Optimal Control Approach for Sedimentation Control in Alluvial Rivers

Abstract

A new methodology is developed for determining optimal reservoir releases to minimize the downstream adverse effects in alluvial rivers. The methodology is based on describing the problem as a discrete-time optimal control problem. The solution methodology is based on a differential dynamic programming approach that uses the U.S. Army Corps of Engineers HEC-6 sediment simulation model for the transition equation. The objective of the model is to determine the release policy of an upstream reservoir that minimizes the bed aggradation and degradation along the downstream river. The constrained discrete-time optimal-control problem is transformed into an unconstrained problem using a hyperbolic penalty function that incorporates the bound constraints and the boundary condition into the loss function. Two application examples were used to demonstrate the capability of the model: These include (1) a hypothetical reservoir-river system; and (2) the New Waddell Dam and the Agua Fria River in Maricopa County, Arizona.