear regulator problem with a log-barrier state constraint

An exact supremum-of-quadratics representation for log-barrier functions is developed for, and subsequently applied in, a state-constrained linear regulator problem. By approximating this representation, it is shown that this regulator problem can be approximated by an unconstrained linear quadratic dynamic game. It is anticipated that this game approximation may facilitate the computation of approximate solutions to such state-constrained regulator problems.

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