This work proposes an algorithm for seeking generalized feedback Nash equilibria (GFNEs) in noncooperative dynamic games. The focus is on cyber-physical systems with dynamics that are linear, stochastic, potentially unstable, and partially observed. We employ system-level synthesis (SLS) to reformulate the problem as the search for an equilibrium profile of closed-loop responses to noise, which can then be used to reconstruct a stabilizing output-feedback policy. Under this setup, we leverage monotone operator theory to design a GFNE-seeking algorithm capable of enforcing closed-loop stability, operational constraints, and communication constraints onto the control policies. This algorithm is amenable to numerical implementation, and we provide conditions for its convergence. We demonstrate our approach in a simulated experiment on the noncooperative stabilization of a decentralized power grid.

In system monitoring, automatic fault diagnosis seeks to infer the systems' state based on sensor readings, e.g., through machine learning models. In this context, it is of key importance that, based on historical data, these systems are able to generalize to incoming data. In parallel, many factors may induce changes in the data probability distribution, hindering the possibility of such models to generalize. In this sense, domain adaptation is an important framework for adapting models to different probability distributions. In this paper, we propose a new benchmark, based on the Tennessee Eastman Process of Downs and Vogel (1993), for benchmarking domain adaptation methods in the context of chemical processes. Besides describing the process, and its relevance for domain adaptation, we describe a series of data processing steps for reproducing our benchmark. We then test 11 domain adaptation strategies on this novel benchmark, showing that optimal transport-based techniques outperform other strategies.

This work proposes an automatic control solution for the operation of conventional wastewater treatment plants (WWTPs) as energy-autonomous water resource recovery facilities. We first conceptualize a classification of the quality of treated water for three resource recovery applications (environmental, industrial, and agricultural water reuse). We then present an output-feedback model predictive controller (Output MPC) that operates a plant to produce water of specific quality class, while also producing sufficient biogas to ensure nonpositive energy costs. The controller is demonstrated in the long-term operation of a full-scale WWTP subjected to typical influent loads and periodically changing quality targets. Our results provide a proof-of-concept on the energy-autonomous operation of existing wastewater treatment infrastructure with control strategies that are general enough to accommodate a wide range of resource recovery objectives.

This work proposes a policy learning algorithm for seeking generalised feedback Nash equilibria (GFNE) in N_P-player noncooperative dynamic games. We consider linear-quadratic games with stochastic dynamics and design a best-response dynamics in which players update and broadcast a parametrisation of their state-feedback policies. Our approach leverages the System Level Synthesis (SLS) framework to formulate each player's update rule as the solution to a robust optimisation problem. Under certain conditions, rates of convergence to a feedback Nash equilibrium can be established. The algorithm is showcased in exemplary problems ranging from the decentralised control of unstable systems to competition in oligopolistic markets.

Digital twin models offer great potential for process improvements in wastewater treatment plants (WWTPs). Such models require a constant real-time input data feed from the physical process. Collecting these data is challenging, especially in the harsh conditions in the headworks of the process. In this study, data-driven models and process and sewer system expertise were combined to design soft-sensors for primary effluent COD and NH4-N prediction. Ordinary least squares regression and the seasonal autoregressive integrated moving average model with exogenous variables were tested using flow rate and suspended solids concentration as model input. An excellent NH4-N prediction was achieved, and the prediction accuracy was further improved by implementing process-insight-driven weights. The tested models were able to achieve either good COD estimation accuracy or effectively capture the variability in the target data. However, achieving both simultaneously remained challenging, with or without weights. Simulation tests using the calibrated process model demonstrated that the developed soft-sensors were able to provide real-time predictions leading to goodness-of-fit in simulations comparable to or better than that achieved using laboratory data influent quality.

In the context of the recent water crisis, the development and improvement of technologies for efficiently treating wastewater becomes increasingly necessary. Aligned with this, the activated sludge process is widely used in biological wastewater treatment plants to remove carbon and nutrients from wastewater. Although significant advancements have been achieved in recent years in modelling these processes to improve their performance and energy efficiency, the models are still complex and difficult to calibrate using data from real plants. In this work, we use Bayesian inference frameworks to estimate the parameters of the activated sludge process. We employ Gaussian processes to estimate the solution to the differential equations of the activated sludge process model and we fit this estimation to manufactured data of the observations of the wastewater. We find that the use of the Bayesian inference framework outperforms the classical approach in scenarios where measurements are more strongly affected by noise.

