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1. Lyapunov-Based Nonlinear Control Strategies for Manipulation of Particles and Biomolecules Using Optical Tweezers

   Golgoon, Melika (December 2024, UTD Theses and Dissertations)

   Tweezers-based nanorobots, optical tweezers in particular, are renowned for their exceptional precision, and among their biomedical applications are cellular manipulation, unzipping DNAs, and elongating polypeptide chains. This thesis introduces a series of Lyapunov-based feedback control frameworks that address both stability and controlled instability for biological manipulation, applied within the context of optical tweezers. At the core of this work are novel controllers that stabilize or destabilize specific molecular configurations, enabling fine manipulation of particles like polystyrene beads and tethered polymers under focused laser beams. Chapter 1 covers the foundational principles and surveys existing literature on the modeling and control of optical tweezers, emphasizing gaps in the stability and instability control of molecular systems. Chapter 2 presents a robust Control Lyapunov Function (CLF) approach, designed to stabilize spherical particles under optical trapping. By formulating a smooth, norm-bounded feedback controller, we achieve lateral stabilization despite external disturbances, using a real-time, static nonlinear programming (NLP) solution. Simulations verify the effectiveness of this CLF framework, even with significant initial displacements from the laser focus and under thermal forces modeled as a white Gaussian noise. Chapter 3 addresses controlled instability through a Control Chetaev Function (CCF) framework, specifically targeting protein unfolding applications. Linearization with respect to the control input facilitates the application of destabilizing universal controls for affine- in-control system dynamics. The resulting CCF-based norm-bounded feedback controller induces system instability by laterally extending the trapped DNA handle, thereby increasing the molecular extension and providing insights into protein denaturation and unfolding pathways. This controller is robust to stochastic thermal forces and optimized for real-time computational efficiency. These Lyapunov and Chetaev-based control designs collectively expand the capabilities of optical tweezers, advancing single-molecule manipulation under both stable and unstable conditions. These findings advance precision nanomanipulation, opening new avenues for exploring the molecular mechanics of protein unfolding and DNA elasticity. 

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2. Active Control and Sustained Oscillations in actSIS Epidemic Dynamics

   Zhou, Yunxiu; Levin, Simon A.; Leonard, Naomi Ehrich (December 2020, 3rd IFAC Workshop on Cyber-Physical & Human Systems)

   null (Ed.)

   An actively controlled Susceptible-Infected-Susceptible (actSIS) contagion model is presented for studying epidemic dynamics with continuous-time feedback control of infection rates. Our work is inspired by the observation that epidemics can be controlled through decentralized disease-control strategies such as quarantining, sheltering in place, social distancing, etc., where individuals can actively modify their contact rates in response to observations of the infection levels in the population. Accounting for a time lag in observations and categorizing individuals into distinct sub-populations based on their risk profiles, we show that the actSIS model manifests qualitatively different features as compared with the SIS model. In a homogeneous population of risk-averters, the endemic equilibrium is always reduced, although the transient infection level can overshoot or undershoot. In a homogeneous population of risk-tolerating individuals, the system exhibits bistability, which can also lead to reduced infection. For a heterogeneous population comprised of risk-tolerators and risk-averters, we prove conditions on model parameters for the existence of a Hopf bifurcation and sustained oscillations in the infected population. 

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3. Periodic event‐triggered control for incrementally quadratic nonlinear systems

   https://doi.org/10.1002/rnc.5537  

   Xu, Xiangru; Tahir, Adam M.; Açıkmeşe, Behçet (April 2021, International Journal of Robust and Nonlinear Control)

   Abstract Periodic event‐triggered control (PETC) evaluates triggering conditions only at periodic sampling times, based on which it is decided whether the controller needs to be updated. This article investigates the global stabilization of nonlinear systems that are affected by external disturbances under PETC mechanisms. Sufficient conditions are provided to ensure the resulting closed‐loop system is input‐to‐state stable (ISS) for the state feedback and the observer‐based output feedback configurations separately. The sampling period and the triggering functions are chosen such that the ISS‐Lyapunov function of continuous dynamics is also the ISS‐Lyapunov function of the overall system. Based on that, sufficient conditions in the form of linear matrix inequalities are provided for the PETC design of incrementally quadratic nonlinear systems. Two simulation examples are provided to illustrate the effectiveness of the proposed method. 

