Scenario-based optimization and control has proven to be an efficient approach to account for system uncertainty. In particular, the performance of scenario-based model predictive control (MPC) schemes depends on the accuracy of uncertainty quantification. However, current learning-and scenario-based MPC (sMPC) approaches employ a single timeinvariant probabilistic model (learned offline), which may not accurately describe time-varying uncertainties. Instead, this paper presents a model-agnostic meta-learning (MAML) of Bayesian neural networks (BNN) for adaptive uncertainty quantification that would be subsequently used for adaptive-scenario-tree model predictive control design of nonlinear systems with unknown dynamics to enhance control performance. In particular, the proposed approach learns both a global BNN model and an updating law to refine the BNN model. At each time step, the updating law transforms the global BNN model into more precise local BNN models in real time. The adapted local model is then used to generate scenarios for sMPC design at each time step. A probabilistic safety certificate is incorporated in the scenario generation to ensure that the trajectories of the generated scenarios contain the real trajectory of the system and that all the scenarios adhere to the constraints with a high probability. Experiments using closed-loop simulations of a numerical example demonstrate that the proposed approach can improve the performance of scenario-based MPC compared to using only one BNN model learned offline for all time steps.

The implementation of nonlinear model predictive control (NMPC) in applications with fast dynamics remains an open challenge due to the need to solve a potentially non-convex optimization problem in real-time. The offline approximation of NMPC laws using deep learning has emerged as a powerful framework for overcoming these challenges in terms of speed and resource requirements. Deep neural networks (DNNs) are particularly attractive for embedded applications due to their small memory footprint. This work introduces a strategy for achieving offset-free tracking despite the presence of error in DNN-based approximate NMPC. The proposed approach involves a correction factor defined via a small-scale target tracking optimization problem, which is easier to approximate than the tracking NMPC law itself. As such, the overall control strategy is amenable to efficient implementations on low-cost embedded hardware. The effectiveness of the proposed offsetfree DNN-based NMPC is demonstrated on a benchmark problem in which the control strategy is deployed onto a field programmable gate array (FPGA) architecture that is verified using hardware-in-the-loop simulations.

Cold atmospheric plasmas (CAPs) are increasingly used for applications requiring the processing of heat-and pressure-sensitive (bio)materials. A key challenge in modelbased 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 paper 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 kHz-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.

Plasma medicine has emerged as a promising approach for treatment of biofilm-related and virus infections, assistance in cancer treatment, and treatment of wounds and skin diseases. Despite advances in learning-based and predictive control of plasma medical devices, there remain major challenges towards personalized and point-of-care plasma medicine. In particular, an important challenge arises from the need to adapt control policies after each treatment using (often limited) observations of therapeutic effects that can only be measured between treatments. Control policy adaptation is necessary to account for variable characteristics of plasma and target surfaces across different subjects and treatment scenarios, thus personalizing the plasma treatment to enhance its efficacy. To this end, this paper presents a data-efficient, "globally" optimal strategy to adapt deep learning-based controllers that can be readily embedded on resource-limited hardware for portable medical devices. The proposed strategy employs multi-objective Bayesian optimization to adapt parameters of a deep neural network (DNN)-based control law using observations of closedloop performance measures. The proposed strategy for adaptive DNN-based control is demonstrated experimentally on a cold atmospheric plasma jet with prototypical applications in plasma medicine.

Scenario-based model predictive control (MPC) methods can mitigate the conservativeness inherent to open-loop robust MPC. Yet, the scenarios are often generated offline based on worst-case uncertainty descriptions obtained a priori, which can in turn limit the improvements in the robust control performance.To this end, this paper presents a learning-based, adaptive-scenario-tree model predictive control approach for uncertain nonlinear systems with time-varying and/or hard-to-model dynamics. Bayesian neural networks (BNNs) are used to learn a state-and input-dependent description of model uncertainty, namely the mismatch between a nominal (physics-based or data-driven) model of a system and its actual dynamics. We first present a new approach for training robust BNNs (RBNNs) using probabilistic Lipschitz bounds to provide a less conservative uncertainty quantification. Then, we present an approach to evaluate the credible intervals of RBNN predictions and determine the number of samples required for estimating the credible intervals given a credible level. The performance of RBNNs is evaluated with respect to that of standard BNNs and Gaussian process (GP) as a basis of comparison. The RBNN description of plant-model mismatch with verified accurate credible intervals is employed to generate adaptive scenarios online for scenario-based MPC (sMPC). The proposed sMPC approach with adaptive scenario tree can improve the robust control performance with respect to sMPC with a fixed, worst-case scenario tree and with respect to an adaptive-scenario-based MPC (asMPC) using GP regression on a cold atmospheric plasma system. Furthermore, closed-loop simulation results illustrate that robust model uncertainty learning via RBNNs can enhance the probability of constraint satisfaction of asMPC.