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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.

Chlorine, the most widely used disinfectant, needs to be adequately distributed in water distribution networks (WDNs) to maintain consistent residual levels and ensure water safety. This is performed through control node injections at the treatment plant via booster stations scattered in WDNs. While previous studies have applied various optimization metrics for booster station placement, many have failed to consider the coverage of the station injections and the dynamic nature of WDNs. In particular, variations in hydraulics and demand significantly impact the reachability and efficacy of chlorine injections which then impact optimal placement of booster stations. This study introduces a novel formulation that combines control- and graph-theoretic approaches to solve the booster station placement problem. Unlike traditional methods, our approach emphasizes maximizing the system's ability to control disinfectant levels with minimal energy, taking into account the time-varying hydraulic profiles that lead to different optimal station placements. We propose a simple weighting technique to determine the placements by assessing the structural controllability of each configuration, based on the network's topology and independent of specific parameters like decay rates or pipe roughness. This method ensures effective chlorine coverage across the network. Our approach is validated on different networks, demonstrating its operational effectiveness, scalability, and practicality.

Effective disinfection is essential for maintaining water quality standards in distribution networks. Chlorination, as the most used technique, ensures safe water by maintaining sufficient chlorine residuals but also leads to the formation of disinfection byproducts (DBPs). These DBPs pose health risks, highlighting the need for chlorine injection control (CIC) by booster stations to balance safety and DBPs formation. Prior studies have followed various approaches to address this research problem. However, most of these studies overlook the changing flow conditions and their influence on the evolution of the chlorine and DBPs concentrations by integrating simplified transport-reaction models into CIC. In contrast, this paper proposes a novel CIC method that: (i) integrates multi-species dynamics, (ii) allows for a more accurate representation of the reaction dynamics of chlorine, other substances, and the resulting DBPs formation, and (iii) optimizes for the regulation of chlorine concentrations subject to EPA mandates thereby mitigating network-wide DBPs formation. The novelty of this study lies in its incorporation of time-dependent controllability analysis that captures the control coverage of each booster station. The effectiveness of the proposed CIC method is demonstrated through its application and validation via numerical case studies on different water networks with varying scales, initial conditions, and parameters.

The collective behavior of human-driven vehicles (HVs) produces the well-known stop-and-go waves potentially leading to higher fuel consumption and emissions. This paper investigates the stabilization of traffic flow via a minimum number of autonomous vehicles (AVs) subject to constraints on the control parameters aiming to reduce the number of vehicles on the road while achieving lower fuel consumption and emissions. The unconstrained scenario has been well-studied in recent studies. The main motivation to investigate the constrained scenario is that, in realistic engineering applications, lower and upper bounds exist on the control parameters. For the constrained scenario, we optimally find the minimum number of required AVs (via computing the optimal lower bound on the AV penetration rate) to stabilize traffic flow for a given number of HVs. As an immediate consequence, we conclude that for a given number of AVs, the number of HVs in the stabilized traffic flow may not be arbitrarily large in the constrained scenario unlike the unconstrained scenario studied in the literature. We systematically propose a procedure to compute the optimal lower bound on the AV penetration rate using nonlinear optimization techniques. Finally, we validate the theoretical results via numerical simulations. Numerical simulations suggest that enlarging the constraint intervals makes a smaller optimal lower bound on the AV penetration rate attainable. However, it leads to a slower transient response due to a dominant pole closer to the origin.

Optimal sensing nodes selection 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 letter, we address the sensing node selection 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 sensing node selection on nonlinear natural gas combustion networks.

