  In this paper, the CONFIG algorithm, a simple and provably efficient
constrained global optimization algorithm, is applied to optimize the
closed-loop control performance of an unknown system with unmodeled
constraints. Existing Gaussian process based closed-loop optimization methods,
either can only guarantee local convergence (e.g., SafeOPT), or have no known
optimality guarantee (e.g., constrained expected improvement) at all, whereas
the recently introduced CONFIG algorithm has been proven to enjoy a theoretical
global optimality guarantee. In this study, we demonstrate the effectiveness of
CONFIG algorithm in the applications. The algorithm is first applied to an
artificial numerical benchmark problem to corroborate its effectiveness. It is
then applied to a classical constrained steady-state optimization problem of a
continuous stirred-tank reactor. Simulation results show that our CONFIG
algorithm can achieve performance competitive with the popular CEI (Constrained
Expected Improvement) algorithm, which has no known optimality guarantee. As
such, the CONFIG algorithm offers a new tool, with both a provable global
optimality guarantee and competitive empirical performance, to optimize the
closed-loop control performance for a system with soft unmodeled constraints.
Last, but not least, the open-source code is available as a python package to
facilitate future applications.
