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1. A Control Lyapunov Function-Based Approach for Particle Nanomanipulation via Optical Tweezers

   Golgoon, Melika; Mohammadi, Alireza; Spong, Mark W (July 2024, 2024 American Control Conference)

   Considering the non-affine-in-control system governing the motion of a spherical particle trapped inside an optical tweezer, this paper investigates the problem of stabilization of the particle position at the origin through a control Lyapunov function (CLF) framework. The proposed CLF framework enables nonlinear optimization-based closed-loop control of position of tiny beads using optical tweezers and serves as a first step towards design of effective control algorithms for nanomanipulation of biomolecules. After deriving necessary and sufficient conditions for having smooth uniform CLFs for the optical tweezer control system under study, we present a static nonlinear programming problem (NLP) for generation of robustly stabilizing feedback control inputs. Furthermore, the NLP can be solved in real-time with no need for running computationally demanding algorithms. Numerical simulations demonstrate the effectiveness of the proposed control framework in the presence of external disturbances and initial bead positions that are located far away from the laser beam. 

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2. 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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3. Reinforcement Learning for Safety-Critical Control under Model Uncertainty, using Control Lyapunov Functions and Control Barrier Functions

   Choi, Jason; Castañeda, Fernando; Tomlin, Claire J.; Sreenath, Koushil (July 2020, Robotics: Science and Systems (RSS))

   In this paper, the issue of model uncertainty in safety-critical control is addressed with a data-driven approach. For this purpose, we utilize the structure of an input-output linearization controller based on a nominal model along with a Control Barrier Function and Control Lyapunov Function based Quadratic Program (CBF-CLF-QP). Specifically, we propose a novel reinforcement learning framework which learns the model uncertainty present in the CBF and CLF constraints, as well as other control-affine dynamic constraints in the quadratic program. The trained policy is combined with the nominal model based CBF-CLF-QP, resulting in the Reinforcement Learning based CBF-CLF-QP (RL-CBF-CLF-QP), which addresses the problem of model uncertainty in the safety constraints. The performance of the proposed method is validated by testing it on an underactuated nonlinear bipedal robot walking on randomly spaced stepping stones with one step preview, obtaining stable and safe walking under model uncertainty. 

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4. Reinforcement Learning Enabled Safety-Critical Tracking of Automated Vehicles with Uncertainties via Integrated Control-Dependent, Time-Varying Barrier Function, and Control Lyapunov Function

   https://doi.org/10.1016/j.ifacol.2023.12.005  

   Meng, Jingxiong; Zhao, Junfeng; Chen, Yan (December 2023, IFAC-PapersOnLine)

   Model uncertainties are considered in a learning-based control framework that combines control dependent barrier function (CDBF), time-varying control barrier function (TCBF), and control Lyapunov function (CLF). Tracking control is achieved by CLF, while safety-critical constraints during tracking are guaranteed by CDBF and TCBF. A reinforcement learning (RL) method is applied to jointly learn model uncertainties that related to CDBF, TCBF, and CLF. The learning-based framework eventually formulates a quadratic programming (QP) with different constraints of CDBF, TCBF and CLF involving model uncertainties. It is the first time to apply the proposed learning-based framework for safety-guaranteed tracking control of automated vehicles with uncertainties. The control performances are validated for two different single-lane change maneuvers via Simulink/CarSim® co-simulation and compared for the cases with and without learning. Moreover, the learning effects are discussed through explainable constraints in the QP formulation. 

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5. Chetaev Instability Framework for Kinetostatic Compliance-Based Protein Unfolding

   https://doi.org/10.1109/LCSYS.2022.3176433  

   Mohammadi, A; Spong, Mark W. (January 2022, IEEE Control Systems Letters)

   Understanding the process of protein unfolding plays a crucial role in various applications such as design of folding-based protein engines. Using the well-established kinetostatic compliance (KCM)-based method for modeling of protein conformation dynamics and a recent nonlinear control theoretic approach to KCM-based protein folding, this letter formulates protein unfolding as a destabilizing control analysis/synthesis problem. In light of this formulation, it is shown that the Chetaev instability framework can be used to investigate the KCM-based unfolding dynamics. In particular, a Chetaev function for analysis of unfolding dynamics under the effect of optical tweezers and a class of control Chetaev functions for synthesizing control inputs that elongate protein strands from their folded conformations are presented. Based on the presented control Chetaev function, an unfolding input is derived from the Artstein-Sontag universal formula and the results are compared against optical tweezer-based unfolding. 

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