Cost-effective water distribution network (WDN) design with acceptable pressure performance is crucial for the management of drinking water in cities. This paper presents a Microsoft Excel tool to model, simulate, and optimize WDNs with looped pipelines under steady-state incompressible flow simulations. Typically, the hardy-cross method is applied using spreadsheet calculations to estimate discharges. This method requires mass-conservative initial estimates and requires successive iterations to converge. In this paper, however, we develop an alternative method that uses the built-in solver capabilities of Excel, does not require initial mass-conservative estimation, and is free of flow corrections. The main objective of this paper is to develop an open-source accessible tool for simulating hydraulic networks also adapted for teaching and learning purposes. The governing equations and the mathematical basis for the hydraulic modeling of the system are mathematically described, considering the topology of the network, mass and energy conservation, cost of tank material, foundation, and cost of pumping energy to fill the tank. The use of this tool is encouraged at the undergraduate and graduate engineering levels, as it offers the opportunity to address complex concepts in a comprehensive way using a spreadsheet that does not require coding expertise. Hence, users can debug all cells and understand all equations used in the hydraulic model, as well as modify them. To demonstrate the model capabilities, three practical examples are presented, with the first one solved step by step, and the results are compared with the EPANET and with the results reported in the literature. Using the optimization method presented in this paper, it was possible to achieve a cost reduction of 151,790 USD (9.8% of the total cost) in a network that supplies a 44,416 population.

This paper deals with the joint reduction of the number of dynamic and algebraic states of a nonlinear differential-algebraic equation (NDAE) model of a power network. The dynamic states depict the internal states of generators, loads, renewables, whereas the algebraic ones define network states such as voltages and phase angles. In the current literature of power system model order reduction (MOR), the algebraic constraints are usually neglected and the power network is commonly modeled via a set of ordinary differential equations (ODEs) instead of NDAEs. Thus, reduction is usually carried out for the dynamic states only and the algebraic variables are kept intact. This leaves a significant part of the system's size and complexity unreduced. This paper addresses this aforementioned limitation by jointly reducing both dynamic and algebraic variables. As compared to the literature the proposed MOR techniques are endowed with the following features: (i) no system linearization is required, (ii) require no transformation to an equivalent or approximate ODE representation, (iii) guarantee that the reduced order model to be NDAE-structured and thus preserves the differential-algebraic structure of original power system model, and (iv) can seamlessly reduce both dynamic and algebraic variables while maintaining high accuracy. Case studies performed on a 2000-bus power system reveal that the proposed MOR techniques are able to reduce system order while maintaining accuracy.

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

Detention ponds can mitigate flooding and improve water quality by allowing the settlement of pollutants. Typically, they are operated with fully open orifices and weirs (i.e., passive control). Active controls can improve the performance of these systems: orifices can be retrofitted with controlled valves and spillways can have controllable gates. The real-time optimal operation of its hydraulic devices can be achieved with techniques such as Model Predictive Control (MPC). A distributed quasi-2D hydrologic-hydrodynamic coupled with a reservoir flood routing model is developed and integrated with an MPC algorithm to estimate the operation of valves and movable gates. The control optimization problem is adapted to switch from a flood-related algorithm focusing on mitigating floods to a heuristic objective function that aims to increase the detention time when no inflow hydrographs are predicted. The case studies show the potential of applying the methods developed in a catchment in Sao Paulo, Brazil. The performance of MPC compared to alternatives with either fully or partially open valves and gates are tested. Comparisons with HEC-RAS 2D indicate volume and peak flow errors of approximately 1.4% and 0.91% for the watershed module. Simulating two consecutive 10-year storms shows that the MPC strategy can achieve peak flow reductions of 79%. In contrast, passive control has nearly half of the performance. A 1-year continuous simulation results show that the passive scenario with 25% of the valves opened can treat 12% more runoff compared to the developed MPC approach, with an average detention time of approximately 6 hours. For the MPC approach, the average detention time is nearly 14 hours indicating that both control techniques can treat similar volumes; however, the proxy water quality for the MPC approach is enhanced due to the longer detention times.

Observability quantification is a key problem in dynamic network sciences. While it has been thoroughly studied for linear systems, observability quantification 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 paper, we produce three new results. First, we establish that a variational form of discrete-time autonomous 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 paper's second result derives connections between existing 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.

