459 - Provably Safe Dual-mode Controller for a Stormwater Software Model Using a Linear, Time-invariant System Approximation

Autonomous control of stormwater infrastructure via wireless pumps and valves entails a fundamental tradeoff between flood prevention and runoff treatment. To prevent flooding, water should be controlled to exit the system as rapidly as possible. To enhance receiving body water quality, however, water should generally be retained as long as possible to allow for sedimentation and biological removal. Given this tradeoff, a controller with multiple modes is desirable, but present research has focused on single modes. A dual-mode or hybrid controller will optimize water quality whenever the system is not at risk of flooding and switch to flood prevention during extreme precipitation.
When to switch between these modes is a critical question that determines the tradeoff of safety from flooding and stormwater treatment performance. One of the formal tools within control systems theory for addressing this safety and performance tradeoff is barrier certificates, which are functions that split a space into safe and unsafe regions. By developing a bound on the system approximation error of the controller, we synthesize a barrier certificate guaranteeing flooding never occurs given some bound on the precipitation intensity. Additionally, we define a barrier certificate guaranteeing that flooding never occurs in the controlled system when it would not occur in the uncontrolled system. Our results show both enhanced treatment during mild weather and reduced flooding during extreme precipitation.
This work shows how to design more flexible controllers and reduce barriers to adoption by formally verifying that control strategies operate safely.