Publications

Accurate overland runoff and infiltration predictions are critical for effective water resources management, in particular for urban flood management. However, the inherent uncertainty in rainfall patterns, soil properties, and initial conditions makes reliable flood forecasting a challenging task. This paper presents a framework for quantifying the impact of these uncertainties on hydrologic and hydrodynamic simulations via a state space approach based on a differential algebraic equation (DAE) formulation that couples surface and subsurface constraints with the governing dynamics. Under this formulation, the complex interactions between overland flow and infiltration dynamics are captured in realtime. To account for uncertainty in inputs and parameters, the proposed framework quantifies and propagates these uncertainties through the DAE model formulation under partial measurements. The effectiveness of the approach is demonstrated through a series of numerical experiments on synthetic and real world catchments, highlighting its ability to provide probabilistic estimates of watershed state conditions while accounting for uncertainty. An important aspect of the proposed methods is that they are distribution-agnostic, i.e., they only require covariances of uncertainty and not specific types of distributions. The proposed framework is further validated against Monte Carlo (MC) ensemble simulations while providing probabilistic state estimates for measured and unmeasured watershed states under partial gauging.

This letter revisits the classical PBH test through the lens of finite-horizon reachability. By casting state transfer as a minimum energy, primal optimization problem, we show that unreachable state-space maneuvers admit dual infeasibility certificates. These certificates are computable without forming the controllability matrix meaning that uncontrollability can be efficiently certified. We prove that any such certificate is a linear combination of uncontrollable generalized eigenvectors, thereby providing a spectral interpretation without a global eigendecomposition. We also devise algorithms based on Krylov sub-space methods that extract some of the uncontrollable PBH modes from a certificate and demonstrate favorable scaling on large dynamic networks with thousands of nodes.

Network partitioning has gained recent attention as a pathway to enable decentralized operation and control in large-scale systems. This paper addresses the interplay between partitioning, observability, and sensor placement (SP) in dynamic networks. The problem, being computationally intractable at scale, is largely unexplored in the literature. To that end, the paper's objective is designing scalable partitioning of linear systems while maximizing observability metrics of the subsystems. We show that the partitioning problem can be posed as a submodular maximization problem -- and the SP problem can subsequently be solved over the partitioned network. Consequently, theoretical bounds are derived to compare observability metrics of the original network with those of the resulting partitions, highlighting the impact of partitioning on system observability. Case studies on networks of varying sizes corroborate the derived theoretical bounds.

Observability is a key problem in dynamic network sciences. While it has been thoroughly studied for linear systems, observability for nonlinear networks is less intuitive and more cumbersome. One common approach to quantify observability for nonlinear systems is via the Empirical Gramian (Empr-Gram) -- a generalized form of the Gramian of linear systems. In this technical note, we produce three new results. First, we establish that a variational form of nonlinear systems (computed via perturbing initial conditions) yields a so-called Variational Gramian (Var-Gram) that is equivalent to the classic Empr-Gram; the former being easier to compute than the latter. Via Lyapunov exponents derived from Lyapunov's direct method, the technical note's second result derives connections between vintage observability measures and Var-Gram. The third result demonstrates the applicability of these new notions for sensor selection/placement in nonlinear systems. Numerical case studies demonstrate these three developments and their merits.

This paper studies the problem of optimal geographic placement of water quality (WQ) sensors in drinking water distribution networks (WDNs), with a specific focus on chlorine transport, decay, and reaction models. Such models are traditionally used as suitable proxies for WQ. The literature on this topic is indeed inveterate, but has a key limitation: it utilizes simplified single-species decay and reaction models that do not capture WQ transients for nonlinear, multi-species interactions. This results in sensor placements that do not account for nonlinear WQ dynamics. Furthermore, and as WQ simulations are parameterized by hydraulic profiles and demand patterns, the placement of sensors are often hydraulics-dependent. This study produces a simple algorithm that addresses the two aforementioned limitations. The presented algorithm is grounded in nonlinear dynamic system sciences and observability theory, and yields sensor placements that are robust to hydraulic changes. Thorough case studies on benchmark water networks are provided. The key findings provide practical recommendations for WDN operators.

