CPU- and GPU-Based Parallelization of the Robust Reference Governor

TL;DR

This work addresses the computational challenge of enforcing constraints in nonlinear dynamical systems via a robust Reference Governor (RG). It introduces a scenario-based robust RG that handles disturbances by sampling $N_{\text{sim}}$ disturbance sequences and evaluating a grid of $\kappa$ values, enabling parallel execution on multi-core CPUs and CUDA-enabled GPUs; mathematical dependencies are preserved with $v_t = v_{t-1} + \kappa (r_t - v_{t-1})$ and $y_{ss}(v)$ constraints. The authors develop CPU and GPU parallelization strategies, map simulations to a $M \times N_{\text{sim}}$ task grid, and demonstrate substantial performance gains, including up to three orders of magnitude speedups on GPUs, using a nonlinear hydrogen fuel cell model with $j^*=1024$ and $N_{\text{sim}}=8192$. The results show that the robust RG can be implemented in real time on parallel hardware, greatly expanding the practicality of nonlinear, robust constraint enforcement in embedded control systems. The work also outlines future directions, including theoretical guarantees of probabilistic recursive feasibility, precision considerations on GPUs, and extensions to higher-dimensional plants and embedded platforms.

Abstract

Constraint management is a central challenge in modern control systems. A solution is the Reference Governor (RG), which is an add-on strategy to pre-stabilized feedback control systems to enforce state and input constraints by shaping the reference command. While robust formulations of RG exist for linear systems, their extension to nonlinear systems is often computationally intractable. This paper develops a scenario-based robust RG formulation for nonlinear systems and investigates its parallel implementation on multi-core CPUs and CUDA-enabled GPUs. We analyze the computational structure of the algorithm, identify parallelization opportunities, and implement the resulting schemes on modern parallel hardware. Benchmarking on a nonlinear hydrogen fuel cell model demonstrates order-of-magnitude speedups (by as much as three orders of magnitude) compared to sequential implementations.

Figures (5)

• Figure 1: Reference Governor block diagram. The variable $t$ is the discrete time index, $r_t$ is the desired setpoint at timestep $t$, $v_t$ is the modified setpoint, $y_t$ is the constrained output, and ${x}_t$ is the estimated state (or the true state, if available). The goal of RG is to maintain $y_t \in \mathbb{Y}$ for a given constraint set $\mathbb{Y}$.
• Figure 2: Fuel Cell Simulation
• Figure 3: Desktop PC Benchmark (1-32 Disturbances). RTX traces denote GPU implementation; Ryzen traces denote CPU implementations. $N_{\text{sim}}$ on the x-axis denotes the number of disturbance scenarios considered.
• Figure 4: Desktop PC Benchmark (32-8192 Disturbances). RTX traces denote GPU implementation; Ryzen traces denote CPU implementations.
• Figure 5: Laptop PC Benchmark (32-8192 Disturbances). RTX traces denote GPU implementation; i7 traces denote CPU implementations.

Theorems & Definitions (1)

• Remark 1