Approximate Explicit Nonlinear Receding Horizon Control for Decompression of Divers

This paper is based on a comprehensive dynamic mathematical model (Copernicus) of vascular bubble formation and growth during and after decompression from a dive. The model is founded on the statistical correlation between measurable venous gas emboli (VGE) and risk of severe decompression sickness (DCS) where VGE has been shown to be a reliable and sensitive predictor of decompression stress. By using the Copernicus model the diving decompression problem is formulated as a nonlinear optimal control problem, where the objective is to minimize the total ascend time subject to constraints on the maximum bubbles volume in the central venous pool. A recent study reveals that the optimal solution can be obtained by solving the optimization problem with equality constraints. Inspired by which, a simpler approach using barrier function is proposed in this paper, through which we achieve a more efficient and robust numerical implementation. To reduce the complexity of the nonlinear optimization problem this paper also studies the decompression profile parameterization and its effect. Furthermore, by applying multi-parametric nonlinear programming technique, an approximate explicit solution to the nonlinear optimization problem is obtained, which makes the practical implementation on a typical low-cost diving computer possible.