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Differentiable Nonlinear Model Predictive Control

NeurIPS 2026 · Learning theory and algorithms › Combinatorial and search optimization · approach: Constrained neural network optimization · 0 citations (OpenAlex)

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Derives NLP solution sensitivities via the implicit function theorem on smoothed interior-point KKT conditions inside an IP-based SQP solver, and implements forward and adjoint sensitivities for optimal control problems in acados, reporting speedups over mpc.pytorch and cvxpygen.

Problem

Computing parametric solution sensitivities of general nonlinear programs and nonlinear MPC problems efficiently, which learning algorithms need, while existing ML approaches are limited to convex/unconstrained problems or lack efficient implementations.

Approach

Uses IFT on smoothed (barrier-parameter) interior-point KKT conditions within an SQP method with an IPM QP solver, requires the exact Hessian in the sensitivity solve, and reuses the Riccati factorization from the QP solver to get both forward and adjoint sensitivities for OCP-structured NLPs in acados, with a two-solver (nominal plus sensitivity) approach.

Key results

• On bounded LQR batches with umax=1e4, acados solves with adjoint sensitivities in 34.5 ms vs 125 ms for mpc.pytorch (3.6x) and 658 ms for cvxpygen (19x).
• For umax=1.0, acados nominal solve takes 17.6 ms vs 21024 ms for mpc.pytorch (about 1200x), since mpc.pytorch's iLQR fails to converge consistently.
• On the pendulum OCP, sensitivities from acados with tau_min=0 match finite differences, while IFT with a Gauss-Newton Hessian gives completely wrong sensitivities.

Surprising findings

• Using a Gauss-Newton Hessian approximation in the sensitivity computation gives highly degraded, essentially incorrect sensitivities, so the exact Lagrangian Hessian is required.
• mpc.pytorch on GPU shows no significant speedup over its CPU version for the benchmark.

Limitations

• Implementation is CPU-only, written in C with minimal dependencies for embedded deployment; no GPU support.
• Dynamics must be provided in discrete form; acados integrators do not yet support parametric sensitivities.
• Sensitivities are not differentiable at active-set changes; smoothing with tau_min>0 is needed for smooth approximations.

Experimental setup

Benchmarks: bounded LQR batch problems (N=20, nx=8, nu=4, ntheta=248) pendulum-on-cart parametric OCP chain of masses OCP (nmass=3)

Metrics: wall-clock runtime (ms) speedup factor vs baselines agreement with finite differences

Baselines: mpc.pytorch cvxpygen OSQP finite differences Gauss-Newton IFT sensitivities

Builds on: acados HPIPM sIPOPT cvxpylayers IPOPT

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