Optimal Control of Unsteady Combined Sewer Flow

A particularly challenging problem is the development of appropriate optimal control logic for adjustable valves, gates and regulators that includes consideration of unsteady sewer flows and backwater effects. Dynamic programming appears to be a particularly attractive optimization approach, but the multidimensional character of the control problem creates an enormous computational burden. A new dynamic programming algorithm is presented which utilizes orthogonal polynomials to decompose the multidimensional problem into a series of one-dimensional problems. The algorithm is linked with an unsteady flow model which is solved numerically by a fully implicit scheme that uses an interrupted double sweep technique to deal with supercritical flow, abrupt conduit transitions, and control gate linearization errors. The algorithm is applied to the planned San Francisco North Shore Outfalls Consolidation Project.