arXiv subjects

Antoine P. Leeman

Publications and source records attributed to Antoine P. Leeman.

10 recordsLinked to original sources

arXiv2026

Over-Approximating Minimizer Sets of Constrained Convex Programs with Parametric Uncertainty via Reachability Analysis

We study the set of solutions to a parameterized, strongly convex optimization problem whose cost depends on uncertain, bounded parameters. We compute a certified outer approximation of the corresponding set of optimizers, using convergence properties of the projected gradient descent (PGD) algorithm for convex programs. Concretely, by treating the cost parameter as constant but unknown, we interpret the PGD iterates as an uncertain dynamical system and analyze its forward reachable sets. Since PGD converges exponentially to the unique optimizer for each fixed parameter, these reachable sets provide outer approximations of the optimizer set, with an explicit error bound that decays exponentially with the iteration count. We apply system-level synthesis (SLS) on the PGD dynamics to optimize the step-size sequence and obtain reachable-set over-approximations. Our method outperforms existing baselines in over-approximating, with low conservativeness, the minimizer sets of convex programs with uncertain costs and high-dimensional decision variables.

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arXiv2026

VISION-SLS: Safe Perception-Based Control from Learned Visual Representations via System Level Synthesis

We propose VISION-SLS, a method for nonlinear output-feedback control from high-resolution RGB images which provides robust constraint satisfaction guarantees under calibrated uncertainty bounds despite partial observability, sensor noise, and nonlinear dynamics. To enable scalability while retaining guarantees, we propose: (i) a learned low-dimensional observation map from pretrained visual features with state-dependent error bounds, and (ii) a causal affine time-varying output-feedback policy optimized via System Level Synthesis (SLS). We develop a scalable, novel solver for the resulting nonconvex program that leverages sequential convex programming coupled with efficient Riccati recursions. On two simulated visuomotor tasks (a 4D car and a 10D quadrotor) with >= 512 x 512 pixels and a 59D humanoid task with partial observability, our method enables safe, information-gathering behavior that reduces uncertainty while guaranteeing constraint satisfaction with empirically-calibrated error bounds. We also validate our method on hardware, safely controlling a ground vehicle from onboard images, outperforming baselines in safety rate and solve times. Together, these results show that learned visual abstractions coupled with an efficient solver make SLS-based safe visuomotor output-feedback practical at scale. The code implementation of our method is available at https://github.com/trustworthyrobotics/VISION-SLS.

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arXiv2026

Robustly Constrained Dynamic Games for Uncertain Nonlinear Dynamics

We propose a novel framework for robust dynamic games with nonlinear dynamics corrupted by state-dependent additive noise, and nonlinear agent-specific and shared constraints. Leveraging system-level synthesis (SLS), each agent designs a nominal trajectory and a causal affine error feedback law to minimize their own cost while ensuring that its own constraints and the shared constraints are satisfied, even under worst-case noise realizations. Building on these nonlinear safety certificates, we define the novel notion of a robustly constrained Nash equilibrium (RCNE). We then present an Iterative Best Response (IBR)-based algorithm that iteratively refines the optimal trajectory and controller for each agent until approximate convergence to the RCNE. We evaluated our method on simulations and hardware experiments involving large numbers of robots with high-dimensional nonlinear dynamics, as well as state-dependent dynamics noise. Across all experiment settings, our method generated trajectory rollouts which robustly avoid collisions, while a baseline game-theoretic algorithm for producing open-loop motion plans failed to generate trajectories that satisfy constraints.

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arXiv2025

Guaranteed Robust Nonlinear MPC via Disturbance Feedback

Robots must satisfy safety-critical state and input constraints despite disturbances and model mismatch. We introduce a robust model predictive control (RMPC) formulation that is fast, scalable, and compatible with real-time implementation. Our formulation guarantees robust constraint satisfaction, input-to-state stability (ISS) and recursive feasibility. The key idea is to decompose the uncertain nonlinear system into (i) a nominal nonlinear dynamic model, (ii) disturbance-feedback controllers, and (iii) bounds on the model error. These components are optimized jointly using sequential convex programming. The resulting convex subproblems are solved efficiently using a recent disturbance-feedback MPC solver. The approach is validated across multiple dynamics, including a rocket-landing problem with steerable thrust. An open-source implementation is available at https://github.com/antoineleeman/robust-nonlinear-mpc.

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arXiv2025

Robust Nonlinear Optimal Control via System Level Synthesis

This paper addresses the problem of finite horizon constrained robust optimal control for nonlinear systems subject to norm-bounded disturbances. To this end, the underlying uncertain nonlinear system is decomposed based on a first-order Taylor series expansion into a nominal system and an error (deviation) described as an uncertain linear time-varying system. This decomposition allows us to leverage system level synthesis to jointly optimize an affine error feedback, a nominal nonlinear trajectory, and, most importantly, a dynamic linearization error over-bound used to ensure robust constraint satisfaction for the nonlinear system. The proposed approach thereby results in less conservative planning compared with state-of-the-art techniques. We demonstrate the benefits of the proposed approach to control the rotational motion of a rigid body subject to state and input constraints.

