Data-Driven Adaptive Optimal Control Under Model Uncertainty: An Application to Cold Atmospheric Plasmas

Cold atmospheric plasmas (CAPs) are increasingly used for applications requiring the processing of heat- and pressure-sensitive (bio)materials. A key challenge in model-based control of CAPs arises from the high-computational requirements of theoretical plasma models as well as lack of mechanistic understanding of plasma-surface interactions. Thus, control strategies that rely on simple, physics-based models that can be adapted to mitigate plant-model mismatch will be particularly advantageous for CAP applications. This article presents an optimal control approach for controlling the nonlinear and cumulative effects of CAPs delivered to a target surface using a simple system model. Through parsimonious input parameterization, the solution to the optimal control problem (OCP) is given by an arc sequence that does not include any singular arcs. A data-driven adaptive algorithm based on modifier adaptation is proposed to deal with the structural plant-model mismatch by estimating the mismatch in the cost and constraints of the OCP. The adaptive approach is shown to converge to a Karush–Kuhn–Tucker (KKT) point of the OCP for the true system. Moreover, a control strategy based on feedback linearization and derivative estimation is proposed for online tracking of path constraints in the presence of disturbances and model uncertainty. The proposed approach is demonstrated by simulations and real-time control experiments on a kilohertz-excited atmospheric pressure plasma jet in helium, in which the plasma treatment time is minimized while delivering a desired amount of nonlinear thermal effects to the target surface.