A novel approach to chance constrained optimal control problems

This paper presents a new unified framework based on the split-Bernstein approximation and the Legendre-Gauss-Radau (LGR) collocation method for solving optimal control problem under chance constraints. First, the LGR collocation method is employed to transcribe the chance constrained optimal control problem into a nonlinear chance constrained program. Then, the split-Bernstein approximation along with Markov chain Monte Carlo (MCMC) is employed to approximate the chance constraints using a near-optimal deterministic upper bound, transforming the problem into a deterministic nonlinear program (NLP). Finally, the NLP is solved using standard solvers such as SNOPT
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. Numerical examples are presented to illustrate the new framework.