arXiv subjects

Mohamed Serry

Publications and source records attributed to Mohamed Serry.

14 recordsLinked to original sources

arXiv2026

Set-Based Value Function Characterization and Neural Approximation of Stabilization Domains for Input-Constrained Discrete-Time Systems

Analyzing nonlinear systems with stabilizable controlled invariant sets (CISs) requires accurate estimation of their domains of stabilization (DOS) together with associated stabilizing controllers. Despite extensive research, estimating DOSs for general nonlinear systems remains challenging due to fundamental theoretical and computational limitations. In this paper, we propose a novel framework for estimating DOSs for controlled input-constrained discrete-time systems. The DOS is characterized via newly introduced value functions defined on metric spaces of compact sets. We establish the fundamental properties of these value functions and derive the associated Bellman-type (Zubov-type) functional equations. Building on this characterization, we develop a physics-informed neural network (NN) framework that learns the value functions by embedding the derived functional equations directly into the training process. The proposed methodology is demonstrated through two numerical examples, illustrating its ability to accurately estimate DOSs and synthesize stabilizing controllers from the learned value functions.

eess.SY↗

arXiv2026

Safe and Robust Domains of Attraction for Discrete-Time Systems: A Set-Based Characterization and Certifiable Neural Network Estimation

Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging due to both theoretical and computational limitations, particularly in the presence of uncertainties and state constraints. In this paper, we propose a novel framework for the accurate estimation of safe (state-constrained) and robust DOAs for discrete-time nonlinear uncertain systems with continuous dynamics, open safe sets, compact disturbance sets, and uniformly locally $\ell_p$-stable compact RISs. The notion of uniform $\ell_p$ stability is quite general and encompasses, as special cases, uniform exponential and polynomial stability. The DOAs are characterized via newly introduced value functions defined on metric spaces of compact sets. We establish their fundamental mathematical properties and derive the associated Bellman-type (Zubov-type) functional equations. Building on this characterization, we develop a physics-informed neural network (NN) framework to learn the corresponding value functions by embedding the derived Bellman-type equations directly into the training process. To obtain certifiable estimates of the safe robust DOAs from the learned neural approximations, we further introduce a verification procedure that leverages existing formal verification tools. The effectiveness and applicability of the proposed methodology are demonstrated through four numerical examples involving nonlinear uncertain systems subject to state constraints, and its performance is compared with existing methods from the literature.

eess.SY↗

arXiv2025

Learning Neural Network Safe Tracking Controllers from Backward Reachable Sets

The design of tracking controllers that closely follow a reference trajectory while ensuring safety and robustness against disturbances is a challenging problem in the control of autonomous systems. In this work, we propose a neural network-based safe tracking control framework for nonlinear discrete-time systems with reach-avoid specifications in the presence of disturbances. Our approach begins with generation of a nominal trajectory using standard trajectory synthesis approaches, followed by construction of safe zonotopic backward reachable sets along the nominal trajectory. The states lying within the backward reachable sets are guaranteed to satisfy safe reachability specifications. Then, our key insight is to leverage the computed backward reachable sets to inform the architecture and training of a neural network-based tracking controller such that the neural network drives the system's states through these backward reachable sets, thereby improving the likelihood of safe reachability. We perform formal verification with conformal prediction to achieve statistical safety guarantees on the performance of the learned neural controller. The performance of our approach is illustrated through a numerical example on the discrete-time Dubin's car model.

eess.SY↗

arXiv2025

Safe Domains of Attraction for Discrete-Time Nonlinear Systems: Characterization and Verifiable Neural Network Estimation