The rapid increase in the integration of intermittent and stochastic renewable energy resources (RER) introduces challenging issues related to power system stability. Interestingly, identifying grid nodes that can best support stochastic loads from RER, has gained recent interest. Methods based on Lyapunov stability are commonly exploited to assess the stability of power networks. These strategies approach quantifying system stability while considering: (i) simplified reduced order power system models that do not model power flow constraints, or (ii) datadriven methods that are prone to measurement noise and hence can inaccurately depict stochastic loads as system instability. In this paper, while considering a nonlinear differential algebraic equation (NL-DAE) model, we introduce a new method for assessing the impact of uncertain renewable power injections on the stability of power system nodes/buses. The identification of stable nodes informs the operator/utility on how renewables injections affect the stability of the grid. The proposed method is based on optimizing metrics equivalent to the Lyapunov spectrum of exponents; its underlying properties result in a computationally efficient and scalable stable node identification algorithm for renewable energy resources allocation. The proposed method is validated on the IEEE 9-bus and 200-bus networks

To provide real-time visibility of physics-based states, phasor measurement units (PMUs) are deployed throughout power networks. PMU data enable real-time grid monitoring and control - and are essential in transitioning to smarter grids. Various considerations are taken into account when determining the geographic, optimal PMU placements (OPPs). This article focuses on the control-theoretic, observability aspect of OPP. A myriad of studies have investigated observability-based formulations to determine the OPP within a transmission network. However, they have mostly adopted a simplified representation of system dynamics, ignored basic algebraic equations that model power flows, disregarded renewables such as solar and wind, and did not model their uncertainty. Consequently, this article revisits the observability-based OPP problem by addressing the literature's limitations. A nonlinear differential algebraic (NDAE) representation of the power system is considered. The system is discretized using various discretization approaches while explicitly accounting for uncertainty. A moving horizon estimation (MHE) approach is explored to reconstruct the joint differential and algebraic initial states of the system, as a gateway to the OPP problem, which is then formulated as a computationally tractable integer program (IP). Comprehensive numerical simulations on standard power networks are conducted to validate different aspects of this approach and test its robustness to various dynamical conditions.

Differential-algebraic equation (DAE) systems arise in power networks, multibody mechanics, and chemical processes, where algebraic constraints couple dynamic and algebraic states. Standard control barrier function (CBF) methods, designed for ordinary differential equations, fail for DAE systems because the algebraic constraints impose compatibility requirements that may render safety filters infeasible. This paper develops a framework for safety-critical control of semi-explicit DAE systems using CBFs that consider compatibility with the algebraic constraints, termed DAE-aware CBFs. We construct projected vector fields on the constraint manifold to account for the hidden dynamics, while ensuring compatibility conditions that keep the algebraic constraints satisfied. We then present sum of squares (SOS) verification conditions that certify both correctness and feasibility of the resulting DAE-aware CBF. The framework is validated on power system case studies.

Control barrier certificates (CBCs) have been extensively studied for ordinary differential equation (ODE) systems, but their extension to differential-algebraic equation (DAE) systems has remained an open problem. This paper presents the first CBCs for DAE systems, addressing safety for both index-1 and higher-index systems. We transform DAE-CBF synthesis into ODE-CBF synthesis with additional compatibility constraints and develop an alternating synthesis framework. We propose an anchored sum-of-squares (SOS) formulation that guarantees geometric correctness on the constraint manifold by construction. This formulation reduces verification to feasibility certification and enables lifting back to the full DAE state space. The approach is validated on a 24-dimensional three-link manipulator, demonstrating safe operation under algebraic constraints.