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arXiv2025

Convex Constrained Controller Synthesis for Evolution Equations

We propose a convex controller synthesis framework for a large class of constrained linear systems, including those described by (deterministic and stochastic) partial differential equations and integral equations, commonly used in fluid dynamics, thermo-mechanical systems, quantum control, or transportation networks. Most existing control techniques rely on a (finite-dimensional) discrete description of the system, via ordinary differential equations. Here, we work instead with more general (infinite-dimensional) Hilbert spaces. This enables the discretization to be applied after the optimization (optimize-then-discretize). Using output-feedback SLS, we formulate the controller synthesis as a convex optimization problem. Structural constraints like sensor and communication delays, and locality constraints, are incorporated while preserving convexity, allowing parallel implementation and extending key SLS properties to infinite dimensions. The proposed approach and its benefits are demonstrated on a linear Boltzmann equation.

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arXiv2024

Fast System Level Synthesis: Robust Model Predictive Control using Riccati Recursions

System level synthesis enables improved robust MPC formulations by allowing for joint optimization of the nominal trajectory and controller. This paper introduces a tailored algorithm for solving the corresponding disturbance feedback optimization problem for linear time-varying systems. The proposed algorithm iterates between optimizing the controller and the nominal trajectory while converging q-linearly to an optimal solution. We show that the controller optimization can be solved through Riccati recursions leading to a horizon-length, state, and input scalability of $\mathcal{O}(N^2 ( n_x^3 +n_u^3))$ for each iterate. On a numerical example, the proposed algorithm exhibits computational speedups by a factor of up to $10^3$ compared to general-purpose commercial solvers.

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arXiv2023

Robust Optimal Control for Nonlinear Systems with Parametric Uncertainties via System Level Synthesis

This paper addresses the problem of optimally controlling nonlinear systems with norm-bounded disturbances and parametric uncertainties while robustly satisfying constraints. The proposed approach jointly optimizes a nominal nonlinear trajectory and an error feedback, requiring minimal offline design effort and offering low conservatism. This is achieved by decomposing the affine-in-the-parameter uncertain nonlinear system into a nominal $\textit{nonlinear}$ system and an uncertain linear time-varying system. Using this decomposition, we can apply established tools from system level synthesis to $\textit{convexly}$ over-bound all uncertainties in the nonlinear optimization problem. Moreover, it enables tight joint optimization of the linearization error bounds, parametric uncertainties bounds, nonlinear trajectory, and error feedback. With this novel controller parameterization, we can formulate a convex constraint to ensure robust performance guarantees for the nonlinear system. The presented method is relevant for numerous applications related to trajectory optimization, e.g., in robotics and aerospace engineering. We demonstrate the performance of the approach and its low conservatism through the simulation example of a post-capture satellite stabilization.

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arXiv2023

Predictive safety filter using system level synthesis

Safety filters provide modular techniques to augment potentially unsafe control inputs (e.g. from learning-based controllers or humans) with safety guarantees in the form of constraint satisfaction. In this paper, we present an improved model predictive safety filter (MPSF) formulation, which incorporates system level synthesis techniques in the design. The resulting SL-MPSF scheme ensures safety for linear systems subject to bounded disturbances in an enlarged safe set. It requires less severe and frequent modifications of potentially unsafe control inputs compared to existing MPSF formulations to certify safety. In addition, we propose an explicit variant of the SL-MPSF formulation, which maintains scalability, and reduces the required online computational effort - the main drawback of the MPSF. The benefits of the proposed system level safety filter formulations compared to state-of-the-art MPSF formulations are demonstrated using a numerical example.

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arXiv2023

Asynchronous Computation of Tube-based Model Predictive Control

Tube-based model predictive control (MPC) methods bound deviations from a nominal trajectory due to uncertainties in order to ensure constraint satisfaction. While techniques that compute the tubes online reduce conservativeness and increase performance, they suffer from high and potentially prohibitive computational complexity. This paper presents an asynchronous computation mechanism for system level tube-MPC (SLTMPC), a recently proposed tube-based MPC method which optimizes over both the nominal trajectory and the tubes. Computations are split into a primary and a secondary process, computing the nominal trajectory and the tubes, respectively. This enables running the primary process at a high frequency and moving the computationally complex tube computations to the secondary process. We show that the secondary process can continuously update the tubes, while retaining recursive feasibility of the primary process.

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