Formal controller synthesis for wastewater systems with signal temporal logic constraints: The Barcelona case study

Abstract

We present an approach for formal controller synthesis of the Barcelona wastewater system. The goal of the controller is to minimize overflow in the system and to reduce environmental contamination (pollution). Due to the influence of sudden and unpredictable weather changes within the Mediterranean climate, we propose robust model predictive control strategy. This approach synthesizes control inputs (i.e., flows through network actuators) that make the system robust to uncertainties in the weather forecast; control inputs are updated in an online fashion to incorporate the newly available measurements from the system and the disturbances. We employ signal temporal logic as a formal mechanism to express the desired behavior of the system. The quantitative semantics of the logic is then used to encode the desired behavior in both the set of constraints and the objective function of the optimization problem. We propose a solution approach for the obtained worst-case optimization, which is based on transforming the nonlinear dynamics of the system into a mixed logical dynamical model. Then, we employ Monte Carlo sampling and dual reformulation to get a mixed integer linear or quadratic programming problem. The proposed approach is applied to a catchment of the Barcelona wastewater system to illustrate its effectiveness.

Data-driven verification of stochastic linear systems with signal temporal logic constraints

“…A robust treatment of uncertainties under STL constraints is performed in [14] in the framework of model predictive control. An under-approximation of constraints described as probabilistic STL formulae is proposed in [13] and applied to design control strategies for the Barcelona wastewater system [15].…”

Data-Driven Verification under Signal Temporal Logic Constraints

“…The work in Sadigh and Kapoor (2016) introduces a new definition for the probabilistic STL that assigns probabilities to the atomic propositions and then combines them through Boolean operators. The results in Farahani et al (2018b) utilize probabilistic STL properties to design a control strategy for Barcelona wastewater system. Satisfaction of properties expressed in linear temporal logic on finite traces for linear time-invariant (LTI) systems is investigated in Haesaert et al (2015Haesaert et al ( , 2016 by using Bayesian inference.…”