arXiv subjects

Andreas Völz

Publications and source records attributed to Andreas Völz.

8 recordsLinked to original sources

arXiv2026

Enforcing Convergence in Sensitivity-based Distributed Programming via Transformed Primal-Dual Updates

Sensitivity-based distributed programming (SBDP) is a decomposition method for solving large-scale nonlinear programs over graph-structured networks. However, its convergence depends on the strength and structure of subsystem coupling. To address this limitation, we propose SBDP+, a distributed optimization scheme based on a structured primal-dual operator design. The method employs first-order sensitivities and primal decomposition to construct low-dimensional local subproblems that are solved in parallel using neighbor-to-neighbor communication. In contrast to SBDP, SBDP+ introduces a novel primal-dual update that ensures convergence under general coupling structures. Specifically, we establish local linear convergence for non-convex problems under standard regularity conditions. Numerical experiments demonstrate the effectiveness of SBDP+ and highlight improved robustness compared to SBDP and representative distributed optimization methods in applications such as statistical learning.

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arXiv2026

Sensitivity-Based Distributed Programming for Non-Convex Optimization

This paper presents a novel sensitivity-based distributed programming (SBDP) approach for non-convex, large-scale nonlinear programs (NLP). The algorithm relies on first-order sensitivities to cooperatively solve the central NLP in a distributed manner with only neighbor-to-neighbor communication and parallelizable local computations. The decoupling of the subsystems is based on primal decomposition. We derive sufficient local convergence conditions for non-convex problems. Furthermore, we consider the SBDP method in a distributed optimal control context and derive favorable convergence properties in this setting. We illustrate these theoretical findings and the performance of the proposed method with a comparison to state-of-the-art algorithms and simulations of various distributed optimization and control problems.

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arXiv2026

Robust Meta-Learning of Vehicle Yaw Rate Dynamics via Conditional Neural Processes

Trajectory planners of autonomous vehicles usually rely on physical models to predict the vehicle behavior. However, despite their suitability, physical models have some shortcomings. On the one hand, simple models suffer from larger model errors and more restrictive assumptions. On the other hand, complex models are computationally more demanding and depend on environmental and operational parameters. In each case, the drawbacks can be associated to a certain degree to the physical modeling of the yaw rate dynamics. Therefore, this paper investigates the yaw rate prediction based on conditional neural processes (CNP), a data-driven meta-learning approach, to simultaneously achieve low errors, adequate complexity and robustness to varying parameters. Thus, physical models can be enhanced in a targeted manner to provide accurate and computationally efficient predictions to enable safe planning in autonomous vehicles. High fidelity simulations for a variety of driving scenarios and different types of cars show that CNP makes it possible to employ and transfer knowledge about the yaw rate based on current driving dynamics in a human-like manner, yielding robustness against changing environmental and operational conditions.

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arXiv2025

An Overview of Sensitivity-Based Distributed Optimization and Model Predictive Control

This paper presents a concise overview of sensitivity-based methods for solving large-scale optimization problems in distributed fashion. The approach relies on sensitivities and primal decomposition to achieve coordination between the subsystems while requiring only local computations with neighbor-to-neighbor communication. We give a brief historical synopsis of its development and apply it to both static and dynamic optimization problems. Furthermore, a real-time capable distributed model predictive controller is proposed which is experimentally validated on a coupled watertank system.

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arXiv2025

A software framework for stochastic model predictive control of nonlinear continuous-time systems (GRAMPC-S)

This paper presents the open-source stochastic model predictive control framework GRAMPC-S for nonlinear uncertain systems with chance constraints. It provides several uncertainty propagation methods to predict stochastic moments of the system state and can consider unknown parts of the system dynamics using Gaussian process regression. These methods are used to reformulate a stochastic MPC formulation as a deterministic one that is solved with GRAMPC. The performance of the presented framework is evaluated using examples from a wide range of technical areas. The experimental evaluation shows that GRAMPC-S can be used in practice for the control of nonlinear uncertain systems with sampling times in the millisecond range.

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arXiv2024

Sensitivity-Based Distributed Model Predictive Control for Nonlinear Systems under Inexact Optimization

This paper presents a distributed model predictive control (DMPC) scheme for nonlinear continuous-time systems. The underlying distributed optimal control problem is cooperatively solved in parallel via a sensitivity-based algorithm. The algorithm is fully distributed in the sense that only one neighbor-to-neighbor communication step per iteration is necessary and that all computations are performed locally. Sufficient conditions are derived for the algorithm to converge towards the central solution. Based on this result, stability is shown for the suboptimal DMPC scheme under inexact minimization with the sensitivity-based algorithm and verified with numerical simulations. In particular, stability can be guaranteed with either a suitable stopping criterion or a fixed number of algorithm iterations in each MPC sampling step which allows for a real-time capable implementation.

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arXiv2020

A Modular Framework for Distributed Model Predictive Control of Nonlinear Continuous-Time Systems (GRAMPC-D)

The modular open-source framework GRAMPC-D for model predictive control of distributed systems is presented in this paper. The modular concept allows to solve optimal control problems (OCP) in a centralized and distributed fashion using the same problem description. It is tailored to computational efficiency with the focus on embedded hardware. The distributed solution is based on the Alternating Direction Method of Multipliers (ADMM) and uses the concept of neighbor approximation to enhance convergence speed. The presented framework can be accessed through Cpp and Python and also supports plug-and-play and data exchange between agents over a network.

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arXiv2018

A software framework for embedded nonlinear model predictive control using a gradient-based augmented Lagrangian approach (GRAMPC)

A nonlinear MPC framework is presented that is suitable for dynamical systems with sampling times in the (sub)millisecond range and that allows for an efficient implementation on embedded hardware. The algorithm is based on an augmented Lagrangian formulation with a tailored gradient method for the inner minimization problem. The algorithm is implemented in the software framework GRAMPC and is a fundamental revision of an earlier version. Detailed performance results are presented for a test set of benchmark problems and in comparison to other nonlinear MPC packages. In addition, runtime results and memory requirements for GRAMPC on ECU level demonstrate its applicability on embedded hardware.

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