arXiv subjects

Moritz Diehl

Publications and source records attributed to Moritz Diehl.

At least 19 recordsLinked to original sources

arXiv2026

Distributed AC Optimal Power Flow: A Scalable Solution for Large-Scale Problems

This paper introduces a novel distributed optimization framework for large-scale AC Optimal Power Flow (OPF) problems, offering both theoretical convergence guarantees and rapid convergence in practice. By integrating smoothing techniques and the Schur complement, the proposed approach addresses the scalability challenges and reduces communication overhead in distributed AC OPF. Additionally, optimal network decomposition enables efficient parallel processing under the single program multiple data (SPMD) paradigm. Extensive simulations on large-scale benchmarks across various operating scenarios indicate that the proposed framework outperforms the state-of-the-art centralized solver IPOPT on modest hardware. This paves the way for more scalable and efficient distributed optimization in future power system applications.

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arXiv2026

Bayesian Optimization with Lower Confidence Bounds for Minimization Problems with Known Outer Structure

This paper considers Bayesian optimization (BO) for problems with known outer problem structure. In contrast to the classic BO setting, where the objective function itself is unknown and needs to be iteratively estimated from noisy observations, we analyze the case where the objective has a known outer structure - given in terms of a loss function - while the inner structure - an unknown input-output model - is again iteratively estimated from noisy observations of the model outputs. We introduce a novel lower confidence bound algorithm for this particular problem class which exploits the known outer problem structure. The proposed method is analyzed in terms of regret for the special case of convex loss functions and probabilistic parametric models which are linear in the uncertain parameters. Numerical examples illustrate the superior performance of structure-exploiting methods compared to structure-agnostic approaches.

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arXiv2026

Gray-Box Optimization using Optimism in the Face of Uncertainty

This paper considers sequential gray-box optimization where the objective function is given as the composition of a loss function and a parametric model. Crucially, the parameters of the model are unknown and need to be iteratively estimated from noisy observations of the model outputs. This problem setup generalizes the parametric black-box optimization problem known as (contextual) stochastic linear bandit. To address the sequential gray-box optimization problem, we propose a structure-exploiting method that leverages known problem structure given in terms of the loss function and an a priori set of admissible parameters. The method is based on the principle of optimism in the face of uncertainty and trades off exploration and exploitation by minimizing a lower confidence bound on the true objective function. We provide a detailed regret analysis of the novel method, improving on state-of-the-art results for the special case of linear stochastic bandits due to the use of a recently published bound for the parameter confidence sets arising in multi-output linear least-squares estimation. Numerical examples illustrate the superior performance of structure-exploiting methods compared to structure-agnostic approaches.

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arXiv2026

Riccati-ZORO: An efficient algorithm for heuristic online optimization of internal feedback laws in robust and stochastic model predictive control

We present Riccati-ZORO, an algorithm for tube-based optimal control problems (OCP). Tube OCPs predict a tube of trajectories to capture predictive uncertainty. The tube induces a constraint tightening via additional backoff terms. This backoff can significantly affect the performance, and thus implicitly defines a cost of uncertainty. Optimizing the feedback law used to predict the tube can significantly reduce the backoffs, but its online computation is challenging. Riccati-ZORO jointly optimizes the nominal trajectory and uncertainty tube based on a heuristic uncertainty cost design. The algorithm alternates between two subproblems: (i) a nominal OCP with fixed backoffs, (ii) an unconstrained tube OCP, which optimizes the feedback gains for a fixed nominal trajectory. For the tube optimization, we propose a cost function informed by the proximity of the nominal trajectory to constraints, prioritizing reduction of the corresponding backoffs. These ideas are developed for ellipsoidal tubes under linear state feedback. In this case, the decomposition into the two subproblems substantially reduces the computational complexity with respect to the state dimension from $\mathcal{O}(n_x^6)$ to $\mathcal{O}(n_x^3)$, i.e., the complexity of a nominal OCP. We investigate the algorithm in numerical experiments, and provide two open-source implementations: a prototyping version in CasADi and a high-performance implementation integrated into the acados OCP solver.

