arXiv subjects

Felix Berkel

Publications and source records attributed to Felix Berkel.

7 recordsLinked to original sources

arXiv2026

Efficient Uniform Feasible-Set Sampling for Approximate Linear MPC

Model Predictive Control (MPC) offers safe and near-optimal control but suffers from high computational costs. Approximate MPC (AMPC) mitigates this by learning a cheaper surrogate policy, typically by training a neural network on state-MPC input pairs. Generating training data is a major bottleneck, requiring solving the MPC for numerous states sampled from its feasible set. Since this feasible set is implicitly defined and unknown, efficient sampling is nontrivial but crucial. We propose the linear MPC Hit-and-Run (LMPC-HR) sampler for linear MPC with polyhedral constraints. We identify the feasible set boundaries along search directions, a crucial step within HR, by formulating the problem as a convex linear program, replacing expensive iterative searches with a single optimization step. A numerical study demonstrates that LMPC-HR reduces the computational cost of generating uniformly distributed samples from the feasible set by an order of magnitude compared to standard baselines.

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arXiv2025

Statistically Consistent Approximate Model Predictive Control

Model Predictive Control (MPC) offers rigorous safety and performance guarantees but is computationally intensive. Approximate MPC (AMPC) aims to circumvent this drawback by learning a computationally cheaper surrogate policy. Common approaches focus on imitation learning (IL) via behavioral cloning (BC), minimizing a mean-squared-error loss on a collection of state-input pairs. However, BC fundamentally fails to provide accurate approximations when MPC solutions are set-valued due to non-convex constraints or local minima. We propose a two-stage IL procedure to accurately approximate nonlinear, potentially set-valued MPC policies. The method integrates an approximation of the MPC's optimal value function into a one-step look-ahead loss function, and thereby embeds the MPC's constraint and performance objectives into the IL objective. This is achieved by adopting a stabilizing soft constrained MPC formulation, which reflects constraint violations in the optimal value function by combining a constraint tightening with slack penalties. We prove statistical consistency for policies that exactly minimize our IL objective, implying convergence to a safe and stabilizing control law, and establish input-to-state stability guarantees for approximate minimizers. Simulations demonstrate improved performance compared to BC.

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arXiv2025

Tunable Real-Time Safety Filters via Set-Based Control Barrier Functions

Safety filters for industrial constrained systems are required to combine certified constraint satisfaction, predictable online computation, and a transparent tuning interface. Existing set-based filters are based on a well-established control invariant set design that scales favorably with state and input constraints, but typically intervene only at the set boundary. Control barrier function (CBF)-based filters, by contrast, provide tunable intervention but require a scalar barrier construction. This paper proposes a set-based CBF safety filter that turns a convex control invariant set directly into a tunable barrier via its Minkowski functional. The resulting filter is formulated as a single-level quadratic program (QP) in which one class-$\mathcal{K}^e$ parameter sets the intervention aggressiveness. Explicit convex formulations are derived for polytopic, zonotopic, and MPC-based invariant sets. Under standard bounded-disturbance assumptions, the resulting safety filter guarantees constraint satisfaction and asymptotic recovery into the invariant set. For tight real-time budgets, a learning-based approximation enables online acceleration, while the formal safety guarantees remain tied to the exact formulation. The method is validated in numerical studies and on a permanent-magnet synchronous motor drive, where an explicit QP implementation evaluates within a 150 microseconds sampling window and has a worst-case execution time of 28.04 microseconds.

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arXiv2025

Contract-based hierarchical control using predictive feasibility value functions

Today's control systems are often characterized by modularity and safety requirements to handle complexity, resulting in the use of hierarchical control structures. Although hierarchical model predictive control offers favorable properties, achieving a provably safe, yet modular design remains a challenge. This paper introduces a contract-based hierarchical control strategy to improve the performance of control systems facing challenges related to model inconsistency and independent controller design across hierarchies. We consider a setup where a higher-level controller generates references that affect the constraints of a lower-level controller, which is based on a soft-constrained MPC formulation. The optimal slack variables of the lower-level MPC serve as the basis for a contract that allows the higher-level controller to assess the feasibility of the reference trajectory without exact knowledge of the model, constraints, and cost of the lower-level controller. To ensure computational efficiency while maintaining model confidentiality, we propose using an explicit function approximation, such as a neural network, to represent the cost of optimal slack values. The approach is tested for a hierarchical control setup consisting of a planner and a motion controller as commonly found in autonomous driving.

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arXiv2024

Stability Mechanisms for Predictive Safety Filters

Predictive safety filters enable the integration of potentially unsafe learning-based control approaches and humans into safety-critical systems. In addition to simple constraint satisfaction, many control problems involve additional stability requirements that may vary depending on the specific use case or environmental context. In this work, we address this problem by augmenting predictive safety filters with stability guarantees, ranging from bounded convergence to uniform asymptotic stability. The proposed framework extends well-known stability results from model predictive control (MPC) theory while supporting commonly used design techniques. As a result, straightforward extensions to dynamic trajectory tracking problems can be easily adapted, as outlined in this article. The practicality of the framework is demonstrated using an automotive advanced driver assistance scenario, involving a reference trajectory stabilization problem.

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arXiv2024

Vehicle single track modeling using physics guided neural differential equations

In this paper, we follow the physics guided modeling approach and integrate a neural differential equation network into the physical structure of a vehicle single track model. By relying on the kinematic relations of the single track ordinary differential equations (ODE), a small neural network and few training samples are sufficient to substantially improve the model accuracy compared with a pure physics based vehicle single track model. To be more precise, the sum of squared error is reduced by 68% in the considered scenario. In addition, it is demonstrated that the prediction capabilities of the physics guided neural ODE model are superior compared with a pure black box neural differential equation approach.

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arXiv2024

Learning Soft Constrained MPC Value Functions: Efficient MPC Design and Implementation providing Stability and Safety Guarantees

Model Predictive Control (MPC) can be applied to safety-critical control problems, providing closed-loop safety and performance guarantees. Implementation of MPC controllers requires solving an optimization problem at every sampling instant, which is challenging to execute on embedded hardware. To address this challenge, we propose a framework that combines a tightened soft constrained MPC formulation with supervised learning to approximate the MPC value function. This combination enables us to obtain a corresponding optimal control law, which can be implemented efficiently on embedded platforms. The framework ensures stability and constraint satisfaction for various nonlinear systems. While the design effort is similar to that of nominal MPC, the proposed formulation provides input-to-state stability (ISS) with respect to the approximation error of the value function. Furthermore, we prove that the value function corresponding to the soft constrained MPC problem is Lipschitz continuous for Lipschitz continuous systems, even if the optimal control law may be discontinuous. This serves two purposes: First, it allows to relate approximation errors to a sufficiently large constraint tightening to obtain constraint satisfaction guarantees. Second, it paves the way for an efficient supervised learning procedure to obtain a continuous value function approximation. We demonstrate the effectiveness of the method using a nonlinear numerical example.

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