Analysis of nonlinear autonomous systems typically involves estimating domains of attraction, which have been a topic of extensive research interest for decades. Despite that, accurately estimating domains of attraction for nonlinear systems remains a challenging task, where existing methods are conservative or limited to low-dimensional systems. The estimation becomes even more challenging when accounting for state constraints. In this work, we propose a framework to accurately estimate safe (state-constrained) domains of attraction for discrete-time autonomous nonlinear systems. In establishing this framework, we first derive a new Zubov equation, whose solution corresponds to the exact safe domain of attraction. The solution to the aforementioned Zubov equation is shown to be unique and continuous over the whole state space. We then present a physics-informed approach to approximating the solution of the Zubov equation using neural networks. To obtain certifiable estimates of the domain of attraction from the neural network approximate solutions, we propose a verification framework that can be implemented using standard verification tools (e.g., $\alpha,\!\beta$-CROWN and dReal). To illustrate its effectiveness, we demonstrate our approach through numerical examples concerning nonlinear systems with state constraints.

eess.SY↗

arXiv2024

Underapproximating Safe Domains of Attraction for Discrete-Time Systems Using Implicit Representations of Backward Reachable Sets

Analyzing and certifying stability and attractivity of nonlinear systems is a topic of research interest that has been extensively investigated by control theorists and engineers for many years. Despite that, accurately estimating domains of attraction for nonlinear systems remains a challenging task, where available estimation approaches are either conservative or limited to low-dimensional systems. In this work, we propose an iterative approach to accurately underapproximate safe (i.e., state-constrained) domains of attraction for general discrete-time autonomous nonlinear systems. Our approach relies on implicit representations of safe backward reachable sets of safe regions of attraction, where such regions can be be easily constructed using, e.g., quadratic Lyapunov functions. The iterations of our approach are monotonic (in the sense of set inclusion), where each iteration results in a safe region of attraction, given as a sublevel set, that underapproximates the safe domain of attraction. The sublevel set representations of the resulting regions of attraction can be efficiently utilized in verifying the inclusion of given points of interest in the safe domain of attraction. We illustrate our approach through two numerical examples, involving two- and four-dimensional nonlinear systems.

math.OC↗

arXiv2024

Reach-Avoid Control Synthesis for a Quadrotor UAV with Formal Safety Guarantees

Reach-avoid specifications are one of the most common tasks in autonomous aerial vehicle (UAV) applications. Despite the intensive research and development associated with control of aerial vehicles, generating feasible trajectories though complex environments and tracking them with formal safety guarantees remain challenging. In this paper, we propose a control framework for a quadrotor UAV that enables accomplishing reach-avoid tasks with formal safety guarantees. In this proposed framework, we integrate geometric control theory for tracking and polynomial trajectory generation using Bezier curves, where tracking errors are accounted for in the trajectory synthesis process. To estimate the tracking errors, we revisit the stability analysis of the closed-loop quadrotor system, when geometric control is implemented. We show that the tracking error dynamics exhibit local exponential stability when geometric control is implemented with any positive control gains, and we derive tight uniform bounds of the tracking error. We also introduce sufficient conditions to be imposed on the desired trajectory utilizing the derived uniform bounds to ensure the well-definedness of the closed-loop system. For the trajectory synthesis, we present an efficient algorithm that enables constructing a safe tube by means of sampling-based planning and safe hyper-rectangular set computations. Then, we compute the trajectory, given as a piecewise continuous Bezier curve, through the safe tube, where a heuristic efficient approach that utilizes iterative linear programming is employed. We present extensive numerical simulations with a cluttered environment to illustrate the effectiveness of the proposed framework in reach-avoid planning scenarios.

eess.SY↗

arXiv2023

Under-Approximate Reachability Analysis for a Class of Linear Systems with Inputs

