Potential Canals for Control of Nonlinear Stochastic Systems in the Absence of State Measurements

This paper considers design of an open-loop control to direct the state of a nonlinear stochastic system from a random initial state toward a targeted stable equilibrium generated by a predefined constant control. Under this constant control, the system is assumed to have multiple stable equilibria, so that starting from a random initial state, the system can settle eventually at any of these equilibria, not necessarily the targeted one. To direct the system toward the targeted equilibrium, an initial phase of dynamic (time-varying) control is needed before application of the constant control. The concept of potential canal is introduced in this paper to develop a methodology for design of such dynamic control. This methodology is primarily intended to be used in directed self-assembly—a technology for ordering charged nanoparticles into desired nanostructures by manipulating external electrical fields. The features of the developed control are demonstrated for directed self-assembly in one dimension.