arXiv subjects

Ján Drgoňa

Publications and source records attributed to Ján Drgoňa.

34 records · Page 2Linked to original sources

arXiv2026

Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems

This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approaches must be re-solved whenever objectives change, resulting in prohibitive computational costs for applications requiring frequent evaluation and adaptation. The proposed method learns a reusable set of neural basis functions that spans the control policy space, enabling efficient zero-shot adaptation to new tasks through either projection from data or direct mapping from problem specifications. The key idea is an offline-online decomposition: basis functions are learned once during offline imitation learning, while online adaptation requires only lightweight coefficient estimation. Numerical experiments across diverse dynamics, dimensions, and cost structures show our method delivers near-optimal performance with minimal overhead when generalizing across tasks, enabling semi-global feedback policies suitable for real-time deployment.

math.OC↗

arXiv2026

Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates

Solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to construct a multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of the feasible Mehrotra's interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with $1040$ variables and $2080$ inequalities at a kHz rate.

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arXiv2026

Time-Certified and Efficient NMPC via Koopman Operator

Certifying and accelerating execution times of nonlinear model predictive control (NMPC) implementations are two core requirements. Execution-time certificate guarantees that the NMPC controller returns a solution before the next sampling time, and achieving faster worst-case and average execution times further enables its use in a wider set of applications. However, NMPC produces a nonlinear program (NLP) for which it is challenging to derive its execution time certificates. Our previous works, \citep{wu2025direct,wu2025time} provide data-independent execution time certificates (certified number of iterations) for box-constrained quadratic programs (BoxQP). To apply the time-certified BoxQP algorithm \citep{wu2025time} for state-input constrained NMPC, this paper i) learns a linear model via Koopman operator; ii) proposes a dynamic-relaxation construction approach yields a structured BoxQP rather than a general QP; iii) exploits the structure of BoxQP, where the dimension of the linear system solved in each iteration is reduced from $5N(n_u+n_x)$ to $Nn_u$ (where $n_u, n_x, N$ denote the number of inputs, states, and length of prediction horizon), yielding substantial speedups (when $n_x \gg n_u$, as in PDE control).

eess.SY↗

arXiv2026

$\partial$CBDs: Differentiable Causal Block Diagrams

Modern cyber-physical systems (CPS) integrate physics, computation, and learning, demanding modeling frameworks that are simultaneously composable, learnable, and verifiable. Yet existing approaches treat these goals in isolation: causal block diagrams (CBDs) support modular system interconnections but lack differentiability for learning; differentiable programming (DP) enables end-to-end gradient-based optimization but provides limited correctness guarantees; while contract-based verification frameworks remain largely disconnected from data-driven model refinement. To address these limitations, we introduce differentiable causal block diagrams ($\partial$CBDs), a unifying formalism that integrates these three perspectives. Our approach (i) retains the compositional structure and execution semantics of CBDs, (ii) incorporates assume--guarantee (A--G) contracts for modular correctness reasoning, and (iii) introduces residual-based contracts as differentiable, trajectory-level certificates compatible with automatic differentiation (AD), enabling gradient-based optimization and learning. Together, these elements enable a scalable, verifiable, and trainable modeling pipeline that preserves causality and modularity while supporting data-, physics-, and constraint-informed optimization for CPS.

eess.SY↗

arXiv2025

Learning to Optimize for Mixed-Integer Non-linear Programming with Feasibility Guarantees

Mixed-integer nonlinear programs (MINLPs) arise in domains such as energy systems, process engineering, and transportation, and are notoriously difficult to solve at scale due to the interplay of discrete decisions and nonlinear constraints. In many practical settings, these problems appear in parametric form, where objectives and constraints depend on instance-specific parameters, creating the need for fast and reliable solutions across related instances. While learning-to-optimize (L2O) methods have shown strong performance in continuous optimization, extending them to MINLPs requires enforcing both feasibility and integrality within a data-driven framework. We propose an L2O approach tailored to parametric MINLPs that generates instance-specific solutions using integer correction layers to enforce integrality and a gradient-based projection to ensure feasibility of the inequality constraints. Theoretically, we provide asymptotic and non-asymptotic convergence guarantees of the projection step. Empirically, the framework scales to MINLPs with tens of thousands of variables and produces feasible high-quality solutions within milliseconds, often outperforming traditional solvers and heuristic baselines in repeated-solve settings.

cs.LG↗

arXiv2025

Learning to Solve Parametric Mixed-Integer Optimal Control Problems via Differentiable Predictive Control

