arXiv subjects

Nathan van de Wouw

Publications and source records attributed to Nathan van de Wouw.

At least 37 records · Page 2Linked to original sources

arXiv2024

Abstracted Model Reduction: A General Framework for Efficient Interconnected System Reduction

This paper introduces the concept of abstracted model reduction: a framework to improve the tractability of structure-preserving methods for the complexity reduction of interconnected system models. To effectively reduce high-order, interconnected models, it is usually not sufficient to consider the subsystems separately. Instead, structure-preserving reduction methods should be employed, which consider the interconnected dynamics to select which subsystem dynamics to retain in reduction. However, structure-preserving methods are often not computationally tractable. To overcome this issue, we propose to connect each subsystem model to a low-order abstraction of its environment to reduce it both effectively and efficiently. By means of a high-fidelity structural-dynamics model from the lithography industry, we show, on the one hand, significantly increased accuracy with respect to standard subsystem reduction and, on the other hand, similar accuracy to direct application of expensive structure-preserving methods, while significantly reducing computational cost. Furthermore, we formulate a systematic approach to automatically determine sufficient abstraction and reduction orders to preserve stability and guarantee a given frequency-dependent error specification. We apply this approach to the lithography equipment use case and show that the environment model can indeed be reduced by over 80\% without significant loss in the accuracy of the reduced interconnected model.

eess.SY↗

arXiv2024

Impact-Aware Control using Time-Invariant Reference Spreading

With the goal of increasing the speed and efficiency in robotic manipulation, a control approach is presented that aims to utilize intentional simultaneous impacts to its advantage. This approach exploits the concept of the time-invariant reference spreading framework, in which partly-overlapping ante- and post-impact reference vector fields are used. These vector fields are coupled via an impact model in proximity of the expected impact area, minimizing the otherwise large impact-induced velocity errors and control efforts. We show how a nonsmooth physics engine can be used to construct this impact model for complex scenarios, which warrants applicability to a large range of possible impact states without requiring contact stiffness and damping parameters. In addition, a novel interim-impact control mode provides robustness in the execution against the inevitable lack of exact impact simultaneity and the corresponding unreliable velocity error during the time when contact is only partially established. This interim mode uses a position feedback signal that is derived from the ante-impact velocity reference to promote contact completion, and smoothly transitions into the post-impact mode. An experimental validation of time-invariant reference spreading control is presented for the first time through a set of 600 robotic hit-and-push and dual-arm grabbing experiments.

cs.RO↗

arXiv2024

Impact-Aware Robotic Manipulation: Quantifying the Sim-To-Real Gap for Velocity Jumps

Impact-aware robotic manipulation benefits from an accurate map from ante-impact to post-impact velocity signals to support, e.g., motion planning and control. This work proposes an approach to generate and experimentally validate such impact maps from simulations with a physics engine, allowing to model impact scenarios of arbitrarily large complexity. This impact map captures the velocity jump assuming an instantaneous contact transition between rigid objects, neglecting the nearly instantaneous contact transition and impact-induced vibrations. Feedback control, which is required for complex impact scenarios, will affect velocity signals when these vibrations are still active, making an evaluation solely based on velocity signals as in previous works unreliable. Instead, the proposed validation approach uses the reference spreading control framework, which aims to reduce peaks and jumps in the control feedback signals by using a reference consistent with the rigid impact map together with a suitable control scheme. Based on the key idea that selecting the correct rigid impact map in this reference spreading framework will minimize the net feedback signal, the rigid impact map is experimentally determined and compared with the impact map obtained from simulation, resulting in a 3.1% average error between the post-impact velocity identified from simulations and from experiments.

cs.RO↗

arXiv2024

Optimal Controller Realizations against False Data Injections in Cooperative Driving

