Stochastic Modeling and Optimal Control for Colloidal Organization, Navigation, and Machines

Colloidal suspensions consisting of particles undergoing Brownian motion are ubiquitous in scientific research and emerging technologies. Longstanding challenges in strategic control of complex colloidal systems are to investigate the principle of optimal control, overcome the curse of dimensionality, design efficient algorithms, and develop generalizable control strategies. In the first part of this dissertation, we present methods and results from three case studies to illustrate how these challenges are addressed from the perspectives of modeling and optimal control. Single-agent optimal navigation in complex mazes. We investigate the optimal navigation principle of a self-propelled colloidal particle in complex mazes. We construct approximate Markov chain model and use the Markov decision process framework to obtain the general principle of optimal navigation. Multiple-agent cooperation and coordination for colloidal machines. Using self-propelled Janus motors as the model system, we illustrate a new paradigm for cargo capture and transport based on multiple-agent feedback control. The control algorithm can coordinate multiple motors to cooperate on forming a reconfigurable machine for cargo capture and transport. Low-dimensional modeling and ensemble control. Optimal control in a high dimensional self-assembly processes with limited actuations presents a challenge in both modelling and controller design. We use colloidal crystallization in an electric field as a model system to illustrate the methodologies of low-dimensional modeling and control for self-assembly processes. We use a nonlinear machine learning algorithm to characterize the dimensionality and parametrize the low-dimension manifold on which the system evolves. A low-dimensional Smoluchowski model is constructed and calibrated to illustrate the dynamic pathways of the assembly process. The resulting model is further leveraged to perform optimal control of the assembly process. In the second part of dissertation, we report three additional relevant research projects on colloidal interaction, dynamics, and control. The first project extends ensemble control from finite-size systems to infinite-size systems using feedback control in sedimentation. The second project develops a computational method to model depletion interactions between general geometric objects The third project develops modified Stokesian dynamics methods to investigate the colloidal rod motion near a planar wall with hydrodynamic interactions

A framework for understanding and controlling batch cooling crystallization

In taking a different view of crystallization dynamics, this thesis reveals a new framework for addressing a prevalent process engineering challenge: control over the size of crystals produced by batch cooling crystallization. The thesis divides roughly into halves. In the first half, the crystal size control problem is introduced and the proposed framework for addressing this problem—termed the mass-count (MC) framework—is developed. This new framework is laid out along side the population balance (PB) framework, which is the prevailing framework for modeling crystallization dynamics and addressing the crystal size control problem. In putting the proposed and established frameworks side by side, the intent is not to say that one or the other is correct. Rather, the point is to show that they are different perspectives that facilitate different control approaches. The PB framework is built up from first principles; it is intellectually stimulating and mathematically complete, but it has a drawback for application: it does not directly enable feedback control. The MC framework, on the other hand, takes a less detailed view of crystallization dynamics and does not connect to crystallization theory as directly; it is also more conducive to application. In the second half of the thesis, the utility of the MC framework is put to the test. The framework is first applied to understand and model the crystallization dynamics for two widely different systems: darapskite salt crystallization from water and paracetamol crystallization from ethanol. Once the dynamics have been modeled, the framework is then used to develop feedback control schemes. These schemes are applied to both experimental systems and, in both cases, crystal size control is demonstrated.Ph.D