Split-Bernstein Approach to Chance-Constrained Optimal Control

In this paper, a semianalytical parametric approximation of chance constraints, called the split-Bernstein approximation, is employed to construct a framework for posing and solving chance-constrained optimal control problems. Dynamic systems with deterministic as well as stochastically perturbed dynamics are considered. In both cases, the chance-constrained optimal control problem is converted into a chance-constrained program, which is transcribed to a nonlinear program using the split-Bernstein approximation. Discretization of deterministic optimal control problems is performed via pseudospectral collocation. For systems perturbed by white noise, a shooting method is used that imposes dynamic constraints implicitly via ensemble propagation. The split-Bernstein approximation of chance constraints allows the solution of the resulting nonlinear program using off-the-shelf gradient-based nonlinear program solvers.