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

•A formal approach is presented to synthesize controller for Barcelona wastewater system.•We employ signal temporal logic to express the desired closed-loop behavior.•We use robust MPC strategy to incorporate the new measurements in the optimization.•The optimization is transformed to non-convex MIQP and solved iteratively.•The approach is applied to a catchment of Barcelona wastewater system with 12 tanks. 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.