(744d) Embedded Deep Learning-Based Robust Model Predictive Control for Fast-Sampling Atmospheric Pressure Plasma Jets Using Field Programmable Gate Arrays

With the increasing need for optimal control of complex and safety-critical systems, there has been a growing interest in model predictive control (MPC) strategies that are fast, while also guaranteeing safety and achieving high-performance system operation. Generally, robust and stochastic MPC methods are often computationally expensive, which renders them inapt for fast-sampling system applications. Thus, there has been extensive work on fast MPC. One class of fast MPC methods is based on fast optimization techniques [1], [2]. Alternatively, learning methods, such as deep learning, are becoming increasingly viable options for deriving cheap-to-evaluate, explicit surrogates for robust MPC laws [3], [4]. It has recently been shown that deep neural network- (DNN) based approximation of robust MPC laws are useful not only for their quick evaluation time, but also for their potential low-memory footprint [5], [6], [7], which is especially important for controller implementation on resource-limited hardware. Implementation of approximate MPC laws on embedded systems has become increasingly desired as it addresses the limitation of latency between capturing data and receiving results to perform an operation due to the nature of system level modeling languages on the software side and direct implementation of the “system on chip” (SoC) on the hardware side [8]. Despite this, there remains several open challenges pertaining to efficient and reliable hardware implementation of embedded DNN-based controllers [9].

In this work, we investigate embedded implementation of a DNN-based approximate robust MPC strategy to control the effects of a fast-sampling atmospheric pressure plasma jet (APPJ) with prototypical applications in plasma medicine. APPJs are increasingly being considered for use in biomedical applications [10], [11], for example, to shrink cancerous tumors [12], increase the rate of wound healing [13], and deactivate antibiotic-resistant bacteria [14]. However, controlling the nonlinear effects of the plasma on the target substrate in the presence of intrinsic variabilities as well as exogenous disturbances is crucial in achieving safe and effective operation of the APPJ. In addition, the fast dynamics of the APPJ require fast control implementations [15]. To this end, we first develop an approximate closed-loop robust MPC strategy, where a scenario-based MPC problem is solved offline to train the DNN. Once the DNN is trained, it is deployed onto a proposed field programmable gate array (FPGA) architecture. FPGAs are chosen not only because of their increased computational power over standard microcontrollers, but also because of their configurability and potential to further speed up control performance via methods such as parallelization and pipelining [16]. We investigate the FPGA implementation and the memory footprint of the DNN-based controller in relation to the complexity of the underlying system model, control policy parametrization, prediction horizon, as well as amount of data used to learn the DNN-based controller. The embedded implementation is performed first as prototyping and designing the DNN-based controller in a system-level language, and then testing in both computer simulations and hardware-in-loop simulations. Real-time control experiments on an APPJ testbed demonstrate the effectiveness of the proposed embedded DNN-based robust MPC strategy in controlling the highly nonlinear APPJ at fast time-scales for use in biomedical applications.

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