2022 Annual Meeting

(11e) Bayesian Optimization for Performance-Oriented Model Learning: An Application to Learning-Based Predictive and Parameter-Varying Control of Cold Plasmas

Authors

Kimberly Chan - Presenter, University of California, Berkeley
Yajie Bao, University of Georgia
Ali Mesbah, University of California, Berkeley
Javad Mohammadpour Velni, University of Georgia
Cold atmospheric plasma (CAP) treatment has become a promising technology for biomedical applications [1]. CAPs are a class of weakly ionized gasses that exist at ambient temperature and pressure. This non-equilibrium existence enables CAPs to exhibit an assortment of synergistic effects that have shown to elicit effective decontamination [2], [3] as well as therapeutic effects, including activating wound healing in chronic wounds [4] and selectively killing cancerous cells [5]. A clear challenge to bringing CAP treatments to practice is the safe and effective control of the CAP administration to surfaces and biological media. Modeling plasma effects on complex interfaces plays a key role in effective control [6], [7], but faces several challenges: (i) plasma behavior/dynamics are intricate and span over several length and time scales [8]; (ii) plasma interactions with varied interfaces are poorly understood and thus hard to model and poorly understood [9]; and (iii) highly-fidelity plasma models are computationally expensive for control design purposes [10].

In one aspect, the modeling challenges may be addressed by the abundance of work in robust and stochastic model-based control [11], [12]. These strategies deal with the available reduced- order models by systematically accounting for model uncertainties and disturbances in the control formulation. [13], [14]. While useful in ensuring robust controller performance, these strategies can suffer from overly-conservative control actions, as well as the inability account for the time-varying nature of plasma systems. An alternative perspective to combat the modeling challenges emphasizes the performance-oriented quality of models over the general predictive quality, i.e., the notion of identification for control (I4C) [15]. Traditionally, models are developed independent of how their predictive quality impacts closed-loop control performance. In I4C, model development coincides with closed-loop performance, and relies on the idea that the best-performing model may not be the best predictive model. This implies that data-driven models should be identified or adapted with respect to predefined closed-loop performance metrics.

In this work, we demonstrate the a performance-oriented model learning approach for the control of CAPs for biomedical applications. In particular, we use Bayesian optimization (BO) [16] for the performance-oriented model adaptation of artificial neural network (ANN)-based linear parameter-varying (LPV) models utilized for model predictive control (MPC) of atmospheric pressure plasma jets (APPJs). We consider the use of APPJs to deliver a desired amount of thermal effects to heat-sensitive bio-materials [17], [18]. First, we developed a nominal data-driven LPV plasma model to capture the nonlinear dynamics over the operating window for plasma treatment using ANNs [19]. The strategy for this initial identification has been termed state integrated matrix estimation, which simultaneously estimates the state(s) and model matrix functions which have been approximated by ANNs [19]. This model is then used in a MPC which optimizes control actions for the delivery of the the desired thermal effects. For model adaptation and taking inspiration from transfer learning, we freeze the ANN representations of the state-space LPV model except the last layers, which are updated based on new closed-loop data. BO is used to guide the performance-oriented model learning by adapting the neural network parameters of the last layers. In this way, BO balances exploration of new model parameters and exploitation of currently available information of the model based on previous data. In real-time experiments with a kHz-excited APPJ in Helium, we compare the performance-oriented strategy to closed-loop identification. We demonstrate that BO offers improved closed-loop performance compared to closed-loop identification with an equivalent number of process runs. Furthermore, we demonstrate the capability of such a performance-oriented strategy to overcome variations in the system environment by testing the strategy’s performance over substrates with significantly different properties. A mismatched model-substrate environment can be overcome with this strategy using an order of magnitude less data than needed to train the nominal model.

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