Markov state model-based optimal control for colloidal self-assembly

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Tang, Xun
Grover, Martha A.
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Colloidal self-assembly is widely studied as a promising route to manufacture highly ordered structures for applications as metamaterials. While near-equilibrium self-assembly could produce defect-free crystal, the time required is usually unmanageable in practical applications. On the contrary, rapid assembly via out-of-equilibrium approaches could reduce the amount of process time, but the assembled structure is usually terminated in defective states. Therefore, a gap exists between the speed and the quality of the structure in a colloidal self-assembly system. To overcome this challenge, this thesis proposes a model-based optimization framework for optimal feedback control over a colloidal self-assembly process for rapid assembly of defect-free two-dimensional crystals. The proposed framework features: first, the use of an externally applied electric field as a global actuator to influence the particle movement; second, the use of two order parameters to represent the high-dimensional system in a reduced dimension state space; third, the use of the Markov state model to capture the stochasticity in the system; fourth, the use of dynamic programming to design the optimal control policy; and fifth, the use of an optical microscope for in situ measurements as feedback. The feasibility of the framework is first demonstrated with a static optimal control policy, and its performance is evaluated against fast quench and near-equilibrium approaches. The framework is then expanded to construct a time-dependent optimal control policy, and the performance is compared with widely used time-varying control strategies in both simulation and experiments. The refinement of the framework, more specifically, the construction of the Markov state model is also revisited for better efficiency. The major contributions of this thesis include: (1) it proposes a novel approach to rapidly control colloidal self-assembly processes for perfect crystal with optimal control theories; (2) it demonstrates for the first time in lab, the realization of optimal feedback control of a colloidal self-assembly process; (3) it reveals the benefits of feedback in a stochastic process control, not only to compensate for model inaccuracy, but also to shorten the process time; (4) it also investigates the Markov state model accuracy and provides a more efficient construction of accurate Markov state models. The framework in this study is built on first-principle concepts, and it can be generalized to any molecular, nano-, or micro-scale assembly process where there exists a global actuator to affect the dynamics, a model to represent the relation between the actuator and the system, and a measurement of system state for feedback. Since micron-sized colloidal particles also serve as model systems to study the phase transition behavior and crystallization kinetics for atomic and molecular crystals, the framework can also be extended to these systems for optimal control.
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