Optimal Control of Colloid Delivery Based on Control Parameterization

The colloid delivery technology is widely used in many fields like biomedical engineering, environmental governance, and food processing. The main mechanism is focused on the diffusiophoresis, which induces the migration of colloidal particles by a gradient of the solute concentration. In this paper, a micro‐channel colloid delivery control system is designed, and based on established mathematical models, the optimal control problem of the terminal colloidal particle distribution in the dead‐end micro‐channel is proposed. As it is constrained by coupled partial differential equations, the methods of spatial discretization and control parameterization are introduced respectively to convert the optimal control problem into a finite‐dimensional nonlinear programming problem. The methods of gradient computation and gradient‐based optimization algorithm are described in detail. To prove the effectiveness of the control method, a numerical simulation is conducted, and the results show that the colloidal particles are successfully delivered into the micro‐channel according to the target setting during the control time.