arXiv subjects

Mohamad H. Kazma

Publications and source records attributed to Mohamad H. Kazma.

14 recordsLinked to original sources

arXiv2026

Verification and Forward Invariance of Control Barrier Functions for Differential-Algebraic Systems

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.

eess.SY↗

arXiv2026

Safe Control of Semi-Explicit Differential-Algebraic Systems: Control Barrier Functions with SOS Verification

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 safety-critical control framework for 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.

eess.SY↗

arXiv2026

Connections Between Determinantal Point Processes and Gramians in Control

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.

math.OC↗

arXiv2026

Observability for Nonlinear Systems: Connecting Variational Dynamics, Lyapunov Exponents, and Empirical Gramians

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 yields a so-called Variational Gramian (Var-Gram) that is equivalent to the classic Empr-Gram under linear output mappings; 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.

eess.SY↗

arXiv2026

Partitioning and Observability in Linear Systems via Submodular Optimization

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 a largely unexplored, open problem 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.

eess.SY↗

arXiv2026

Exploring Uncertainty Propagation in Coupled Hydrologic and Hydrodynamic Systems via Distribution-Agnostic State Space Analysis

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.

eess.SY↗

arXiv2026

Revisiting The PBH Test: Fast Uncontrollability Certificates via Krylov Methods

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.

math.OC↗

arXiv2026

Nonsmooth Hydraulics, Smooth Control: System Theory Framework for Analyzing Water Networks

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.

eess.SY↗

arXiv2025

Observability and Generalized Sensor Placement for Nonlinear Quality Models in Drinking Water Networks

This paper studies the problem of optimal placement of water quality (WQ) sensors in water distribution networks (WDNs), with a focus on chlorine transport, decay, and reaction models. Such models are traditionally used as suitable proxies for WQ. The literature on this topic is 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 (SP) that do not account for nonlinear WQ dynamics. Furthermore, as WQ simulations are parameterized by hydraulic profiles and demand patterns, the placement of sensors are often hydraulics-dependent. This study produces a greedy algorithm that addresses the two aforementioned limitations. The algorithm is grounded in nonlinear dynamic systems and observability theory, and yields SPs that are submodular and robust to hydraulic changes. Case studies on benchmark water networks are provided. The key findings provide practical recommendations for WDN operators.

eess.SY↗

arXiv2025

Quality-Aware Hydraulic Control in Drinking Water Networks via Controllability Proxies

The operation of water distribution networks simply aims at efficiently delivering consumers adequate water while maintaining safe water quality (WQ). However, this process entails a multi-scale interplay between hydraulic and WQ dynamics evolving spatio-temporally within such a complex infrastructure network. While prior research has addressed the hydraulic optimization problem and WQ regulation as decoupled or coupled, they often overlook control-theoretic guided solutions. This paper takes a novel approach by investigating the coupling between hydraulic and WQ dynamics from a control networks perspective. We propose a quality-aware control framework that embeds WQ controllability metrics into the network-level pump scheduling problem, acknowledging the direct influence of system hydraulics on WQ controller behavior. We examine the trade-offs between pump control energy cost and WQ performance across various network sizes and scenarios. Our results showcase how network topology, hydraulic constraints, and WQ metrics jointly impact optimal pump schedules and, accordingly, the achievable level of WQ regulation, offering insights into designing efficient control strategies for water infrastructure networks governed by interdependent dynamics.

eess.SY↗

arXiv2025

Multilinear Extensions in Submodular Optimization for Optimal Sensor Scheduling in Nonlinear Networks

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.

math.OC↗

arXiv2024

Revisiting the Optimal PMU Placement Problem in Multi-Machine Power 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 (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.

eess.SY↗

arXiv2024

ODE Transformations of Nonlinear DAE Power Systems

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.

eess.SY↗

arXiv2023

State-Robust Observability Measures for Sensor Selection in Nonlinear Dynamic Systems

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.

eess.SY↗