A neural controller takes over nonlinear time-optimal MPC: half the training data and 1 kHz instead of 1.4 Hz
Synopsis
Nonlinear time-optimal model predictive control (TOMPC) drives constrained systems to a target in minimum time, but online solving is too slow for fast dynamics. This work imitates a long-horizon, nonconvex TOMPC with hard terminal constraints using a neural network, and introduces self-informed sampling: the network also predicts time-to-go, and the expert solver is queried only where a rollout departs from time-optimal behavior. On a Furuta pendulum, this sampling reaches the performance of standard dataset aggregation in roughly one-third of the training time and less than half the data, while the resulting controller keeps the expert's region of attraction and GPU inference raises the control frequency from about 1.4 Hz to 1 kHz.
Interpretation
A neural network can replace online solving of nonlinear time-optimal MPC, keeping the expert controller's region of attraction while raising the control frequency by about three orders of magnitude. Earlier neural imitation mostly targeted quadratic tracking objectives and stayed in simulation, with few hardware demonstrations; the long-horizon, hard-terminal-constraint time-optimal form is expensive enough that even generating training data is limited. Over 1000 randomly sampled initial states of the Furuta pendulum, the expert MPC and the neural controller converge in the same fraction of cases, with a median convergence time of 1.62 s for the neural controller versus 1.35 s for the expert; GPU inference averages 0.409 ms with a 0.998 ms maximum, supporting up to about 1 kHz, while the expert MPC averages 114.165 ms with a maximum reliable frequency of about 1.36 Hz.
Training data need not cover the state space uniformly, because the network's own time-to-go prediction shows where expert labels are needed. Standard dataset aggregation (DAgger) queries the expert at every visited state alike, without distinguishing states already handled well from those still needing supervision. Replacing state selection with DAgger or with MC-dropout using 20 forward passes at a 30% dropout rate, self-informed sampling reaches comparable performance about three times faster and with less than half the training data.
The full training and control pipeline handles dataset correlation, conflicting expert labels, covariate shift, constraint satisfaction and model mismatch together, and swings up and stabilizes a physical Furuta pendulum. Prior work addressed these challenges separately, and a complete architecture integrating them was lacking. On hardware the I/O thread runs at 1 kHz and the neural controller at 250 Hz; the real state trajectory closely matches simulation, with high-frequency oscillatory control effort near the inverted equilibrium attributed to sensor noise and residual model mismatch, without compromising stability.
Perspective
The demonstrated setting is a long-horizon, nonconvex, hard-terminal-constraint time-optimal MPC on one Furuta pendulum, with simulation comparisons over 1000 randomly sampled initial states in the region of interest and a hardware swing-up and stabilization task. Readers should treat it as a demonstration for this plant and this MPC formulation, not a guarantee for other systems or MPC forms.
In simulation the neural controller's median convergence time remains longer than the expert MPC's, and the authors attribute the remaining gap to insufficient training or incomplete handling of conflicting expert labels. On hardware, high-frequency oscillatory control effort appears near the inverted equilibrium, attributed to sensor noise and residual model mismatch, which the authors say a low-pass filter could further suppress. The authors also note that conflicting labels from equally time-optimal modes remain unresolved.