A Scenario-Based Stochastic MPC Approach for Problems with Normal and Rare Operations with an Application to Rivers

This paper formulates a control problem for systems that are affected by uncertain inputs and are vulnerable to risks as a chance-constrained optimization problem (CCP) with two chance-constraints (CCs). The first CC encompasses requirements of the normal operations of the system, whereas the second CC ensures the avoidance of risks associated with rare events. CCPs are in general difficult to solve, and this paper proposes a scenario-based optimization, testing, and improving algorithm to find approximate solutions to such problems within a stochastic model predictive control setting in a computationally cheap manner. The proposed approach is applied to a river control problem with flood avoidance, and the controller performed well in realistic simulations of the upper part of Murray River in Australia.