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arXiv2026

CCOpt: an Open-Source Solver for Large-Scale Mathematical Programs with Complementarity Constraints

This paper presents the Julia package CCOpt, built on top of the interior-point solver MadNLP. CCOpt implements a suite of algorithms for Mathematical Programs with Complementarity Constraints (MPCCs). The solver additionally comes with interfaces for use in Matlab, Python, and C++. MPCCs have recently gained renewed attention in engineering optimization, as complementarity provides a powerful modeling tool for nonsmooth functions and logical conditions. These problems are inherently challenging since their nonlinear programming reformulations violate classical regularity conditions at all feasible points, complicating both theoretical analysis and numerical treatment. Consequently, specialized algorithms are required to handle this degeneracy, and several approaches have been proposed. We implement a toolbox of methods, including relaxation and penalty approaches, as well as a crossover to recently proposed active-set methods. Our solver is based on nonlinear interior-point algorithms that couple the relaxation or penalty parameter with the barrier parameter, yielding substantial speedups compared to standard implementations. Both monotone and nonmonotone strategies for updating this joint parameter update are proposed and investigated. In addition, we propose regularization techniques that improve the conditioning of the KKT system for small relaxation parameters, enhancing robustness and computational efficiency. The implementation is validated on the classical MacMPEC benchmark, large-scale problems in security-constrained optimal power flow, optimal control of nonsmooth systems, as well as on quadratic programs with complementarity constraints arising in model predictive control. This benchmarking reveals an algorithmically driven improvement of often an entire order of magnitude over other methods, including commercial solvers.

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arXiv2026

Identification of a Kalman filter: consistency of local solutions

Prediction error and maximum likelihood methods are powerful tools for identifying linear dynamical systems and, in particular, enable the joint estimation of model parameters and the Kalman filter used for state estimation. A key limitation, however, is that these methods require solving a generally non-convex optimization problem to global optimality. This paper analyzes the statistical behavior of local minimizers in the special case where only the Kalman gain is estimated. We prove that these local solutions are statistically consistent estimates of the true Kalman gain. This follows from asymptotic unimodality: as the dataset grows, the objective function converges to a limit with a unique local (and therefore global) minimizer. We further provide guidelines for designing the optimization problem for Kalman filter tuning and discuss extensions to the joint estimation of additional linear parameters and noise covariances. Finally, the theoretical results are illustrated using three examples of increasing complexity. The main practical takeaway of this paper is that difficulties caused by local minimizers in system identification are, at least, not attributable to the tuning of the Kalman gain.

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arXiv2026

Real-Time Algorithms for Model Predictive Control of Hybrid Dynamical Systems

Model predictive control (MPC) of hybrid dynamical systems is challenging because the associated optimization problem is nonsmooth and the resulting feedback law is discontinuous. This paper develops real-time MPC algorithms for nonlinear hybrid systems modeled as dynamical complementarity systems. The resulting optimal control problems are formulated as mathematical programs with complementarity constraints (MPCCs). We show that the solution map of parametric MPCCs is discontinuous, and that standard nonlinear-programming-based approaches may become infeasible when the hybrid system switches. To address this, we introduce three real-time hybrid MPC schemes whose feedback phase solves a quadratic program with complementarity constraints per sample, yielding local discontinuous piecewise affine approximations of the MPC feedback law. Moreover, we derive continuity and differentiability results for parametric MPCCs, and establish conditions under which the approximation error of our new hybrid MPC algorithms remains uniformly bounded despite solution discontinuities. The algorithms are demonstrated on a robotic manipulation example, where contact sequences are discovered online.

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arXiv2026

Anderson Acceleration for Linearly Converging SQP-Type Methods

Although Anderson acceleration (AA) is known to speed up fixed-point iterations, it is rarely applied in constrained optimization, in particular sequential quadratic programming (SQP). We show that the local convergence behavior of a general family of (inexact) SQP-type methods can benefit from AA and introduce a simple heuristic to alleviate slower convergence farther from the solution. The method is implemented in the software framework acados. Numerical examples from optimal control illustrate consistent improvements in convergence of different SQP-type methods.

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arXiv2026

Rollout Then Optimize: A One-Step Newton Refinement of Learned Policies for Nonlinear Model Predictive Control

We propose a computationally efficient rollout-then-optimize method to improve a learned control policy at deployment time. A learned policy provides a nominal trajectory, which is refined online by a single Newton step implemented via a Riccati recursion within a model predictive control (MPC) scheme. This refinement combines model knowledge with the learned policy at minimal additional computational cost. We establish bounds on the approximation error of the learned policy relative to the MPC policy and show that one Newton step reduces the suboptimality of the learned rollout quadratically in the policy approximation error. The proposed controller is validated in simulation on a constrained trajectory-tracking task for a quadcopter with nonlinear dynamics. Results highlight that the Newton step significantly improves the learned policy, achieving performance close to a fully converged MPC solution while requiring roughly half of the computational time. The code is available at https://github.com/aghezz1/rl-riccati.