To enhance the robustness of cooperative driving to cyberattacks, we study a controller-oriented approach to mitigate the effect of a class of False-Data Injection (FDI) attacks. By reformulating a given dynamic Cooperative Adaptive Cruise Control scheme (the base controller), we show that a class of new but equivalent controllers (base controller realizations) can represent the base controller. This controller class exhibits the same platooning behavior in the absence of attacks, but in the presence of attacks, their robustness varies with the realization. We propose a prescriptive synthesis framework where the base controller and the system dynamics are written in new coordinates via an invertible coordinate transformation on the controller state. Because the input-output behavior is invariant under coordinate transformations, the input-output behavior is unaffected (so controller realizations do not change the system's closed-loop performance). However, each controller realization may require a different combination of sensors. Subsequently, we obtain the optimal combination of sensors that minimizes the effect of FDI attacks by solving a linear matrix inequality while quantifying the FDI's attack impact through reachability analysis. Through simulation studies, we demonstrate that this approach enhances the robustness of cooperative driving without relying on a detection scheme and maintaining all system properties.

eess.SY↗

arXiv2024

Privacy in Cloud Computing through Immersion-based Coding

Cloud computing enables users to process and store data remotely on high-performance computers and servers by sharing data over the Internet. However, transferring data to clouds causes unavoidable privacy concerns. Here, we present a synthesis framework to design coding mechanisms that allow sharing and processing data in a privacy-preserving manner without sacrificing data utility and algorithmic performance. We consider the setup where the user aims to run an algorithm in the cloud using private data. The cloud then returns some data utility back to the user (utility refers to the service that the algorithm provides, e.g., classification, prediction, AI models, etc.). To avoid privacy concerns, the proposed scheme provides tools to co-design: 1) coding mechanisms to distort the original data and guarantee a prescribed differential privacy level; 2) an equivalent-but-different algorithm (referred here to as the target algorithm) that runs on distorted data and produces distorted utility; and 3) a decoding function that extracts the true utility from the distorted one with a negligible error. Then, instead of sharing the original data and algorithm with the cloud, only the distorted data and target algorithm are disclosed, thereby avoiding privacy concerns. The proposed scheme is built on the synergy of differential privacy and system immersion tools from control theory. The key underlying idea is to design a higher-dimensional target algorithm that embeds all trajectories of the original algorithm and works on randomly encoded data to produce randomly encoded utility. We show that the proposed scheme can be designed to offer any level of differential privacy without degrading the algorithm's utility. We present two use cases to illustrate the performance of the developed tools: privacy in optimization/learning algorithms and a nonlinear networked control system.

cs.CR↗

arXiv2024

Stable Sparse Operator Inference for Nonlinear Structural Dynamics

Structural dynamics models with nonlinear stiffness appear, for example, when analyzing systems with nonlinear material behavior or undergoing large deformations. For complex systems, these models become too large for real-time applications or multi-query workflows. Hence, model reduction is needed. However, the mathematical operators of these models are often not available since, as is common in industry practice, the models are constructed using commercial simulation software. In this work, we propose an operator inference-based approach aimed at inferring, from data generated by the simulation model, reduced-order models (ROMs) of structural dynamics systems with stiffness terms represented by polynomials of arbitrary degree. To ensure physically meaningful models, we impose constraints on the inference such that the model is guaranteed to exhibit stability properties. Convexity of the optimization problem associated with the inference is maintained by applying a sum-of-squares relaxation to the polynomial term. To further reduce the size of the ROM and improve numerical conditioning of the inference, we also propose a novel clustering-based sparsification of the polynomial term. We validate the proposed method on several numerical examples, including a representative 3D Finite Element Model (FEM) of a steel piston rod.

math.NA↗

arXiv2024

Quadratic Programming-based Reference Spreading Control for Dual-Arm Robotic Manipulation with Planned Simultaneous Impacts