The main objective of the connected and automated vehicle (CAV) platoon control problem is to regulate CAVs' position while ensuring stability and accounting for vehicle dynamics. Although this problem has been studied in the literature, existing research has some limitations. This paper presents two new theoretical results that address these limitations: (i) the synthesis of unrealistic high-gain control parameters due to the lack of a systematic way to incorporate the lower and upper bounds on the control parameters, and (ii) the performance sensitivity to the communication delay due to inaccurate Taylor series approximation. To be more precise, taking advantage of the wellknown Pade approximation, this paper proposes a constrained CAV platoon controller synthesis that (i) systematically incorporates the lower and upper bounds on the control parameters, and (ii) significantly improves the performance sensitivity to the communication delay. The effectiveness of the presented results is verified through conducting extensive numerical simulations. The proposed controller effectively attenuates the stop-and-go disturbance -- a single cycle of deceleration followed by acceleration -- amplification throughout the mixed platoon (consisting of CAVs and human-driven vehicles). Modern transportation systems will benefit from the proposed CAV controls in terms of effective disturbance attenuation as it will potentially reduce collisions.

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.

System identification through learning approaches is emerging as a promising strategy for understanding and simulating dynamical systems, which nevertheless faces considerable difficulty when confronted with power systems modeled by differential-algebraic equations (DAEs). This paper introduces a neural network (NN) framework for effectively learning and simulating solution trajectories of DAEs. The proposed framework leverages the synergy between Implicit Runge-Kutta (IRK) time-stepping schemes tailored for DAEs and NNs (including a differential NN (DNN)). The framework enforces an NN to cooperate with the algebraic equation of DAEs as hard constraints and is suitable for the identification of the ordinary differential equation (ODE)-modeled dynamic equation of DAEs using an existing penalty-based algorithm. Finally, the paper demonstrates the efficacy and precision of the proposed NN through the identification and simulation of solution trajectories for the considered DAE-modeled power system.

In the domain of network biology, the interactions among heterogeneous genomic and molecular entities are represented through networks. Link prediction (LP) methodologies are instrumental in inferring missing or prospective associations within these biological networks. In this review, we systematically dissect the attributes of local, centrality, and embedding-based LP approaches, applied to static and dynamic biological networks. We undertake an examination of the current applications of LP metrics for predicting links between diseases, genes, proteins, RNA, microbiomes, drugs, and neurons. We carry out comprehensive performance evaluations on established biological network datasets to show the practical applications of standard LP models. Moreover, we compare the similarity in prediction trends among the models and the specific network attributes that contribute to effective link prediction, before underscoring the role of LP in addressing the formidable challenges prevalent in biological systems, ranging from noise, bias, and data sparseness to interpretability. We conclude the review with an exploration of the essential characteristics expected from future LP models, poised to advance our comprehension of the intricate interactions governing biological systems.

Due to the rapid developments in synchronized measurement technologies, there exist enormous opportunities to attenuate disturbances in future power grids with high penetration of renewables and complex load demands. To that end, this paper investigates the effectiveness of new robust feedback controllers for interconnected power systems with advanced power electronics-based models of photovoltaic (PV) power plants, composite load dynamics, and detailed higher-order synchronous generator models. Specifically, we design new, advanced control-theoretic wide-area controllers to improve the transient stability of nonlinear differential-algebraic models. Thorough simulation studies are carried out to assess the performance of the proposed controllers. Several fundamental questions on the proposed controllers' computational complexity and disturbance attenuation performance are raised and addressed. Simulation results demonstrate that with the proposed controllers as a secondary control layer, the overall transient stability and system robustness against load and renewables disturbances/uncertainties can be significantly improved compared to the state-of-the-art.