Under-approximations of reachable sets and tubes have been receiving growing research attention due to their important roles in control synthesis and verification. Available under-approximation methods applicable to continuous-time linear systems typically assume the ability to compute transition matrices and their integrals exactly, which is not feasible in general, and/or suffer from high computational costs. In this note, we attempt to overcome these drawbacks for a class of linear time-invariant (LTI) systems, where we propose a novel method to under-approximate finite-time forward reachable sets and tubes, utilizing approximations of the matrix exponential and its integral. In particular, we consider the class of continuous-time LTI systems with an identity input matrix and initial and input values belonging to full dimensional sets that are affine transformations of closed unit balls. The proposed method yields computationally efficient under-approximations of reachable sets and tubes, when implemented using zonotopes, with first-order convergence guarantees in the sense of the Hausdorff distance. To illustrate its performance, we implement our approach in three numerical examples, where linear systems of dimensions ranging between 2 and 200 are considered.

eess.SY↗

arXiv2022

Design and Simulation of a Micro-coiled Digitally-Controlled Variable Inductor with a Monolithically Integrated MEMS Switch

This work introduces the design analysis simulation and a standard MEMS fabrication process for a three dimensional microcoil with a magnetic core and a digital switch configuration using a completely integrated fully MEMS compatible process to achieve a digitally controlled inductance. The proposed design can also be utilized as a micro transformer. The proposed design consists of five identical 3D coils and their corresponding MEMS switches. These coils are digitally controlled to achieve a variable inductor ranging from one fifth of the coil inductance up to five times the coil inductance. A standard five layer Polymumps process is proposed to fabricate the microcoils and the integrated switches. Each micro coil is anchored directly on chip connected to the input signal from one side and the other is connected to the switch. The Ni based magnetic core improves the coil response by confining and guiding the magnetic field in the magnetic device compared to Si core based by more than five times. The presented coil has the number of windings limited by the designed length and the minimum spacing that can be realized by standard optical lithography. The coil diameter is also restricted by the limits defined by optical lithography whereas the maximum height realizable by the Polymumps process limits the height of the magnetic core and accordingly results in lower inductor performance. Based on this technique we present coils ranging from 100 um in length and ten winding up to 1000 um in length and 100 windings. The new monolithically integrated MEMS switches act as selectors to achieve a variable inductance with digital control to allow the selection among n inductance steps where n is the number of coils.

eess.SY↗

arXiv2021

Over-approximating reachable tubes of linear time-varying systems

We present a method to over-approximate reachable tubes over compact time-intervals, for linear continuous-time, time-varying control systems whose initial states and inputs are subject to compact convex uncertainty. The method uses numerical approximations of transition matrices, is convergent of first order, and assumes the ability to compute with compact convex sets in finite dimension. We also present a variant that applies to the case of zonotopic uncertainties, uses only linear algebraic operations, and yields zonotopic over-approximations. The performance of the latter variant is demonstrated on an example.

math.OC↗

arXiv2020

Convergent Under-Approximations of Reachable Sets and Tubes for Linear Uncertain Systems

In this note, we propose a method to under-approximate finite-time reachable sets and tubes for a class of continuous-time linear uncertain systems. The class under consideration is the linear time-varying (LTV) class with integrable time-varying system matrices and uncertain initial and input values belonging to known convex compact sets. The proposed method depends upon the iterative use of constant-input reachable sets which results in convergent under-approximations in the sense of Hausdorff distance. We illustrate our approach through two numerical examples.

eess.SY↗

arXiv2019

Performance-Enhanced Non-Enzymatic Glucose Sensor Based on Graphene-Heterostructure

