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