We propose a novel approach to solving input- and state-constrained parametric mixed-integer optimal control problems using Differentiable Predictive Control (DPC). Our approach follows the differentiable programming paradigm by learning an explicit neural policy that maps control parameters to integer- and continuous-valued decision variables. This policy is optimized via stochastic gradient descent by differentiating the quadratic model predictive control objective through the closed-loop finite-horizon response of the system dynamics. To handle integrality constraints, we incorporate three differentiable rounding strategies. The approach is evaluated on a conceptual thermal energy system, comparing its performance with the optimal solution for different lengths of the prediction horizon. The simulation results indicate that our self-supervised learning approach can achieve near-optimal control performance while significantly reducing inference time by avoiding online optimization, thus implying its potential for embedded deployment even on edge devices.

eess.SY↗

arXiv2025

Physics-informed machine learning for building performance simulation-A review of a nascent field

Building performance simulation (BPS) is critical for understanding building dynamics and behavior, analyzing performance of the built environment, optimizing energy efficiency, improving demand flexibility, and enhancing building resilience. However, conducting BPS is not trivial. Traditional BPS relies on an accurate building energy model, mostly physics-based, which depends heavily on detailed building information, expert knowledge, and case-by-case model calibrations, thereby significantly limiting their scalability. With the development of sensing technology and increased data availability, there is a growing attention and interest in data-driven BPS. However, purely data-driven models often suffer from limited generalization ability and a lack of physical consistency, resulting in poor performance in real-world applications. To address these limitations, recent studies have started to incorporate physics priors into data-driven models, a methodology called physics-informed machine learning (PIML). PIML is an emerging field with the definitions, methodologies, evaluation criteria, application scenarios, and future directions that remain open. To bridge those gaps, this study systematically reviews the state-of-art PIML for BPS, offering a comprehensive definition of PIML, and comparing it to traditional BPS approaches regarding data requirements, modeling effort, performance and computation cost. We also summarize the commonly used methodologies, validation approaches, application domains, available data sources, open-source packages and testbeds. In addition, this study provides a general guideline for selecting appropriate PIML models based on BPS applications. Finally, this study identifies key challenges and outlines future research directions, providing a solid foundation and valuable insights to advance R&D of PIML in BPS.

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arXiv2024

Differentiable Predictive Control for Large-Scale Urban Road Networks

Transportation is a major contributor to CO2 emissions, making it essential to optimize traffic networks to reduce energy-related emissions. This paper presents a novel approach to traffic network control using Differentiable Predictive Control (DPC), a physics-informed machine learning methodology. We base our model on the Macroscopic Fundamental Diagram (MFD) and the Networked Macroscopic Fundamental Diagram (NMFD), offering a simplified representation of citywide traffic networks. Our approach ensures compliance with system constraints by construction. In empirical comparisons with existing state-of-the-art Model Predictive Control (MPC) methods, our approach demonstrates a 4 order of magnitude reduction in computation time and an up to 37% improvement in traffic performance. Furthermore, we assess the robustness of our controller to scenario shifts and find that it adapts well to changes in traffic patterns. This work proposes more efficient traffic control methods, particularly in large-scale urban networks, and aims to mitigate emissions and alleviate congestion in the future.

eess.SY↗

arXiv2023

Physics-Informed Machine Learning for Modeling and Control of Dynamical Systems

Physics-informed machine learning (PIML) is a set of methods and tools that systematically integrate machine learning (ML) algorithms with physical constraints and abstract mathematical models developed in scientific and engineering domains. As opposed to purely data-driven methods, PIML models can be trained from additional information obtained by enforcing physical laws such as energy and mass conservation. More broadly, PIML models can include abstract properties and conditions such as stability, convexity, or invariance. The basic premise of PIML is that the integration of ML and physics can yield more effective, physically consistent, and data-efficient models. This paper aims to provide a tutorial-like overview of the recent advances in PIML for dynamical system modeling and control. Specifically, the paper covers an overview of the theory, fundamental concepts and methods, tools, and applications on topics of: 1) physics-informed learning for system identification; 2) physics-informed learning for control; 3) analysis and verification of PIML models; and 4) physics-informed digital twins. The paper is concluded with a perspective on open challenges and future research opportunities.

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arXiv2023

Proceedings of AAAI 2022 Fall Symposium: The Role of AI in Responding to Climate Challenges

Climate change is one of the most pressing challenges of our time, requiring rapid action across society. As artificial intelligence tools (AI) are rapidly deployed, it is therefore crucial to understand how they will impact climate action. On the one hand, AI can support applications in climate change mitigation (reducing or preventing greenhouse gas emissions), adaptation (preparing for the effects of a changing climate), and climate science. These applications have implications in areas ranging as widely as energy, agriculture, and finance. At the same time, AI is used in many ways that hinder climate action (e.g., by accelerating the use of greenhouse gas-emitting fossil fuels). In addition, AI technologies have a carbon and energy footprint themselves. This symposium brought together participants from across academia, industry, government, and civil society to explore these intersections of AI with climate change, as well as how each of these sectors can contribute to solutions.