This study proposes a novel design of glucose sensor with enhanced selectivity and sensitivity by using graphene Schottky diodes, which is composed of Graphene (G)/Platinum Oxide (PtO)/n-Silicon (Si) heterostructure. The sensor was tested with different glucose concentrations and interfering solutions to investigate its sensitivity and selectivity. Different structures of the device were studied by adjusting the platinum oxide film thickness to investigate its catalytic activity. It was found that the film thickness plays a significant role in the efficiency of glucose oxidation and hence in overall device sensitivity. 0.8-2 uA output current was obtained in the case of 4-10 mM with a sensitivity of 0.2 uA/mM.cm2. Besides, results have shown that 0.8 uA and 15 uA were obtained by testing 4 mM glucose on two different PtO thicknesses, 30 nm, and 50 nm, respectively. The sensitivity of the device was enhanced by 150% (i.e., up to 30 uA/mM.cm2) by increasing the PtO layer thickness. This was attributed to both the increase of the number of active sites for glucose oxidation as well as the increase in the graphene layer thickness, which leads to enhanced charge carriers concentration and mobility. Moreover, theoretical investigations were conducted using the Density Function Theory (DFT) to understand the detection method and the origins of selectivity better. The working principle of the sensors puts it in a competitive position with other non-enzymatic glucose sensors. DFT calculations provided a qualitative explanation of the charge distribution across the graphene sheet within a system of a platinum substrate with D-glucose molecules above. The proposed G/PtO/n-Si heterostructure has proven to satisfy these factors, which opens the door for further developments of more reliable non-enzymatic glucometers for continuous glucose monitoring systems.

physics.app-ph↗

arXiv2017

Static Stability Analysis of a Thin Plate with a Fixed Trailing Edge in Axial Subsonic Flow: Possio Integral Equation Approach

In this work, the static stability of plates with fixed trailing edges in axial airflow is studied using the framework of Possio integral equation. First, we introduce a new derivation of a Possio integral equation that relates the pressure jump along thin plates to their downwash based on the linearization of the governing equations of an ideal compressible fluid. The steady state solution to the Possio equation is used to account for the aerodynamic forces in the steady state plate governing equation resulting in a singular differential-integral equation which is transformed to an integral equation. Next, we verify the solvability of the integral equation based on the Fredholm alternative for compact operators in Banach spaces and the contraction mapping theorem. Then, we derive explicit formulas for the characteristic equations of free-clamped and free-pinned plates. The minimum solutions to the characteristic equations are the divergence speeds which indicate when static instabilities start to occur. We show analytically that free-pinned plates are statically unstable. After that, we move to derive analytically flow speed intervals that correspond to static stability regions for free-clamped plates. We also resort to numerical computations to obtain an explicit formula for the divergence speed of free-clamped plates. Finally, we apply the obtained results on piezoelectric plates and we show that free-clamped piezoelectric plates are statically more stable than conventional free-clamped plates due to the piezoelectric coupling.

physics.flu-dyn↗

arXiv2017

Subsonic Flow over a Thin Airfoil in Ground Effect

In this paper, the problem of compressible flow over a thin airfoil located near the ground is studied. A singular integral equation, also known as Possio equation, that relates the pressure jump along the airfoil to its downwash is derived. The derivation of the equation utilizes Laplace transform, Fourier transform, method of images, and theory of Mikhlin multipliers. The existence and uniqueness of solution to the Possio equation is verified for the steady state case and an approximate solution is obtained. The aerodynamic loads are then calculated based on the approximate solution. Moreover, the divergence speed of a continuum wing structure located near the ground is obtained based on the derived expressions for the aerodynamic loads.

physics.flu-dyn↗

arXiv2015

Non-Enzymatic Graphene-Based Biosensors for Continuous Glucose Monitoring

A novel mediator-free, non-enzymatic electrochemical sensor, based on a graphene-Schottky junction, was fabricated for glucose detection. The sensor offers a promising alternative to the conventional enzyme-catalyzed electrochemical continuous glucose monitoring systems (CGM), as it overcomes many of the drawbacks attributed to the enzymatic nature; namely, irreversibility, drift, and interference with body fluids, which affect their accuracy, reliability and longevity. Enhanced performance of the sensors is demonstrated through the band interaction at the graphene-Schottky junction, which yields stronger forward/reverse currents in response to 50 μL glucose drop. Under optimized conditions, the linear response of the sensor to glucose concentration was valid in the range from 0 to 15 mmol/L with a detection limit of 0.5 mmol/L. The results indicated that the proposed sensor provided a highly sensitive, more facile method with good reproducibility for continuous glucose detection.

physics.chem-ph↗