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arXiv2026

A Sequential Benders-based Mixed-Integer Quadratic Programming Algorithm and Its Implementation in the CAMINO Toolbox

Sequential quadratic programming and sequential convex programming efficiently solve nonlinear programs (NLPs) by linearizing inner nonlinearities while preserving the outer convex structure. This paper introduces a sequential mixed-integer quadratic programming (MIQP) algorithm to extend this methodology to mixed-integer nonlinear problems (MINLPs), leveraging the efficiency of modern MIQP solvers. The algorithm uses a three-step iterative process. First, the MINLP is linearized around the current iterate. Second, an MIQP is formulated and solved, with its feasible region restricted to a specific area around the linearization point. This region is defined using objective values and derivatives from previous iterations, drawing on concepts from generalized Benders' decomposition. Third, the integer variables from the MIQP solution are fixed, and an NLP involving only the continuous variables is solved. The best solution among all iterates becomes the linearization point for the next iteration. A fallback strategy based on a mixed-integer linear program (MILP) is used when MIQP progress stalls. This guarantees convergence to the global optimal solution for convex MINLPs. For nonconvex problems, the algorithm functions as a heuristic without global optimality guarantees. Numerical experiments show its competitiveness with other MINLP solvers on benchmark problems. In addition, the algorithm was successfully applied to mixed-integer optimal control problems, demonstrating its effectiveness in handling challenging nonlinear equality constraints. The proposed algorithm is publicly available at https://github.com/minlp-toolbox/CAMINO with the name s-b-miqp.

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arXiv2026

Semi-Infinite Programming for Collision-Avoidance in Optimal and Model Predictive Control

This paper presents a novel approach for collision avoidance in optimal and model predictive control, in which the environment is represented by a large number of points and the robot as a union of padded polygons. The conditions that none of the points shall collide with the robot can be written in terms of an infinite number of constraints per obstacle point. We show that the resulting semi-infinite programming (SIP) optimal control problem (OCP) can be efficiently tackled through a combination of two methods: local reduction and an external active-set method. Specifically, this involves iteratively identifying the closest point obstacles, determining the lower-level distance minimizer among all feasible robot shape parameters, and solving the upper-level finitely-constrained subproblems. In addition, this paper addresses robust collision avoidance in the presence of ellipsoidal state uncertainties. Enforcing constraint satisfaction over all possible uncertainty realizations extends the dimension of constraint infiniteness. The infinitely many constraints arising from translational uncertainty are handled by local reduction together with the robot shape parameterization, while rotational uncertainty is addressed via a backoff reformulation. A controller implemented based on the proposed method is demonstrated on a real-world robot running at 20Hz, enabling fast and collision-free navigation in tight spaces. An application to 3D collision avoidance is also demonstrated in simulation.

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arXiv2026

Finite-sample bounds for multi-output system identification

This paper presents uniform-in-time finite-sample bounds for regularized linear regression with vector-valued outputs and conditionally zero-mean subgaussian noise. By revisiting classical self-normalized martingale arguments, we obtain bounds that apply directly to multi-output regression, unlike most of the prior work. Compared to the state of the art, the new results are more general and yield tighter bounds, even for scalar-valued outputs. The mild assumptions we use allow for unknown dependencies between regressors and past noise terms, typically induced by system dynamics or feedback mechanisms. Therefore, these novel finite-sample bounds can be applied to many affine-in-parameter system identification problems, including the identification of a linear time-invariant system from full-state measurements. These new results may lead to significant improvements in stochastic learning-based controllers for safety-critical applications.

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arXiv2026

Gauss-Newton accelerated MPPI Control

Model Predictive Path Integral (MPPI) control is a sampling-based optimization method that has recently attracted attention, particularly in the robotics and reinforcement learning communities. MPPI has been widely applied as a GPU-accelerated random search method to deterministic direct single-shooting optimal control problems arising in model predictive control (MPC) formulations. MPPI offers several key advantages, including flexibility, robustness, ease of implementation, and inherent parallelizability. However, its performance can deteriorate in high-dimensional settings since the optimal control problem is solved via Monte Carlo sampling. To address this limitation, this paper proposes an enhanced MPPI method that incorporates a Jacobian reconstruction technique and the second-order Generalized Gauss-Newton method. This novel approach is called \textit{Gauss-Newton accelerated MPPI}. The numerical results show that the Gauss-Newton accelerated MPPI approach substantially improves MPPI scalability and computational efficiency while preserving the key benefits of the classical MPPI framework, making it a promising approach even for high-dimensional problems.