In this paper, we propose a novel update of a nominal stabilizing static output feedback (SOF) controller for a perturbed linear system. In almost every classical feedback controller design problem, a stabilizing feedback controller is designed given a stabilizable unstable system. In realistic scenarios, the system model is usually imperfect and subject to perturbations. A typical approach to attenuate the impacts of such perturbations on the system stability is repeating the whole controller design procedure to find an updated stabilizing SOF controller. Such an approach can be inefficient and occasionally infeasible. Using the notion of minimum destabilizing real perturbation (MDRP), we construct a simple norm minimization problem (a least-squares problem) to propose an efficient update of a nominal stabilizing SOF controller that can be applied to various control engineering applications in the case of perturbed scenarios like abrupt changes or inaccurate system models. In particular, considering norm-bounded known or unknown perturbations, this paper presents updated stabilizing SOF controllers and derives sufficient stability conditions. Geometric metrics to quantitatively measure the approach's robustness are defined. Moreover, we characterize the corresponding guaranteed stability regions, and specifically, for the case of norm-bounded unknown perturbations, we propose non-fragility-based robust updated stabilizing SOF controllers. Through extensive numerical simulations, we assess the effectiveness of the theoretical results.

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 $H_{2}/O_{2}$ combustion reaction network., Comment: To Appear in the 62$^{\text{nd}}$ IEEE Conference on Decision and Control (CDC'2023), Singapore, Decemeber 2023

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 \textit{not}. DAE system theory is less understood in the context of power system dynamics. To that end, this letter presents two new mathematical transformations for nonlinear DAE models that yield nonlinear ODE models whilst 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.

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 (OPP). This paper 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 including renewables such as solar and wind, and did not model their uncertainty. Consequently, this paper revisits the observability-based OPP problem by addressing the literature's limitations. A nonlinear differential algebraic representation (NDAE) of the power system is considered. The system is discretized using various discretization approaches while explicitly accounting for uncertainty. A moving horizon estimation 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 the different aspects of this approach and test its robustness to various dynamical conditions.

This work investigates traffic control via controlled connected and automated vehicles (CAVs) using novel controllers derived from the linear-quadratic regulator (LQR) theory. CAV-platoons are modeled as moving bottlenecks impacting the surrounding traffic with their speeds as control inputs. An iterative controller algorithm based on the LQR theory is proposed along with a variant that allows for penalizing abrupt changes in platoons speeds. The controllers use the Lighthill-Whitham-Richards (LWR) model implemented using an extended cell transmission model (CTM) which considers the capacity drop phenomenon for a realistic representation of traffic in congestion. The impact of various parameters of the proposed controller on the control performance is analyzed. The effectiveness of the proposed traffic control algorithms is tested using a traffic control example and compared with existing proportional-integral (PI)- and model predictive control (MPC)- based controllers from the literature. A case study using the TransModeler traffic microsimulation software is conducted to test the usability of the proposed controller as well as existing controllers in a realistic setting and derive qualitative insights. It is observed that the proposed controller works well in both settings to mitigate the impact of the jam caused by a fixed bottleneck. The computation time required by the controller is also small making it suitable for real-time control.

This paper presents a new approach to approximate the AC optimal power flow (ACOPF). By eliminating the need to solve the ACOPF every few minutes, the paper showcases how a realtime feedback controller can be utilized in lieu of ACOPF and its variants. By (i) forming the grid dynamics as a system of differential-algebraic equations (DAE) that naturally encode the non-convex OPF power flow constraints, (ii) utilizing DAELyapunov theory, and (iii) designing a feedback controller that captures realtime uncertainty while being uncertainty-unaware, the presented approach demonstrates promises of obtaining solutions that are close to the OPF ones without needing to solve the OPF. The proposed controller responds in realtime to deviations in renewables generation and loads, guaranteeing improvements in system transient stability, while always yielding approximate solutions of the ACOPF with no constraint violations. As the studied approach herein yields slightly more expensive realtime generator controls, the corresponding price of realtime control and regulation is examined. Cost comparisons with the traditional ACOPF are also showcased -- all via case studies on standard power networks.

