Convex Relaxations for Nonlinear Stochastic Optimal Control Problems

摘要

This article presents a new method for computing guaranteed convex andconcave relaxations of nonlinear stochastic optimal control problems withfinal-time expected-value cost functions. This method is motivated by similarmethods for deterministic optimal control problems, which have beensuccessfully applied within spatial branch-and-bound (B&B) techniques to obtainguaranteed global optima. Relative to those methods, a key challenge here isthat the expected-value cost function cannot be expressed analytically inclosed form. Nonetheless, the presented relaxations provide rigorous lower andupper bounds on the optimal objective value with no sample-based approximationerror. In principle, this enables the use of spatial B&B global optimizationtechniques, but we leave the details of such an algorithm for future work.