Performance-Guaranteed Reference Tracking With Power Directionality Constraints: Application to Controlled Stochastic Watersheds

Abstract

Modern stormwater infrastructure faces increased demands that require a corresponding increase in capacity. Traditionally, these demands have been met by constructing new infrastructure assets, which is a costly endeavor. More recently, many system operators have achieved great success in employing feedback control techniques to improve system performance. However, the resulting closed-loop system exhibits power directionality constraints that introduce nonlinear constraints in feedback synthesis. In this work, we develop a stochastic control synthesis procedure with provable performance bounds on mean-square reference tracking for a general class of problems in which power directionality constraints arise. The proposed method is then applied to a flood mitigation example using a numerical model of a real-world smart water system. The key result is an extension of the performance-guaranteed control (PGC) framework, which was originally designed for disturbance rejection, to accommodate reference tracking control objectives.