Compositional Control Synthesis for Water Management System

The increased frequency and severity of ex-treme weather events are challenging traditional static control strategies for stormwater detention ponds, which are critical components in urban water management infrastructures. This paper introduces a compositional control methodology, rooted in formal verification and reinforcement learning, and tailored for the synthesis of a joint optimal control strategy for the management of distributed but interconnected ponds. Combining hybrid Markov Decision Processes (HMDPs) and reinforcement learning via Uppaal Stratego, the compositional control strategy provides a balance between fully centralized and decentralized control strategies, both in terms of quality and computational complexity. Based on a real-world case study we analyze and compare the proposed methodology and show how the synthesized strategies can control the timing and volume of water discharge, reducing the risk of overflow caused by the simultaneous discharge of rainwater collected in multiple ponds.

I. Introduction

Complex Cyber-Physical Systems (CPSs) integrate computational and physical processes, making their manage-ment and control intricate [1]. For hybrid systems, controller synthesis is further complicated by the coexistence of con-tinuous and discrete dynamics [2]. Traditional centralized controllers are becoming increasingly complex and ineffi-cient for such advanced CPS architectures. This underscores the pressing need for innovative approaches that address the nuanced challenges posed by CPSs and hybrid system's controller design while bypassing the inefficiencies inherent in centralized control methods.