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arXiv2026

Toward a Decision Support System for Energy-Efficient Ferry Operation on Lake Constance based on Optimal Control

The maritime sector is undergoing a disruptive technological change driven by three main factors: autonomy, decarbonization, and digital transformation. Addressing these factors necessitates a reassessment of inland vessel operations. This paper presents the design and development of a decision support system for ferry operations based on a shrinking-horizon optimal control framework. The problem formulation incorporates a mathematical model of the ferry's dynamics and environmental disturbances, specifically water currents and wind, which can significantly influence the dynamics. Real-world data and illustrative scenarios demonstrate the potential of the proposed system to effectively support ferry crews by providing real-time guidance. This enables enhanced operational efficiency while maintaining predefined maneuver durations. The findings suggest that optimal control applications hold substantial promise for advancing future ferry operations on inland waters. A video of the real-world ferry MS Insel Mainau operating on Lake Constance is available at: https://youtu.be/i1MjCdbEQyE

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arXiv2026

Robust Rigid Body Assembly via Contact-Implicit Optimal Control with Exact Second-Order Derivatives

Efficient planning of assembly motions is a long standing challenge in the field of robotics that has been primarily tackled with reinforcement learning and sampling-based methods by using extensive physics simulations. This paper proposes a sample-efficient robust optimal control approach for the determination of assembly motions, which requires significantly less physics simulation steps during planning through the efficient use of derivative information. To this end, a differentiable physics simulation is constructed that provides second-order analytic derivatives to the numerical solver and allows one to traverse seamlessly from informative derivatives to accurate contact simulation. The solution of the physics simulation problem is made differentiable by using smoothing inspired by interior-point methods applied to both the collision detection as well as the contact resolution problem. We propose a modified variant of an optimization-based formulation of collision detection formulated as a linear program and present an efficient implementation for the nominal evaluation and corresponding first- and second-order derivatives. Moreover, a multi-scenario-based trajectory optimization problem that ensures robustness with respect to sim-to-real mismatches is derived. The capability of the considered formulation is illustrated by results where over 99\% successful executions are achieved in real-world experiments. Thereby, we carefully investigate the effect of smooth approximations of the contact dynamics and robust modeling on the success rates. Furthermore, the method's capability is tested on different peg-in-hole problems in simulation to show the benefit of using exact Hessians over commonly used Hessian approximations.

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arXiv2025

Differentiable Nonlinear Model Predictive Control

The efficient computation of parametric solution sensitivities is a key challenge in the integration of learning-enhanced methods with nonlinear model predictive control (MPC), as their availability is crucial for many learning algorithms. This paper discusses the computation of solution sensitivities of general nonlinear programs (NLPs) using the implicit function theorem (IFT) and smoothed optimality conditions treated in interior-point methods (IPM). We detail sensitivity computation within a sequential quadratic programming (SQP) method which employs an IPM for the quadratic subproblems. Previous works presented in the machine learning community are limited to convex or unconstrained formulations, or lack an implementation for efficient sensitivity evaluation. The publication is accompanied by an efficient open-source implementation within the acados framework, providing both forward and adjoint sensitivities for general optimal control problems, achieving speedups exceeding 3x over the state-of-the-art solvers mpc.pytorch and cvxpygen.

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arXiv2025

Real-Time Non-Smooth MPC for Switching Systems: Application to a Three-Tank Process

Real-time model predictive control of non-smooth switching systems remains challenging due to discontinuities and the presence of discrete modes, which complicate numerical integration and optimization. This paper presents a real-time feasible non-smooth model predictive control scheme for a physical three-tank process, implemented without mixed-integer formulations. The approach combines Filippov system modeling with finite elements and switch detection for time discretization, leading to a finite-dimensional optimal control problem formulated as a mathematical program with complementarity constraints. The mathematical program is solved via a homotopy of smooth nonlinear programs. We introduce modeling adjustments that make the three-tank dynamics numerically tractable, including additional modes to avoid non-Lipschitz points and undefined function values. Hardware experiments demonstrate efficient handling of switching events, mode-consistent tracking across reference changes, correct boundary handling, and constraint satisfaction. Furthermore, we investigate the impact of model mismatch and show that the tracking performance and computation times remain within real-time limits for the chosen sampling time. The complete controller is implemented using the non-smooth optimal control framework NOSNOC

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arXiv2025

L4acados: Learning-based models for acados, applied to Gaussian process-based predictive control

Incorporating learning-based models, such as artificial neural networks or Gaussian processes, into model predictive control (MPC) strategies can significantly improve control performance and online adaptation capabilities for real-world applications. Still, enabling state-of-the-art implementations of learning-based models for MPC is complicated by the challenge of interfacing machine learning frameworks with real-time optimal control software. This work aims at filling this gap by incorporating external sensitivities in sequential quadratic programming solvers for nonlinear optimal control. To this end, we provide L4acados, a general framework for incorporating Python-based dynamics models in the real-time optimal control software acados. By computing external sensitivities via a user-defined Python module, L4acados enables the implementation of MPC controllers with learning-based residual models in acados, while supporting parallelization of sensitivity computations when preparing the quadratic subproblems. We demonstrate significant speed-ups and superior scaling properties of L4acados compared to available software using a neural-network-based control example. Last, we provide an efficient and modular real-time implementation of Gaussian process-based MPC using L4acados, which is applied to two hardware examples: autonomous miniature racing, as well as motion control of a full-scale autonomous vehicle for an ISO lane change maneuver.

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