cs.AI↗

arXiv2022

Domain-aware Control-oriented Neural Models for Autonomous Underwater Vehicles

Conventional physics-based modeling is a time-consuming bottleneck in control design for complex nonlinear systems like autonomous underwater vehicles (AUVs). In contrast, purely data-driven models, though convenient and quick to obtain, require a large number of observations and lack operational guarantees for safety-critical systems. Data-driven models leveraging available partially characterized dynamics have potential to provide reliable systems models in a typical data-limited scenario for high value complex systems, thereby avoiding months of expensive expert modeling time. In this work we explore this middle-ground between expert-modeled and pure data-driven modeling. We present control-oriented parametric models with varying levels of domain-awareness that exploit known system structure and prior physics knowledge to create constrained deep neural dynamical system models. We employ universal differential equations to construct data-driven blackbox and graybox representations of the AUV dynamics. In addition, we explore a hybrid formulation that explicitly models the residual error related to imperfect graybox models. We compare the prediction performance of the learned models for different distributions of initial conditions and control inputs to assess their accuracy, generalization, and suitability for control.

math.DS↗

arXiv2022

Constructing Neural Network-Based Models for Simulating Dynamical Systems

Dynamical systems see widespread use in natural sciences like physics, biology, chemistry, as well as engineering disciplines such as circuit analysis, computational fluid dynamics, and control. For simple systems, the differential equations governing the dynamics can be derived by applying fundamental physical laws. However, for more complex systems, this approach becomes exceedingly difficult. Data-driven modeling is an alternative paradigm that seeks to learn an approximation of the dynamics of a system using observations of the true system. In recent years, there has been an increased interest in data-driven modeling techniques, in particular neural networks have proven to provide an effective framework for solving a wide range of tasks. This paper provides a survey of the different ways to construct models of dynamical systems using neural networks. In addition to the basic overview, we review the related literature and outline the most significant challenges from numerical simulations that this modeling paradigm must overcome. Based on the reviewed literature and identified challenges, we provide a discussion on promising research areas.

cs.LG↗

arXiv2022

Learning Stochastic Parametric Differentiable Predictive Control Policies

The problem of synthesizing stochastic explicit model predictive control policies is known to be quickly intractable even for systems of modest complexity when using classical control-theoretic methods. To address this challenge, we present a scalable alternative called stochastic parametric differentiable predictive control (SP-DPC) for unsupervised learning of neural control policies governing stochastic linear systems subject to nonlinear chance constraints. SP-DPC is formulated as a deterministic approximation to the stochastic parametric constrained optimal control problem. This formulation allows us to directly compute the policy gradients via automatic differentiation of the problem's value function, evaluated over sampled parameters and uncertainties. In particular, the computed expectation of the SP-DPC problem's value function is backpropagated through the closed-loop system rollouts parametrized by a known nominal system dynamics model and neural control policy which allows for direct model-based policy optimization. We provide theoretical probabilistic guarantees for policies learned via the SP-DPC method on closed-loop stability and chance constraints satisfaction. Furthermore, we demonstrate the computational efficiency and scalability of the proposed policy optimization algorithm in three numerical examples, including systems with a large number of states or subject to nonlinear constraints.

cs.LG↗

arXiv2022

Neural Lyapunov Differentiable Predictive Control

We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.

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arXiv2022

Neural Ordinary Differential Equations for Nonlinear System Identification

Neural ordinary differential equations (NODE) have been recently proposed as a promising approach for nonlinear system identification tasks. In this work, we systematically compare their predictive performance with current state-of-the-art nonlinear and classical linear methods. In particular, we present a quantitative study comparing NODE's performance against neural state-space models and classical linear system identification methods. We evaluate the inference speed and prediction performance of each method on open-loop errors across eight different dynamical systems. The experiments show that NODEs can consistently improve the prediction accuracy by an order of magnitude compared to benchmark methods. Besides improved accuracy, we also observed that NODEs are less sensitive to hyperparameters compared to neural state-space models. On the other hand, these performance gains come with a slight increase of computation at the inference time.

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arXiv2021

On the Stochastic Stability of Deep Markov Models

Deep Markov models (DMM) are generative models that are scalable and expressive generalization of Markov models for representation, learning, and inference problems. However, the fundamental stochastic stability guarantees of such models have not been thoroughly investigated. In this paper, we provide sufficient conditions of DMM's stochastic stability as defined in the context of dynamical systems and propose a stability analysis method based on the contraction of probabilistic maps modeled by deep neural networks. We make connections between the spectral properties of neural network's weights and different types of used activation functions on the stability and overall dynamic behavior of DMMs with Gaussian distributions. Based on the theory, we propose a few practical methods for designing constrained DMMs with guaranteed stability. We empirically substantiate our theoretical results via intuitive numerical experiments using the proposed stability constraints.

cs.LG↗