Risk-Averse Optimal Control Model Under Uncertainty and Its Modified Progressive Hedging Algorithm

It is of practical importance to incorporate a risk-averse objective in an optimal control problem under uncertainty. By leveraging the dual relationship between risk and regret measures, the risk-averse optimal control problem can be equivalently transformed into an optimal control problem with nonanticipativity constraints and expectation objective function. A modified progressive hedging algorithm is then proposed to solve the transformed problem, in which the descent conditions are enforced to ensure global convergence of the algorithm. Numerical results of three different types of problems are presented to show the applicability and effectiveness of the modified progressive hedging algorithm.