The inherently nonlinear, large-scale, and time-varying nature of district heating systems pose significant challenges from a control perspective. In this paper, we address these challenges by applying an economic MPC. Economic MPC is a dynamic real-time optimization method, enabling both optimal planning and stability of the closed-loop system. Our strategy constitutes several steps. First, we introduce a discrete-time modular framework for the district heating system, establishing its strict dissipativity with respect to a desired, potentially time-varying, equilibrium. We identify a set of meaningful objective functions for the district heating systems, preserving this property. Second, we show how strict dissipativity implies the turnpike property, which, in turn, guarantees approximate optimality, practical stability, and recursive feasibility for the EMPC closed-loop. Finally, we provide numerical simulations to demonstrate the effectiveness of our work.

Proper monitoring of large complex spatially critical infrastructures often requires a sensor network capable of inferring the state of the system. Such networks enable the design of distributed estimators considering only local (partial) measurements, local communication capabilities with nearby sensors, as well as the system model. Solutions often assume perfect knowledge of the system model, and white process and measurement noise, which are limiting in engineering settings. In this paper, we consider the minimum energy setting where the model uncertainty and process and measurement noises are bounded but unknown. We provide the first distributed minimum energy estimator for discrete-time linear time-invariant systems, and we show that the error dynamics is input-to-state stable. Lastly, we illustrate the performance in some pedagogical examples, and compare the performance with respect to the centralized implementation of the minimum energy estimator.

In this paper, we introduce a novel model selection approach to time series forecasting. For linear stationary processes, such as AR processes, the direction of time is independent of the model parameters. By combining theoretical principles of time-reversibility in time series with conventional modeling approaches such as information criteria, we construct a criterion that employs the backwards prediction (backcast) as a proxy for the forecast. Hereby, we aim to adopt a theoretically grounded, data-driven approach to model selection. The novel criterion is named the backwards validated information criterion (BVIC). The BVIC identifies suitable models by trading off a measure of goodness-of-fit and a models ability to predict backwards. We test the performance of the BVIC by conducting experiments on synthetic and real data. In each experiment, the BVIC is examined in contrast to conventionally employed criteria. Our experimental results suggest that the BVIC has comparable performance as conventional information criteria. Specifically, in most of the experiments performed, we did not find statistically significant differences between the forecast error of the BVIC under certain parameterizations and that of the different information criteria. Nonetheless, it is worth emphasizing that the BVIC guarantees are established by design where the model order penalization term depends on strong mathematical properties of time-reversible time series forecasting properties and a finite data assessment. In particular, the penalization term is replaced by a weighted trade-off between functional dimensions pertaining to forecasting.That said, we observed that the BVIC recovered more accurately the real order of the underlying process than the other criteria, which rely on a static penalization of the model order. Lastly, leveraging the latter property we perform the assessment of the order model (or, memory) of time series pertaining to epileptic seizures recorded using electrocorticographic data. Our results provide converging evidence that the order of the model increases during the epileptic events.