Safe and Fast Learning-based Model Predictive Control of Nonlinear Systems with Applications to Cold Atmospheric Plasmas

Model predictive control (MPC) is a widely-used optimization-based control strategy for the control of multivariable constrained systems. However, the effectiveness of MPC is hindered by computational and modeling challenges, especially when dealing with systems that are hard-to-model, safety-critical, and/or exhibit fast sampling times. This has led to the advent of learning-based MPC (LB-MPC), which combines machine learning (ML) with MPC to address these challenges. Even so, enabling fast LB-MPC with safety guarantees remains an open area of research. Thus, the overarching objective of this dissertation is to develop novel LB-MPC frameworks to enable safe and fast predictive control of hard-to-model dynamical systems subject to uncertainty. This is primarily explored through the lens of real-time control of cold atmospheric plasmas (CAPs) towards automated processing of (bio)materials as well as automated medical applications./nSpecifically, the objective of this work is broken down into the following sub-aims: (i) control- oriented model learning with uncertainty quantification; (ii) safe control; and (iii) fast control. To learn a dynamical model for the purposes of control, we start from an approximate base (linear) state-space model and capture the plant-model mismatch using Gaussian Process (GP) regression. This is closely related to safe control, as it enables decoupling safety from performance. On the one hand, the GP term corrects the baseline model, while, on the other hand, it yields state-dependent uncertainty bounds in the form of confidence intervals, which can be used to provide safety guarantees; for example, using tube-based or scenario-based approaches. However, solving the MPC problem online, particularly when the GP regression is embedded in the model predictions, constitutes a significant bottleneck in terms of computational cost. In addition, robust approaches such as scenario-trees are notorious for their poor scalability with respect to both the number of scenarios as well as the prediction horizon. To this end, we use deep neural networks (DNNs) approximate the LB-MPC online to derive an explicit and cheap-to-evaluate control law along with a set projection step to retain safety guarantees./nThe proposed LB-MPC frameworks are implemented on a CAP system both in simulations and real-time control experiments. The main results are summarized below./n(i). Using ML to augment a base model within the MPC significantly improves closed-loop performance compared to MPC approaches that do not incorporate learning./n(ii). ML is a very powerful tool for quantifying the uncertainty of a model and thus providing less conservative safety guarantees for the controller. This is shown to enable safe operation in both robust and chance-constrained settings, which are lower-bounded by a pre-determined desired probability level./n(iii). Approximating the controller using DNNs can speed up computations by a factor of 10-100. Safety guarantees can be recovered by projecting the DNN-based system input onto a robust admissible input set, which can be constructed online based on already- existing invariance tools./nFurthermore, in order to examine the transferability of LB-MPC to other domains, we draw parallels with automated driving applications. Stability and recursive feasibility of various permutations of the proposed LB-MPC approaches are also investigated throughout this dissertation./nEven though this work develops novel LB-MPC frameworks to achieve safe and fast control of complex systems, there remain a plethora of open challenges to address in future work. Transferability of the proposed control algorithms to clinical settings for plasma medicine, fully embedded/point-of-care applications, scalable implementations (particularly as they relate to safety and invariance tools), and modeling of uncertain environments constitute only a few of the research directions that can be pursued towards a more automated world.

Advisor: Mesbah, Ali