This work presents a general framework for the advanced control of a common class of activated sludge plants (ASPs). Based on a dynamic model of the process and plant sensors and actuators, we design and configure a highly customisable Output Model-Predictive Controller (Output MPC) for the flexible operation of ASPs as water resource recovery facilities. The controller consists of a i) Moving-Horizon Estimator for determining the state of the process, from plant measurements, and ii) a Model-Predictive Controller for determining the optimal actions to attain high-level operational goals. The Output MPC can be configured to satisfy the technological limits of the plant equipment, as well as operational desiderata defined by plant personnel. We consider exemplary problems and show that the framework is able to control ASPs for tasks of practical relevance, ranging from wastewater treatment subject to normative limits, to the production of an effluent with varying nitrogen content, and energy recovery.

This chapter provides a comprehensive overview of the main steps for algorithmic sensor signal quality assessment, which can enhance the decision-making process for water resource recovery facility (WRRF) operation and optimization. It introduces the concept of redundancy as the basis for data quality assessment. It also explains the typical data processing pipeline, which consists of preliminary analysis, data pre-processing, and specific algorithmic approaches. Each of these processes is presented and discussed in three separate sections. Importantly, this chapter introduces the main approaches for data quality assessment, provides guidelines for selecting the most suitable one and the key performance indicators to evaluate them and explains how to collect metadata through such an algorithmic approach.

Adequate housing protects from diarrhea, which is a substantial health concern in low-and middle-income countries. The purpose of this study was to quantify the relationship between severe diarrhea and housing features at the municipal level to help in public health planning. Regression analyses were performed on annual (2000-2012) datasets on Brazilian municipalities (5570) in six household feature categories (e.g., waste management) and four severe diarrhea outcomes (e.g., diarrhea deaths of under-5 children). Household data were not available elsewhere of this magnitude and granularity, high-lighting the scientific value-add of this study. Municipalities were clustered prior to regression analysis because of data heterogeneity. The compositional household feature data were also subjected to principal component analysis to diminish feature variable multicollinearity. The highest explanatory power was found for diarrhea deaths of under-5 children (R2 = 10-22 %), while those in the over-5 population were the least best explained (R2 = 0.3-7 %). Household features predicted diarrhea outcomes more accurately in the "advanced" housing municipality cluster (R2 = 16-22 %) than in the "mid-level" (R2 = 7-20 %) and "basic" (R2 = 6-12 %) ones (over-5 diarrhea deaths excluded). Under-5 children's diarrhea death prevalence was three times higher in the "basic" cluster than in the "advanced" cluster. Importantly, the impact of waste management was overall the largest of all household features, even larger than those of WASH, i.e., water supply, sanitation, and household drinking water treatment. This is surprising in the context of existing literature because WASH is generally regarded as the most important household factor affecting gastrointestinal health. In conclusion, public health interventions could benefit from customizing interventions for diarrhea outcomes, municipality types, and household features. Waste management's identified stronger association with diarrhea compared to WASH may have important implications beyond the water field and Brazil.

Fault diagnosis is an essential component in process supervision. Indeed, it determines which kind of fault has occurred, given that it has been previously detected, allowing for appropriate intervention. Automatic fault diagnosis systems use machine learning for predicting the fault type from sensor readings. Nonetheless, these models are sensible to changes in the data distributions, which may be caused by changes in the monitored process, such as changes in the mode of operation. This scenario is known as Cross-Domain Fault Diagnosis (CDFD). We provide an extensive comparison of single and multi-source unsupervised domain adaptation (SSDA and MSDA respectively) algorithms for CDFD. We study these methods in the context of the Tennessee-Eastmann Process, a widely used benchmark in the chemical industry. We show that using multiple domains during training has a positive effect, even when no adaptation is employed. As such, the MSDA baseline improves over the SSDA baseline classification accuracy by 23% on average. In addition, under the multiple-sources scenario, we improve classification accuracy of the no adaptation setting by 8.4% on average.