Discrete-time descriptor systems are systems with dynamics described by difference equations that are subject to algebraic constraints. These constraints make standard state-space control design approaches significantly more challenging. Recent works have designed control barrier certificates (CBCs) to ensure safety of unknown discrete-time systems via data-driven parameterization methods. However, the singular nature of a descriptor system ensures that collected data trajectories will not satisfy the full-row rank condition required for persistence of excitation. Essentially, the data will not be rich enough to replace knowing the full descriptor system. In this work, we derive an algorithmic approach to design a safe control policy online for unknown discrete-time nonlinear descriptor systems, certified by a CBC. We prove that data collected from the subspace described by the algebraic constraints is rich enough to guarantee persistence of excitation. We then demonstrate autonomous takeover, a user (who selects safe input choices until autonomous takeover is ready) passes system control fully to a safe autonomous control strategy, guaranteeing safe behavior for all future time steps. We consider two unstable descriptor systems; an ecological case study and a (trigonometric) constrained inverted pendulum.

This paper studies unreachability screening for power systems, focusing on the inadequate control authority that arises under stressed grid conditions. Its main result is an infeasibility margin for linearized differential algebraic equation models that quantifies how far a prescribed terminal target lies from the reachable set over a fixed time horizon under bounded controller magnitudes. This result follows from a simple theoretical characterization. Building on it, the paper develops a conic benchmark method together with two first order methods based on projected subgradients and bundle updates for scalable repeated screening. Studies on IEEE benchmark systems show that the proposed framework captures the degradation of terminal reachability under stressed operating conditions and tighter actuation limits, while the first order methods remain accurate and substantially faster on large scale systems. Comparisons with standard reachability methods further demonstrate the usefulness and scalability of the proposed infeasibility margins.

Optimal sensing nodes selection (SNS) in dynamic systems is a combinatorial optimization problem that has been thoroughly studied in the recent literature. This problem can be formulated within the context of set optimization. For high-dimensional nonlinear systems, the problem is extremely difficult to solve. It scales poorly too. Current literature poses combinatorial submodular set optimization problems via maximizing observability performance metrics subject to matroid constraints. Such an approach is typically solved using greedy algorithms that require lower computational effort yet often yield sub-optimal solutions. In this paper, we address the SNS problem for nonlinear dynamical networks using a variational form of the system dynamics, that basically perturb the system physics. As a result, we show that the observability performance metrics under such system representation are indeed submodular. The optimal problem is then solved using the multilinear continuous extension. This extension offers a computationally scalable and approximate continuous relaxation with a performance guarantee. The effectiveness of the extended submodular program is studied and compared to greedy algorithms. We demonstrate the proposed set optimization formulation for SNS on nonlinear natural gas combustion networks.

Power grid stability assessment is a classic dynamic system problem which has become paramount with decarbonizing and fleeing dependence on fossil fuels. The relevant literature approaches studying power system stability using: (i) simplified, reduced order models that do not incorporate power flow constraints (and hence decouple generator transients from network topology), (ii) data-driven methods that are prone to measurement noise, (iii) inaccurate depictions of stochastic loads and renewables, (iv) specific metrics that are narrowly applied separately to various system states. This paper produces a fresh perspective—not necessarily superior—on stability assessment and uncertainty propagation by deriving generalizable stability metrics for assessing the impact of uncertain loads and renewables on network buses. The metrics use a purely model-driven nonlinear differential algebraic equation (NL-DAE) model. By generalizable, we mean that the metrics can be applied to various system states including frequencies, angles, and voltages. The proposed metrics are based on quantifying system stability via Lyapunov spectra of Exponents (LEs) of NL-DAEs. The metrics allow the identification of stable nodes, hence informing the operator on how uncertain load perturbations affect grid stability. We produce some case studies to demonstrate how this all works.

