Full-Order Safety for Nonlinear Reduced-Order MPC

Luis Pabon, Johannes K\"{o}hler, Revant Kasichainula, Marco Pavone · N/A · 2026

Summary

Reduced-order models (ROMs) make model predictive control (MPC) of high-dimensional nonlinear systems tractable, but the resulting modeling error can lead to constraint violations on the real system.

Abstract Summary

Reduced-order models (ROMs) make model predictive control (MPC) of high-dimensional nonlinear systems tractable, but the resulting modeling error can lead to constraint violations on the real system. We introduce CoRE-MPC, a robust MPC formulation that plans with a nonlinear ROM and guarantees recursive feasibility and constraint satisfaction for the full-order system. It can be applied with a broad class of nonlinear model reduction techniques and the resulting MPC does not require evaluating the full-order model online, thus ensuring computational efficiency. The key insight is in how the ROM affects the dynamics of the prediction error. We account for this with two error radii that are propagated alongside the ROM and provide a guaranteed bound on the prediction error. The approach is validated in simulation on an 80-state oscillator chain, a Burgers equation, and a 9,768-state finite-element soft robot, where a two-state ROM with data-driven bounds keeps all 1,628 nodes clear of a wall at a median solve time below 1 ms for a 20 ms control period. Across these examples, CoRE-MPC is 13 to 61 times faster than full-order robust MPC at only 27 to 35% higher closed-loop cost, whereas existing certified schemes are either infeasible or at least twice as conservative. Code: [released upon publication].

Key Points

Reduced-order models (ROMs) make model predictive control (MPC) of high-dimensional nonlinear systems tractable, but the resulting modeling error can lead to constraint violations on the real system.
We introduce CoRE-MPC, a robust MPC formulation that plans with a nonlinear ROM and guarantees recursive feasibility and constraint satisfaction for the full-order system.
It can be applied with a broad class of nonlinear model reduction techniques and the resulting MPC does not require evaluating the full-order model online, thus ensuring computational efficiency.
The key insight is in how the ROM affects the dynamics of the prediction error
We account for this with two error radii that are propagated alongside the ROM and provide a guaranteed bound on the prediction error.

Problem Formulation

Consider the full-order model (FOM) with state $x\in\mathbb{R}^{N}$, input $u\in\mathbb{R}^{m}$, $C^{1}$ dynamics $F$, and an unknown piecewise continuous disturbance $d$ with $\/d(t)\/\leq\bar{d}$. We impose the input and state constraints at all times, with a compact set $\mathcal{U}\subset\mathbb{R}^{m}$ and a $C^{1}$ constraint function $h=(h_{1},\ldots,h_{n_{h}})$.

The input constraints encode, for instance, actuator limits, and the state constraints collision avoidance and workspace bounds over the entire body of a soft robot (Fig. 1 ).

Problem Formulation — Full-Order Safety for Nonlinear Reduced-Order MPC — Fig. 2: Oscillator chain. FOM-MPC (purple), CoRE-MPC (blue), Constant CoRE (orange), RN-ROMPC (green), and nominal ROM-MPC (gray). (a) Forty masses driven by one actuator with the shape of the first mode; every displacement is constrained. (b) Largest normalized displacement over all masses in the case with the largest nominal violation. (c) Median closed-loop cost over the $48$ cases relative to FOM-MPC; nominal ROM-MPC is excluded because it violates the constraint. (d) Solve times over $495$ warm updates per controller from five cases run serially in balanced order on one thread. Boxes show quartiles, lines medians, whiskers the most extreme samples within $1.5$ interquartile ranges, and circles outliers.

Coupled Reduction-Error Certificates

Guaranteeing ( 2 ) for the FOM requires bounding the prediction error $x-\widehat{x}=x-\Phi(z)$ of the ROM. We do so with radii $\rho=(\rho_{\parallel},\rho_{\perp})$ for its two components ( 5 ). Section III-A derives the exact error dynamics, and Section III-B bounds their growth and coupling rates and constructs the bounds offline.

CoRE-MPC: Predictive Control with Coupled Error Certificates

We now use the radii of Theorem 1 to tighten the FOM constraints inside a reduced-order MPC and establish its closed-loop guarantees (Theorem 5 ). Constraint tightening: By ( 6 ), $x=\Phi(z+e_{\parallel})+e_{\perp}$ with $(e_{\parallel},e_{\perp})\in\mathcal{E}_{\rho}$ whenever the errors lie within the radii $\rho$.

Experiments

We evaluate CoRE-MPC on three systems of increasing dimension: the oscillator chain (Section V-A ) quantifies the trade-off between full-order safety, closed-loop cost, and computation on a reduction where the invariant-manifold assumption of RN-ROMPC [ 15 ] holds (Remark 3 ).

the Burgers equation (Section V-B ) tests the certificate on a POD reduction whose manifold is not invariant, with closed-form bounds that hold for every state and radius.

Sources and Demonstrations

Figures are reproduced from Pabon et al. See the full paper for experimental details and the project page, when the paper links one, for demonstrations and videos.