: This paper presents a systemic viewpoint making use of modeling and control tools to promote the flexibility of a water reuse chain and dynamically adapt the quality of treated waters to plant needs, notably using output feedbacks. The proposed approach is developed within the framework of the European Control4Reuse project dedicated to the development of an integrated approach for improving water and nutrient recycling in agronomy. Within this framework, the notion of flexibility of treatment systems for reuse is developed together with its evaluation using a dedicated simulation platform.

To protect human health and natural ecosystems, wastewater treatment plants (WWTPs) have been traditionally designed to remove pollutants from wastewater. With remarkable success WWTPs have adapted to increasingly stringent discharge limits over the years. Nowadays, municipal wastewater treatment facilities are facing a double transition. On the one hand, the transition towards sustainability and the circular water economy, in which resource recovery from wastewater (water recovery, energy recovery and nutrient recovery) plays a fundamental role for its effective implementation. Note that the incorporation of any resource recovery process in a WWTP will immediately turn it into a water resource recovery facility (WRRF). On the other hand, the digital transition, which aims at making the operation of these facilities smart and that undoubtedly could have a synergistic effect together with the paradigm shift towards the effective implementation of circular water economy. To make our current facilities smart, there is a growing interest in finding the way to convert the collected process data into intelligent actions for improving their operation. This is not an easy task for many reasons: - the harsh environment in which the instrumentation has to work (corrosive, sludgy, biofilm formation with biological activity…), - almost complete absence of metadata that would make it easy the interpretation of the process data that it is being collected and that would enable its future use, - the almost complete absence of automated data quality assurance, required to avoid “garbage in – garbage out”- the ever-increasing number of process sensors available (data overload), that must be properly processed and made easily available for further use to make them useful- large amounts of data are collected and stored in databases but not wisely used, thus, resulting in data graveyards, - the excessive cost of nutrient and organic matter sensors/analysers which moreover are labour maintenance intensive, fact that restrict their availability to the range of large facilities, thus, they are not usually available for small size facilities (which are the vast majority). - the intelligent sensors and data-driven models must be maintainable by the plant workers (not by Data scientists), - the lack of process expertise in the development of the artificial intelligent tools, - plant operators are often accustomed to their operational routines and, therefore, cultural change is needed in the organization for successful digital transition and adopting new intelligent tools. The progress in computing capabilities together with the large amount of collected process data in WWTPs have created the perfect storm for the machine learning boom we are observing, but all the aforementioned issues can make the incredible digital transition opportunity that exists today completely lost. In an attempt to avoid this disaster, this paper tries to shed light on the path towards increasing the value of the large amount of data that nowadays are being collected in WWTPs and WWRFs. Thus, digital transition could be safely embraced and the enormous potential of data analytics fully exploited, enabling it to play an essential role in the future automation and operation of our municipal facilities.

In this work, we design an output predictive controller that operates a common class of activated sludge plants. The controller solves a state-feedback model predictive control problem in which the process state and disturbances are determined by a moving horizon estimator. We illustrate the behaviour of the controller when operating the plant to produce an effluent water of varying nitrogen content. The close tracking of the effluent profiles is enforced by stabilizing the system around optimal steady-state points that satisfy the output reference trajectories. Considering the generality of the formulation, the predictive controller can be configured to operate this class of activated sludge plants to achieve alternative objectives.

Fault diagnosis is a key task for developing safer control systems, especially in chemical plants. Nonetheless, acquiring good labeled fault data involves sampling from dangerous system conditions. A possible workaround to this limitation is to use simulation data for training data-driven fault diagnosis systems. However, due to modelling errors or unknown factors, simulation data may differ in distribution from real-world data. This setting is known as cross-domain fault diagnosis (CDFD). We use optimal transport for: (i) exploring how modelling errors relate to the distance between simulation (source) and real-world (target) data distributions, and (ii) matching source and target distributions through the framework of optimal transport for domain adaptation (OTDA), resulting in new training data that follows the target distribution. Comparisons show that OTDA outperforms other CDFD methods.

In this work, the stability, controllability and observability properties of a class of activated sludge plants are analysed. Specifically, the five biological reactors and the secondary settler in the Benchmark Simulation Model no. 1 (BSM1) are studied. For the task, we represented the plant as a dynamical system consisting of 145 state variables, 13 controls, 14 disturbances and 15 outputs and as a complex networks to study its full-state controllability and observability properties from a structural and a classical point of view. By analysing the topology of the network, we show how this class of systems is controllable but not observable in a structural sense, and thus how it is controllable but not observable in a classical sense for almost all possible realisations. We also show how a linearisation commonly used in the literature is neither full-state controllable nor full-state observable in the classical sense. The control and observation efforts are quantified in terms of energy- and centrality-based based metrics.