The operation and regulation of water distribution networks is a complex procedure aimed at efficiently supplying consumers with sufficient water while ensuring its safe quality. A critical aspect is the direct impact of the network's hydraulics on the dynamics of water quality; the former is typically needed to inform the latter. Previous studies have tackled hydraulic optimization and water quality regulation as separate problems, although they are naturally coupled. While some attempts have been made to couple these problems into a single one, such studies have neglected control-theoretic virtues of the integrated problems. This paper fills this research gap by formulating a pump control problem that accounts for water quality controllability via classic Gramians. This is achieved by integrating water quality controllability metrics into the control problem, the goal is to enhance both water quality regulation and reducing pumping costs. A case study is presented to illustrate that utilizing controllability Gramians leads to an improved overall system performance.

Efficient water quality (WQ) control in distribution networks is pivotal for ensuring the delivery of safe and clean drinking water to consumers. Attaining this goal is complex due to the inherent intricacies of WQ systems, which often pose substantial challenges to achieving full controllability over their dynamics. Controllability, in this context, refers to the ability to effectively steer, regulate, and maintain disinfectant levels within the network to consistently meet the established water health standards. In addition, hydraulic conditions play a crucial role in influencing the level of WQ controllability. Hydraulic settings, including flow rates and directions, pressures, and network components, have a direct impact on how water quality dynamics propagate thereby influencing its controllability. In this study, we explore various metrics that provide both qualitative and quantitative assessments of water quality systems controllability. We examine the applicability of these metrics to the water quality systems taking into consideration network topology, booster stations' locations, and changes in hydraulic settings. By applying a comprehensive framework to various case studies, we assess the performance, practicality, and limitations of these metrics across different network configurations and scenarios. The outcomes of this assessment not only enable water system operators to evaluate the state of system controllability but also provide a pathway for leveraging these metrics to enhance the efficiency and effectiveness of control and regulation strategies.

Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator transients and the algebraic one captures network power flow. While the literature on control and monitoring for ordinary differential equation (ODE) models of power systems is indeed rich, that on DAE systems is not. DAE system theory is less understood in the context of power system dynamics. To that end, this paper presents two new mathematical transformations for nonlinear DAE models that yield nonlinear ODE models while retaining the complete nonlinear DAE structure and algebraic variables. Such transformations make (more accurate) power system DAE models more amenable to a host of control and state estimation algorithms designed for ODE dynamical systems. We showcase that the proposed models are effective, simple, and computationally scalable.

This paper explores the problem of selecting sensor nodes for a general class of nonlinear dynamical networks. In particular, we study the problem by utilizing altered definitions of observability and open-loop lifted observers. The approach is performed by discretizing the system's dynamics using the implicit Runge- Kutta method and by introducing a state-averaged observability measure. The observability measure is computed for a number of perturbed initial states in the vicinity of the system's true initial state. The sensor node selection problem is revealed to retain the submodular and modular properties of the original problem. This allows the problem to be solved efficiently using a greedy algorithm with a guaranteed performance bound while showing an augmented robustness to unknown or uncertain initial conditions. The validity of this approach is numerically demonstrated on a H2/O2 combustion reaction network.

This paper revisits the optimal phasor measurement unit (PMU) placement problem (P3) in transmission networks. We examine P3 from a control-theoretic and dynamic systems perspectives. Relevant prior literature studied this problem through formulations that are based on empirical observability maximization for nonlinear dynamic power system models. While such studies addressed a plethora of challenges, they mostly adopt a simple representation of system dynamics, ignore basic algebraic equations modeling power flows, forgo including renewables and their uncertainty. This paper offers a fresh perspective on this problem by leveraging the observability matrix's modularity property under a moving horizon estimation theoretic. A nonlinear differential algebraic representation of the system is implicitly discretized while explicitly accounting for uncertainty. To that end, the posed challenges are addressed for the optimal P3 via a computationally tractable integer program formulation. The validity of the approach is illustrated on an IEEE 39-bus power system.