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4. Lyapunov Neural Network with Region of Attraction Search

   https://doi.org/10.23919/ACC60939.2024.10644877  

   Wang, Zili; Andersson, Sean B; Tron, Roberto (July 2024, Proceedings of the American Control Conference)

   Deep learning methods have been widely used in robotic applications, making learning-enabled control design for complex nonlinear systems a promising direction. Although deep reinforcement learning methods have demonstrated impressive empirical performance, they lack the stability guarantees that are important in safety-critical situations. One way to provide these guarantees is to learn Lyapunov certificates alongside control policies. There are three related problems: 1) verify that a given Lyapunov function candidate satisfies the conditions for a given controller on a region, 2) find a valid Lyapunov function and controller on a given region, and 3) find a valid Lyapunov function and a controller such that the region of attraction is as large as possible. Previous work has shown that if the dynamics are piecewise linear, it is possible to solve problem 1) and 2) by solving a Mixed-Integer Linear Program (MILP). In this work, we build upon this method by proposing a Lyapunov neural network that considers monotonicity over half spaces in different directions. We 1) propose a specific choice of Lyapunov function architecture that ensures non-negativity and a unique global minimum by construction, and 2) show that this can be leveraged to find the controller and Lyapunov certificates faster and with a larger valid region by maximizing the size of a square inscribed in a given level set. We apply our method to a 2D inverted pendulum, unicycle path following, a 3-D feedback system, and a 4-D cart pole system, and demonstrate it can shorten the training time by half compared to the baseline, as well as find a larger ROA. 

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5. Detecting and quantifying heterogeneity in susceptibility using contact tracing data

   https://doi.org/10.1371/journal.pcbi.1012310  

   Tuschhoff, Beth M; Kennedy, David A (July 2024, PLOS Computational Biology)

   Lau, Eric HY (Ed.)

   The presence of heterogeneity in susceptibility, differences between hosts in their likelihood of becoming infected, can fundamentally alter disease dynamics and public health responses, for example, by changing the final epidemic size, the duration of an epidemic, and even the vaccination threshold required to achieve herd immunity. Yet, heterogeneity in susceptibility is notoriously difficult to detect and measure, especially early in an epidemic. Here we develop a method that can be used to detect and estimate heterogeneity in susceptibility given contact by using contact tracing data, which are typically collected early in the course of an outbreak. This approach provides the capability, given sufficient data, to estimate and account for the effects of this heterogeneity before they become apparent during an epidemic. It additionally provides the capability to analyze the wealth of contact tracing data available for previous epidemics and estimate heterogeneity in susceptibility for disease systems in which it has never been estimated previously. The premise of our approach is that highly susceptible individuals become infected more often than less susceptible individuals, and so individuals not infected after appearing in contact networks should be less susceptible than average. This change in susceptibility can be detected and quantified when individuals show up in a second contact network after not being infected in the first. To develop our method, we simulated contact tracing data from artificial populations with known levels of heterogeneity in susceptibility according to underlying discrete or continuous distributions of susceptibilities. We analyzed these data to determine the parameter space under which we are able to detect heterogeneity and the accuracy with which we are able to estimate it. We found that our power to detect heterogeneity increases with larger sample sizes, greater heterogeneity, and intermediate fractions of contacts becoming infected in the discrete case or greater fractions of contacts becoming infected in the continuous case. We also found that we are able to reliably estimate heterogeneity and disease dynamics. Ultimately, this means that contact tracing data alone are sufficient to detect and quantify heterogeneity in susceptibility. 

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