We report the preliminary results of a feasibility study in which we investigate the possibility to operate a common class of activated sludge plants to produce effluent wastewater of varying quality for crop irrigation. Firstly, a nitrogen reference trajectory is computed as solution to a higher-level optimal control problem that aims at maximizing plant biomass in a crop growth system. We then study how to control the treatment plant with a zero-offset predictive control strategy designed to operate the treatment process to supply nitrogen according to this optimal planning for crop growth. We show how an ad hoc tuning of the predictive controller allows to define alternative policies that favour the manipulation of different forms of nitrogen in the treatment plant. We show that the designed controllers are only partially capable to operate the treatment plant to meet the nitrogen demand, when subjected to typical municipal wastewater influent conditions. However, zero-offset can be achieved under constant influent conditions. We analyse the performance of the controller in terms of tracking accuracy and operational energy.

Energy costs in the wastewater industry are increasing due to increasing trends in electricity rates and more stringent requirements for effluent quality. Wastewater aeration process is typically the largest energy consumer of the treatment plant and the optimization of the aeration process can offer significant savings for the wastewater treatment plants (WWTPs). Utilization of dynamic models can offer optimization solutions for improving the energy efficiency and process performance. In this work a simplified modelling approach emphasizing the control valves and the blowers is tested by developing aeration system models for two Finnish WWTPs. The developed model requires calibration of only a single parameter and the results from the simulations showed that reasonable estimations of the aeration systems energy demand could be made with a limited knowledge on the details of the physical system. The promising results highlight the strong influence of the control valve positioning to the whole system and indicate that airflow distribution along the system could be estimated simply from the positioning of the valves. The presented modelling approach allows the comparison between different blower and control valve alternatives during operation and for the process upgrades and offers prospect for improving the aeration operation control strategies.

In 3D reconstruction applications, matching between corresponding point clouds is commonly resolved using variants of the Iterative Closest Point (ICP). However, ICP and its variants suffer from some limitations, functioning properly only for some contexts with well-behaved data distribution; outdoor scene, for example, poses many challenges. Indeed, the literature has suggested that the ability of some of these algorithms to find a match was reduced by the presence of geometric disorder in the scene, for example. This article presents a method based on the characterization of the eigentropy and omnivariance properties of clouds to indicate which variant of the ICP is best suited for each context considered here, namely, object or outdoor scene alignment. In addition to the context selector, we suggest a partitioning step prior to alignment, which in most cases allows for reduced computational cost. In summary, the proposal as a whole worked satisfactorily to the alignment as a multipurpose registration technique, serving to pose correction of data from different contexts and thus being useful for computer vision and robotics applications.

In this work a model-based controller for a fermentation bioreactor has been developed. By simulating the model of the process that acts as a virtual plant, input-output data have been generated and used to identify the system using sparse identification of nonlinear dynamics methodology. The obtained model is then used in a model-based algorithm to control the bioreactor temperature, where the manipulated action is obtained as a result of a constrained nonlinear optimization problem which minimizes the mismatch between the predicted trajectory and the desired one. Good performances have been obtained by applying the proposed control strategy for set-point changes and disturbance rejection.

In this work, the full-state observability properties of a class of biological wastewater treatment plants are analysed. Specifically, the five biological reactors and the secondary settler in the Benchmark Simulation Model no. 1 are studied. For the task, we represented the activated sludge plant as a dynamical system consisting of 145 states, 8 controls, 14 disturbances and 12 outputs and as a complex network to study its observability properties from a structural and a classical point of view. By analysing the topology of the network, we show how the system is not observable in the structural sense and thus how it is also not observable in the classical sense for all possible realisations of its parameters. As this is also true for a linearisation commonly used in the literature, we analysed a reduced-order system that, based on such linearisation, does not consider the state variables corresponding to dissolved oxygen and alkalinity in the upper-layers of the settler. We show how this system configuration is only observable in a structural sense.