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Articles 1 - 15 of 15
Full-Text Articles in Control Theory
Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox
Safety And Optimality Monitors For Learning-Enabled Systems Using Conformal Prediction, Jackson Cox
McKelvey School of Engineering Graduate Student Theses & Dissertations
The use of machine learning to create data-driven plant models and controllers has led to an increased need for safety and optimality monitors for model-based systems. System plant models are subject to uncertainty due to learning constraints such as unseen data and overfitting or physical constraints such as unknown dynamics and noise. This uncertainty is detrimental to safety-critical systems and must be properly regulated. To curb this uncertainty, we create prediction sets using the guarantees provided by Conformal Prediction. With a user-specified high probability, these prediction sets contain the true plant system states for an entire prediction horizon, which we …
Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan
Theory And Algorithms To Learn, Propagate, And Exploit Uncertainty For Stochastic Optimal Control Of Dynamical Systems, Vignesh Sivaramakrishnan
Electrical and Computer Engineering ETDs
Non-Gaussian uncertainty frequently arises in learning and control problems involving stochastic dynamical systems, particularly in autonomous vehicles, UAVs, satellites, and robotics. In this dissertation, we propose a new framework that leverages characteristic functions that provides a frequency-domain representation of random variables. The dissertation is structured into three key areas. First, we address model-based stochastic optimal control for linear systems with non-Gaussian noise, demonstrating that characteristic functions can be used to enforce chance constraints and control systems toward desired distributions. Second, we explore data-driven stochastic control, utilizing empirical characteristic functions to handle systems with unknown disturbances. In addition, we derive several …
(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha
(R2108) Global Asymptotic Stability Analysis Of Discrete Time Population Model With Allee Effect Through Lyapunov Function, Govind Jha, Neeraj Kumar, Sarita Jha
Applications and Applied Mathematics: An International Journal (AAM)
This study explores the idea of stability analysis by using Lyapunov functions in discrete time population models; this work focuses on the nth generation. Further, this investigation aims to extend global stability concepts to discrete-time models and considers the influence of the Allee effect on population dynamics. Mathematical formulations and specific modelling approaches are utilized to investigate the behavior of the population system. The results reveal a larger range of stability in comparison to previous findings, emphasizing the effectiveness of the Lyapunov function approach. Specifically highlighted here are the extension of global stability concepts to the nth generation providing insights …
Kreig: Gaining Insight Into Epidemics Through Use Of Mathematical Modeling, Christina Edholm
Kreig: Gaining Insight Into Epidemics Through Use Of Mathematical Modeling, Christina Edholm
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Harvesting Modulation In Three Species Food Chains Using A Robust Control Approach, Hector Puebla, Mariana Rodriguez-Jara, Priti Kumar Roy
Harvesting Modulation In Three Species Food Chains Using A Robust Control Approach, Hector Puebla, Mariana Rodriguez-Jara, Priti Kumar Roy
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Modeling And Control Of Drug Resistance In Cancer Dynamics, James Greene
Modeling And Control Of Drug Resistance In Cancer Dynamics, James Greene
Biology and Medicine Through Mathematics Conference
No abstract provided.
Incorporating Awareness, Misinformation And Optimal Control In A Model Of Sars-Cov-2, Eric Numfor
Incorporating Awareness, Misinformation And Optimal Control In A Model Of Sars-Cov-2, Eric Numfor
Biology and Medicine Through Mathematics Conference
No abstract provided.
Duality Of Ensemble Systems Through Moment Representations, Vignesh Narayanan, Wei Zhang, Jr-Shin Li
Duality Of Ensemble Systems Through Moment Representations, Vignesh Narayanan, Wei Zhang, Jr-Shin Li
Publications
Controlling large-scale dynamic population systems, known as ensemble control, is a pervasive and essential task in many emerging applications from diverse scientific domains. Previous focuses in the area of ensemble control have been placed on seeking open-loop control strategies due to unavailability of state feedback information for each individual system in the ensemble. In this paper, we develop a foundational framework for analysis and control of ensemble systems with closed feedback control loops. We introduce the notion of ensemble moments and construct moment systems associated with the ensemble systems. By extending the classical moment problem in mathematical analysis and statistics, …
Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, William L. Blair
Generalizations Of The Hardy Spaces And The Schwarz Boundary Value Problem, William L. Blair
Graduate Theses and Dissertations
We prove that many of the boundary properties associated with functions in the classic holomorphic Hardy spaces on the complex unit disk are present in Hardy classes of solutions to certain nonhomogeneous Cauchy-Riemann equations and higher-order generalizations of these equations. Also, we explicitly solve generalizations of the Schwarz boundary value problem on the complex unit disk and the upper-half plane when the boundary condition is in terms of boundary values in the sense of distributions.
Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi
Optimal Control Frameworks For A Class Of Epidemiological And Oncological Models, Asma Ali H Alghamdi
Mathematics Dissertations - Archive
In this thesis, we employ optimal control frameworks in two distinct contexts: Human immunodeficiency virus (HIV) and esophageal cancer. For HIV, we introduce a comprehensive data-driven nonlinear optimization framework designed for personalized therapies. This framework utilizes a deterministic in-host nonlinear ordinary differential equation (ODE) model and formulates two optimization problems using individual patient data. The first problem focuses on estimating patient-specific parameters through constrained optimization, while the second problem determines optimal combination therapies to reduce viral load to undetectable levels. Several numerical experiments suggest that our framework can provide a robust and effective optimal dosages with lower toxicity levels to …
Using A Degree-Based Network Model To Understand And Control Traffic Jams In The Atlanta Metropolitan Area, Ian Salamone-Lent, Theresa Washington, Asma Azizi
Using A Degree-Based Network Model To Understand And Control Traffic Jams In The Atlanta Metropolitan Area, Ian Salamone-Lent, Theresa Washington, Asma Azizi
The Kennesaw Journal of Undergraduate Research
Traffic congestion is an enduring problem for major metropolitan areas, such as Atlanta, GA. Our goal is to understand the nature of traffic congestion patterns in the highway system of Cobb County in Atlanta, GA. We created a road network representative of the Cobb County highway system and then superimposed a degree-based SIR model to simulate traffic congestion on that network. The model’s parameters, propagation and dissipation rates, were estimated using empirical traffic data, which are vehicles’ speed time series and speed limit of each road in the network. We then conducted a local sensitivity analysis of the model’s key …
Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, Huan Phan-Van, Keqin Gu
Structured Invariant Subspace And Decomposition Of Systems With Time Delays And Uncertainties, Huan Phan-Van, Keqin Gu
SIUE Faculty Research, Scholarship, and Creative Activity
This article discusses invariant subspaces of a matrix with a given partition structure. The existence of a nontrivial structured invariant subspace is equivalent to the possibility of decomposing the associated system with multiple feedback blocks such that the feedback operators are subject to a given constraint. The formulation is especially useful in the stability analysis of time-delay systems using the Lyapunov-Krasovskii functional approach where computational efficiency is essential in order to achieve accuracy for large scale systems. The set of all structured invariant subspaces are obtained (thus all possible decompositions are obtained as a result) for the coupled differential-difference equations …
A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd
A Class Of Game-Theoretic And Fokker-Planck Optimal Control Frameworks In Colon And Esophageal Cancer, Mesfer Alajmi Phd
Mathematics Dissertations - Archive
In this dissertation, we first present a new stochastic framework for parameter estimation and uncertainty quantification in colon cancer-induced immune responses. A stochastic process that captures the system's inherent randomness determines the dynamics of colon cancer. The stochastic framework is based on the Fokker-Planck equation, which represents the evolution of the probability density function corresponding to the stochastic process. We formulate an optimization problem that takes individual patient data with randomness present and solves it to obtain the unknown parameters corresponding to the individual tumor characteristics. Furthermore, we perform a sensitivity analysis of the optimal parameter set to identify the …
Robot-Based 3d Printing, Aaron Hoffman
Robot-Based 3d Printing, Aaron Hoffman
Williams Honors College, Honors Research Projects
Details of a large-format 3D printer created to print experimental materials, test multi-axis print techniques, and quickly print large objects. The printer consists of a 7-axis robotic arm and pellet extruder, which are controlled by a PC. Experimental materials such as recycled polymers or carbon-fiber reinforced materials can be easily tested with the pellet format of the extruder. The printer can perform different printing techniques and can be used to experiment with material properties when using these techniques with different polymers. The print surface is around 5 times larger than the average commercial 3D printer, and the robotic arm provides …
Optimizing Microbe-Infected Mosquito Release: A Stochastic Model For Malaria Prevention, Steeven Belvinos Affognon, Henri E.Z. Tonnang, Philip Ngare, Benard Kipchumba Kiplangat, Shirley Abelman, Jeremy K. Herren
Optimizing Microbe-Infected Mosquito Release: A Stochastic Model For Malaria Prevention, Steeven Belvinos Affognon, Henri E.Z. Tonnang, Philip Ngare, Benard Kipchumba Kiplangat, Shirley Abelman, Jeremy K. Herren
All Peer-Reviewed Publications
Malaria remains a critical public health challenge in Africa, demanding innovative control strategies. This study introduces a novel approach using Microsporidia MB-infected mosquitoes and stochastic optimal control within a Lévy process framework to regulate mosquito release strategies. The primary goal is to optimize Microsporidia MB prevalence within mosquito populations to disrupt Plasmodium transmission to humans. By incorporating Lévy noise into the modeling process, we capture the inherent randomness of mosquito dynamics, improving intervention accuracy. The model, guided by the Hamilton–Jacobi–Bellman (HJB) equation, optimizes release protocols while accounting for key environmental factors like seasonality and temperature fluctuations. Results show that intervention …