Deep Learning-based Approximate Nonlinear Model Predictive Control with Offset-free Tracking for Embedded Applications

Abstract

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.

Plasma Control: A Review of Developments and Applications of Plasma Medicine Control Mechanisms

“…Plasma medicine can draw parallels to the use of PI controls for plasmas from the successes displayed in fusion applications, where they were first implemented to actively maintain plasma temperature within tokamaks [101]. Similarly, plasma medicine today is expanding and innovating on these early approaches by using PID [102] and MPC [103] controllers to maintain temperature and deposited power for biological substrates. The concept of utilizing reinforcement learning to achieve more flexibility and control of plasmas was also employed to unprecedented success in fusion applications once trained on a simulator model [60].…”

“…The newly founded approach labeled as "personalized control" has produced an adaptive control model that was explored earlier in this review (Section 3.1.1), but in the context of retroactively calibrating the plasma process to avoid drifts during the treatment. Yet, by configuring this approach, of Bayesian optimization, towards personalized and point-of-care plasma medicine the ability to actively adjust treatment parameters with complex substrates becomes attainable as demonstrated by Chan et al Within Chan et al's work a DNN approximated MPC is utilized for controlling the power and flow rate of an APPJ to deliver a desired amount of plasma effects, as quickly as possible, without violating comfort and safety constraints [103]. Unlike BO which can be used to optimize the active process, a multi-output BO (MOBO) can be used to adapt and train DNN parameters for real-time applications by the MPC scheme.…”

“…Unlike BO which can be used to optimize the active process, a multi-output BO (MOBO) can be used to adapt and train DNN parameters for real-time applications by the MPC scheme. Each step of the closed-loop trajectory is a solution and represents a suitable situation in which the closed-loop system is likely to operate [103]. The results demonstrated MOBO could efficiently explore the parameter space of a DNN trained controller in closed-loop simulations to identify and adjust the treatment parameters to stay within acceptable treatment times in relation to the thermal dose being provided.…”

Towards Personalized Plasma Medicine via Data-Efficient Adaptation of Fast Deep Learning-based MPC Policies

“…While BO is commonly used to facilitate hyperparameter tuning, this work focuses on using BO to adapt DNN parameters. Here, the DNN is trained using closed-loop data as described in, e.g., [19]. This way, each step of the closed-loop trajectory is a solution to (5) and represents a suitable situation in which the closed-loop system is likely to operate.…”

“…Approximate MPC [17], which hinges on approximating MPC laws via offline computations of the optimal control problem, enables control of CAP devices at kHz sampling rates [18]. Deep neural network (DNN)-based approximations of MPC laws are especially attractive due to their low memory footprint and versatile embedded implementations on resource-limited, specialized hardware such as field programmable gate arrays (FPGAs) [19], [20]. For plasma treatment of complex interfaces, it is imperative to adapt control policies to account for the variability among different target surfaces, in addition to the time-varying nature of the plasma and surface characteristics.…”