Global energy demand has been increasing exponentially in the last three decades, which has been exacerbated by climate change. To alleviate the energy load, researchers have been exploring innovative passive techniques to enhance the thermal performance of building envelopes. This research evaluates a novel building envelope solution, which includes the development of a Concrete Masonry Unit that is integrated with bio-based micro-encapsulated Phase Changing Materials. The mechanical behaviour of the enhanced CMU is investigated to study the applicability of PCMs into the no-slump concrete mix. Compatibility with the applicable standards opens a broader prospect for thermal characterization and building performance simulations of PCM enhanced CMU building envelopes.

Energy consumption is a prominent issue for achieving sustainability within the built environment. A significant portion of the energy consumed is the building's need of hot domestic water, space heating and cooling. Whereby a promising solution for the reduction of fossil fuel energy consumption and its consequent greenhouse gas emissions is the use of solar energy systems. Being an important renewable energy source, façade integration technology such as, building integrated solar thermal (BIST) system enables the use of renewable solar energy within the building envelope. Thus, allowing a high coverage and enhanced energy efficiency under a Mediterranean climate. The façade is the main architectural feature; hence, the collectors cannot be added as a technical element only, aesthetic integration should be satisfactory. BIST systems also affect heat exchange through the building's envelope in particular, when the operational condition is stagnation of water in the pipes. The aim of this paper is to study the impact of utilizing a BIST system on the façade of a building that is under stagnant conditions using a numerical simulation software TRNSYS-18. The model evaluates the performance of a flat plate solar collector (FPSC) by performing a parametric analysis of effective variables such as insulation thickness, angle of inclination, emissivity, and absorptivity. The main goal is to assess indoor air temperatures and wall temperatures of a modular room that represents a Lebanese office building. The prospect of this study is to validate the developed model with experimental data gathered under outdoor conditions for two experimental rooms built, one being the control room and the other room that is equipped with a FPSC.

Lebanon has been encountering an energy crisis for more than two decades and has a large energy supply deficit. Most of energy demand is for space cooling, heating, and domestic hot water heating. A mitigation measure for such use of conventional fossil fuel energy sources is the use of solar energy. Solar thermal collectors allow to harness solar energy for water heating use; however, the usual techniques lead to overcrowding building roofs. Façade integration technology such as, building integrated solar thermal (BIST) system allow the exploitation of the building's large façade for solar heating. Aesthetic incorporation is important, being the façade an architecture feature. Heat exchange through the building's envelope is also affected, particularly in the case when water is stagnant the pipes of the collector. Thus, the aim of this paper is to assess the impact on thermal comfort that arises from using a BIST system on the façade of a building and is under stagnant conditions using a simulation software TRNSYS-18. The model will evaluate the thermal performance of a room with a flat plate thermal collector (FPTC) directly integrated into the south wall and compare it to a control room. The main goal is to assess indoor air / surface temperatures and the thermal comfort parameters according to the Predicted Mean Vote (PMV) model of the room representing a Lebanese office building.

Determinantal point processes (DPPs) are probability models over subsets of a ground set that favor diverse selections while suppressing redundancy. That is, they tend to assign higher likelihood to collections whose elements complement one another instead of repeating the same information. For example, in recommendation systems, a DPP prefers showing users several relevant items that differ in content or style, rather than many near-duplicates of essentially the same item. Although DPPs have been studied extensively in machine learning, random matrix theory, and popularized through components of YouTube's search recommendation system, they have not been considered in the context of dynamic systems; time domain analysis is not a feature of DPPs. This paper establishes interesting connections between DPPs and control theory. By showing that the observability (controllability) Gramian parameterized by sensor (control) node subsets is a DPP, we provide a probabilistic and spectral perspective on sensor (actuator) selection for linear dynamic systems. This notion of probability here does not represent stochastic uncertainty in the system dynamics; it instead represents a likelihood measure over sensor (actuator) configurations induced by the Gramian. To that end, we derive an effective observable rank condition, characterize the balance between individual node contributions and diversity, and establish node inclusion monotonicity and negative dependence properties. Finally, we show that this formulation recovers classical greedy optimization guarantees and admits a maximum a posteriori interpretation of the sensor/actuator node selection problem. Numerical case studies on three network topologies corroborate the theoretical results.

