A Neural Network-based Multi-timestep Command Governor for Nonlinear Systems with Constraints

TL;DR

The paper tackles the challenge of enforcing nonlinear system constraints with high online computational cost by replacing the online NLP of the multi-timestep command governor (MCG) with an offline-trained regression NN (NN-MCG) that approximates the MCG map, followed by a sensitivity-based tightening to guarantee feasibility. The method yields a quadratically constrained optimization problem (QCQP/QP) in real time, significantly reducing computation while preserving near-MCG performance when the NN is well-trained. Applied to a fuel-cell air-path load governor, NN-MCG demonstrates substantial speedups (roughly 23×) over MCG with only modest performance loss, and successfully enforces surge, choke, and oxygen starvation constraints. This approach offers a practical route to real-time constraint management in fast nonlinear systems and opens avenues for deploying more advanced ML models in similar governor architectures.

Abstract

The multi-timestep command governor (MCG) is an add-on algorithm that enforces constraints by modifying, at each timestep, the reference command to a pre-stabilized control system. The MCG can be interpreted as a Model-Predictive Control scheme operating on the reference command. The implementation of MCG on nonlinear systems carries a heavy computational burden as it requires solving a nonlinear program with multiple decision variables at each timestep. This paper proposes a less computationally demanding alternative, based on approximating the MCG control law using a neural network (NN) trained on offline data. However, since the NN output may not always be constraint-admissible due to training errors, its output is adjusted using a sensitivity-based method. We thus refer to the resulting control strategy as the neural network-based MCG (NN-MCG). As validation, the proposed controller is applied as a load governor for constraint management in an automotive fuel cell system. It is shown that the proposed strategy is significantly more computationally efficient than the traditional MCG, while achieving nearly identical performance if the NN is well-trained.

Figures (5)

• Figure 1: constraint management schemes. The signals are as follows: $y(t)$ is the constrained output, $r(t)$ is the desired reference, $v(t)$ is the modified reference command, $V_{tn}(t)$ is the nominal input sequence, and $x(t)$ is the system state (measured or estimated).
• Figure 2: Simulation response without constraint management: Current, OER, and compressor state trajectories for step changes in current demand. The dashed lines indicate system constraints. The surge region lies to the left of the dashed red line (surge boundary) and the choke region lies to the right of the dashed green line (the choke boundary). The region below $\lambda _{O_{2} } = 1.9$ on the OER plot indicates oxygen starvation and should be avoided for durable operation of FC.
• Figure 3: Simulation results of the MCG applied to the FC system using a comprehensive reference profile for data collection.
• Figure 4: Sensitivity functions of the constrained outputs at a representative operating point.
• Figure 5: Naive NN and NN-MCG on Dynamic test

Theorems & Definitions (5)

• Remark 1
• Remark 2
• Remark 3
• Remark 4
• Remark 5