Tracing disinfectant (e.g., chlorine) and contaminants evolution in water networks requires the solution of 1- D advection-reaction (AR) partial differential equations (PDEs). With the absence of analytical solutions in many scenarios, numerical solutions require high-resolution time- and spacediscretizations resulting in large model dimensions. This adds complexity to the water quality control problem. In addition, considering multi-species water quality dynamics rather than the single-species dynamics produces a more accurate description of the reaction dynamics under abnormal hazardous conditions (e.g., contamination events). Yet, these dynamics introduces nonlinear reaction formulation to the model. To that end, solving nonlinear 1-D AR PDEs in real time is critical in achieving monitoring and control goals for various scaled networks with a high computational burden. In this work, we propose a novel comprehensive framework to overcome the large-dimensionality issue by introducing different approaches for applying model order reduction (MOR) algorithms to the nonlinear system followed by applying real-time water quality regulation algorithm that is based on an advanced model to maintain desirable disinfectant levels in water networks under multi-species dynamics. The performance of this framework is validated using rigorous numerical case studies under a wide range of scenarios demonstrating the challenges associated with regulating water quality under such conditions.

Conventional state estimation routines of electrical grids are mainly reliant on dynamic models of fossil fuel-based resources. These models commonly contain differential equations describing synchronous generator models and algebraic equations modeling power flow/balance equations. Fuel-free power systems that are driven by inertia-less renewable energy resources will hence require new models and upgraded estimation routines. To that end, in this paper we propose a robust estimator for an interconnected model of power networks comprised of a comprehensive ninth order synchronous generator model, advanced power electronics-based models for photovoltaic (PV) power plants, constant power loads, constant impedance loads, and motor loads. The presented state estimator design is based on Lyapunov stability criteria for nonlinear differential algebraic equation (DAE) models and is posed as a convex semi-definite optimization problem. Thorough simulations studies have been carried out on IEEE-39 bus test system to showcase the robustness of the proposed estimator against unknown uncertainty from load demand and solar irradiance., Comment: To Appear in the 61st IEEE Conference on Decision and Control (CDC), Canc\'un, Mexico, December 2022

This paper addresses the problem of traffic state estimation (TSE) in the presence of heterogeneous sensors which include both fixed and moving sensors. Traditional fixed sensors are expensive and cannot be installed throughout the highway. Moving sensors such as Connected Vehicles (CVs) offer a relatively cheap alternative to measure traffic states across the network. Moving forward it is thus important to develop such models that effectively use the data from CVs. One such model is the nonlinear second-order Aw-Rascle-Zhang (ARZ) model which is a realistic traffic model, reliable for TSE and control. A state-space formulation is presented for the ARZ model considering junctions in the formulation which is important to model real highways with ramps. A Moving Horizon Estimation (MHE) implementation is presented for TSE using a linearized ARZ model. Various state-estimation methods used for TSE in the literature along with the presented approach are compared with regard to accuracy and computational tractability with the help of a numerical study using the VISSIM traffic simulation software. The impact of various strategies for querying CV data on the estimation performance is also considered. Several research questions are posed and addressed with a thorough analysis of the results.

This letter focuses on the problem of traffic state estimation for highway networks with junctions in the form of on- and off-ramps while maintaining differential privacy of traffic data. Two types of sensors are considered, fixed sensors such as inductive loop detectors and connected vehicles which provide traffic density and speed data. The celebrated nonlinear second-order Aw-Rascle- Zhang (ARZ) model is utilized to model the traffic dynamics. The model is formulated as a nonlinear state-space difference equation. Sensitivity relations are derived for the given data which are then used to formulate a differentially private mechanism which adds a Gaussian noise to the data to make it differentially private. A Moving Horizon Estimation (MHE) approach is implemented for traffic state estimation using a linearized ARZ model. MHE is compared with Kalman Filter variants namely Extended Kalman Filter, Ensemble Kalman Filter and Unscented Kalman Filter. Several research and engineering questions are formulated and analysis is performed to find corresponding answers., Comment: TO APPEAR IN THE 61ST IEEE CONFERENCE ON DECISION AND CONTROL (CDC), CANCUN, MEXICO, DECEMBER 2022. arXiv admin note: text overlap with arXiv:2209.02848