Energy balance models (EBMs) comprise a simplified physical approach to climate modeling relative to more advanced general circulation model (GCM) counterparts. In particular, EBMs simplify numerous radiative features of Earth's surface-atmosphere system through a singular parameterization of albedo which defines the proportion of reflected to total incoming solar radiation. The literature provides some basic albedo models. However, these models are known to be limited in their real-world application. This paper takes a model identification approach to predicting the rate of change in top-of-atmosphere (TOA) albedo given real climate data. First, we design and implement several regression models for the prediction of the rate of change in albedo. Namely, we consider a variety of polynomial and kernel ridge regression (KRR) solutions, comparing these predictors to benchmark functions from the EBM literature. Second, we evaluate these predictors through a series of case studies in which we justify the selection of simulated temporal resolutions. Third, we quantify the performance of individual albedo predictors and test the impact of coupled temperature and albedo updates. Finally, this work finds that KRR with a radial basis function (RBF) kernel can provide a robust predictor of albedo, but requires careful consideration of tuning, spatial resolution, and input feature selection. In short, the paper delivers a thorough assessment of the limitations of albedo model identification and prediction.

This paper presents a comprehensive control-theoretic analysis of water distribution network (WDN) hydraulics. Starting from a general nonlinear differential algebraic equation (DAE) model of WDNs with arbitrary topology and network components (valves and pumps), we investigate three main questions. First, we study local well-posedness of the network dynamics and characterize the loss of differentiability introduced by pump and valve switching. Second, we introduce regularization methods that smooth flow and pressure trajectories under changing controls. Third, we establish error bounds for DAE linearization, local stability, and finite-horizon controllability, and quantify how network-induced parametric uncertainty impacts these properties. We demonstrate that the developed smoothed DAE models produce trajectories closely matching EPANET, a widely used WDN simulator, for various benchmark networks. The case studies also show that the WDN DAE exposes energy dissipation through a weighted Laplacian, ranks pipes by operating point sensitivity, and reveals that aggressive demand variation changes stability and controllability margins without eliminating local stability or pump authority. The developed theoretical foundations enable network analysis, mitigation strategies, and system design.

Differential-algebraic equations (DAEs) arise in power networks, chemical processes, and multibody systems, where algebraic constraints encode physical conservation laws. The safety of such systems is critical, yet safe control is challenging because algebraic constraints restrict allowable state trajectories. Control barrier functions (CBFs) provide computationally efficient safety filters for ordinary differential equation (ODE) systems. However, existing CBF methods are not directly applicable to DAEs due to potential conflicts between the CBF condition and the constraint manifold. This paper introduces DAE-aware CBFs that incorporate the differential-algebraic structure through projected vector fields. We derive conditions that ensure forward invariance of safe sets while preserving algebraic constraints and extend the framework to higher-index DAEs. A systematic verification framework is developed, establishing necessary and sufficient conditions for geometric correctness and feasibility of DAE-aware CBFs. For polynomial systems, sum-of-squares certificates are provided, while for nonpolynomial and neural network candidates, satisfiability modulo theories are used for falsification. The approach is validated on wind turbine and flexible-link manipulator systems.

