Mohamad H. Kazma

Hongchao Zhang, Mohamad H. Kazma, Meiyi Ma et al.

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.

Mohamad H. Kazma, Ahmad F. Taha

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.

Ahmad F. Taha, Mohamad H. Kazma

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.