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A Physics-Informed Machine Learning Framework for Safe and Optimal Control of Autonomous Systems

ICML 2025 · Learning theory and algorithms › Prediction and decision losses · approach: Determinantal point process inference · 0 citations (OpenAlex)

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Proposes a physics-informed neural approach that solves the epigraph HJB-PDE for state-constrained optimal control, with conformal-prediction safety and performance certificates, co-optimizing safety and performance in 2D to 20D autonomous systems.

Problem

Co-optimizing performance and hard safety for high-dimensional autonomous systems: constrained RL offers only soft safety, safety filters ignore performance, and grid-based HJB solvers suffer the curse of dimensionality.

Approach

Formulate safety-performance co-optimization as a state-constrained optimal control problem, reformulate it in epigraph form with an augmented cost-state z, learn the resulting HJB value function with a physics-informed neural network (PDE residual loss plus boundary loss and curriculum in time), and certify safety and performance using split conformal prediction.

Key results

• On 2D boat navigation, the proposed method achieves a 100% safety rate, while SAC-Lag has 76% safety and 7.5% higher mean cost and MPPI-NCBF has 100% safety but 50.72% higher cost.
• On the 8D pursuer-evader task, MPPI-NCBF reaches 100% safety at 42% higher mean cost, and SAC-Lag has a 66% safety rate with 101% higher cost.
• On the 20D multi-agent task, MPPI, MPPI-NCBF and SAC-Lag show cost increases of 148%, 192% and 164%, with safety rates of 90%, 100% and lower for SAC-Lag; the method reports an optimal policy computed in 2 ms.

Measured effects reported in the paper

Limitations

• Assumes the dynamics model is known, though it could be learned from data.
• Safety and performance guarantees are probabilistic (conformal) rather than deterministic, and depend on dense sampling of states.
• Evaluated only on simulated systems with limited dimensionality (2D, 8D, 20D).

Experimental setup

Datasets: simulated states sampled from state space (boat, pursuer-evader, multi-agent)

Benchmarks: 2D boat navigation 8D pursuer-evader tracking 20D multi-agent navigation

Metrics: mean cumulative cost increase relative to proposed method safety rate offline and online computation time conformal safety level delta conformal performance level psi

Baselines: SAC-Lag PPO-Lag CPO MPPI MPPI-NCBF MPPI-C3BF Level Set Toolbox ground truth

Builds on: DeepReach epigraph formulation of state-constrained optimal control split conformal prediction adaptive loss re-balancing for PINNs

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