The operation of water distribution networks is a complex procedure aimed at efficiently delivering consumers with adequate water quantity while ensuring its safe quality. An added challenge is the dependency of the water quality dynamics on the system's hydraulics, which influences the performance of the water quality controller. Prior research has addressed either solving the optimum operational hydraulic setting problem or regulating the water quality dynamics as separate problems. Additionally, there have been efforts to couple these two problems and solve one compact problem resulting in trade-offs between the contradictory objectives. In contrast, this paper takes a novel approach by examining the water quality dependency on the hydraulics from a control-theoretic standpoint. More specifically, we explore the influence of accountability for water quality controllability improvement when addressing the pump scheduling problem. We examine its effects on the cumulative cost of the interconnected systems as well as the subsequent performance of the water quality controller. To achieve this, we develop a framework that incorporates different controllability metrics within the operational hydraulic optimization problem; its aim is attaining an adequate level of water quality control across the system. We assess the aforementioned aspects' performance on various scaled networks with a wide range of numerical scenarios.

The real-time monitoring of water distribution networks enables water quality (WQ) controllers to trace the evolution of disinfectants and contaminants within the network. Water quality sensors are typically employed within the network to achieve an observable system. However, the expensiveness of sensors along with their installation requires sensors to be optimally placed at certain location of the network. Prior research has approached solving the optimal geographic placement of WQ sensors from an objective-based approach that either assign different public health metrics related to contamination events, and network-wide observability-based metrics to obtain the optimal sensor selection. However, such methods have typically adopted the use of simplified single-species decay and reaction models; the resulting sensor placements are not robust to changes in the network's hydraulic profile or advanced WQ models that capture far more than chlorine decay. To that end, in this work we introduce a state-robust observability-based sensor selection framework. The underlying water network model is based on a multi-species reaction dynamics representation; it enables contaminant reactivity modeling. The proposed sensor placement framework offers the following: (i) a robust solution towards fluctuations in water demand patterns; (ii) a scalable algorithm that enables its applicability to large-scale networks. A comprehensive case study is provided on benchmark water networks with varying hydraulic conditions. The sensor placement framework is solved considering several system observability metrics. This offers different observations that water system operators can consider.

In drinking water networks, hydraulics and water quality stand out as two paramount phenomena, each with its distinct focus and time-scale. Hydraulics is concerned with delivering adequate pressure throughout the network, ensuring that water flows efficiently to meet consumers' needs. On the other hand, water quality focuses on the maintenance of high standards for water safety within the network. These two critical aspects operate on distinct time-scales. Hydraulics undergo changes on a longer time-scale, reflecting the gradual shifts in flow rates and pressure levels across the network. In contrast, water quality dynamics require faster measures, often necessitating the computation of hydraulic profiles in advance. That is, a layer of complexity arises from the interdependency of the water quality dynamics on the system's hydraulics. This interdependence significantly impacts the performance of the water quality control and regulation algorithm in response to hydraulic adjustments. Prior studies have tended to focus on the two problems separately; Some studies have focused on optimizing the operational hydraulic settings, while others have concentrated on regulating water quality dynamics. Moreover, other studies have coupled these two problems leading to trade-offs between conflicting objectives. In this study, we adopt a control-theoretic perspective to investigate the intricate relationship between optimized hydraulic operation and water quality control. Our proposed framework explores the enhancement of water quality controllability while solving the pump schedule optimization problem. We examine the resultant trade-offs of the operational scheduling problem in comparison to the decoupled approach—and evaluate the impact on the water quality control performance. We assess and validate the proposed approach on various case studies with different scales and hydraulic scenarios. This study offers novel approaches to the integration of hydraulic and water quality control, paving the way for more effective and resource-efficient management of water distribution networks.

Future power networks that are dominated by renewables face challenges related to maintaining network-wide stability. To address these challenges, wide-area monitoring systems and phasor measurement units (PMUs) provide real-time sensor data of physics-based states. Various studies have investigated mixed-integer programming formulations to optimally determine the geographic PMU placements. While such studies addressed a plethora of challenges, they mostly adopt a simple representation of system dynamics, ignore basic algebraic equations modeling power flows, forgo including renewables such as solar and wind, and do not model their uncertainty. To that end, the objective of this work is to revisit the PMU placement problem and address these challenges via a novel optimization formulation. The proposed approach is validated on IEEE power networks.