With the aim of further enabling the exploitation of intentional impacts in robotic manipulation, a control framework is presented that directly tackles the challenges posed by tracking control of robotic manipulators that are tasked to perform nominally simultaneous impacts. This framework is an extension of the reference spreading control framework, in which overlapping ante- and post-impact references that are consistent with impact dynamics are defined. In this work, such a reference is constructed starting from a teleoperation-based approach. By using the corresponding ante- and post-impact control modes in the scope of a quadratic programming control approach, peaking of the velocity error and control inputs due to impacts is avoided while maintaining high tracking performance. With the inclusion of a novel interim mode, we aim to also avoid input peaks and steps when uncertainty in the environment causes a series of unplanned single impacts to occur rather than the planned simultaneous impact. This work in particular presents for the first time an experimental evaluation of reference spreading control on a robotic setup, showcasing its robustness against uncertainty in the environment compared to three baseline control approaches.

cs.RO↗

arXiv2024

Robust Fault Estimators for Nonlinear Systems: An Ultra-Local Model Design

This paper proposes a nonlinear estimator for the robust reconstruction of process and sensor faults for a class of uncertain nonlinear systems. The proposed fault estimation method augments the system dynamics with an ultra-local (in time) internal state-space representation (a finite chain of integrators) of the fault vector. Next, a nonlinear state observer is designed based on the known parts of the augmented dynamics. This nonlinear filter (observer) reconstructs the fault signal as well as the states of the augmented system. We provide sufficient conditions that guarantee stability of the estimation error dynamics: firstly, asymptotic stability (i.e., exact fault estimation) in the absence of perturbations induced by the fault model mismatch (mismatch between internal ultra-local model for the fault and the actual fault dynamics), uncertainty, external disturbances, and measurement noise and, secondly, Input-to-State Stability (ISS) of the estimation error dynamics is guaranteed in the presence of these perturbations. In addition, to support performance-based estimator design, we provide Linear Matrix Inequality (LMI) conditions for $\mathcal{L}_2$-gain and $\mathcal{L}_2-\mathcal{L}_\infty$ induced norm and cast the synthesis of the estimator gains as a semi-definite program where the effect of model mismatch and external disturbances on the fault estimation error is minimized in the sense of $\mathcal{L}_2$-gain, for an acceptable $\mathcal{L}_2-\mathcal{L}_\infty$ induced norm with respect to measurement noise. The latter result facilitates a design that explicitly addresses the performance trade-off between noise sensitivity and robustness against model mismatch and external disturbances. Finally, numerical results for a benchmark system illustrate the performance of the proposed methodologies.

eess.SY↗

arXiv2024

Model Updating for Nonlinear Systems with Stability Guarantees

To improve the predictive capacity of system models in the input-output sense, this paper presents a framework for model updating via learning of modeling uncertainties in locally (and thus also in globally) Lipschitz nonlinear systems. First, we introduce a method to extend an existing known model with an uncertainty model so that stability of the extended model is guaranteed in the sense of set invariance and input-to-state stability. To achieve this, we provide two tractable semi-definite programs. These programs allow obtaining optimal uncertainty model parameters for both locally and globally Lipschitz nonlinear models, given uncertainty and state trajectories. Subsequently, in order to extract this data from the available input-output trajectories, we introduce a filter that incorporates an approximated internal model of the uncertainty and asymptotically estimates uncertainty and state realizations. This filter is also synthesized using semi-definite programs with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations for a large data-set of a roll plane model of a vehicle illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while guaranteeing stability.

eess.SY↗

arXiv2024

Fast Collision Probability Estimation for Automated Driving using Multi-circular Shape Approximations

Many state-of-the-art methods for safety assessment and motion planning for automated driving require estimation of the probability of collision (POC). To estimate the POC, a shape approximation of the colliding actors and probability density functions of the associated uncertain kinematic variables are required. Even with such information available, the derivation of the POC is in general, i.e., for any shape and density, only possible with Monte Carlo sampling (MCS). Random sampling of the POC, however, is challenging as computational resources are limited in real-world applications. We present expressions for the POC in the presence of Gaussian uncertainties, based on multi-circular shape approximations. In addition, we show that the proposed approach is computationally more efficient than MCS. Lastly, we provide a method for upper and lower bounding the estimation error for the POC induced by the used shape approximations.

cs.RO↗

arXiv2024

Modular Redesign of Mechatronic Systems: Formulation of Module Specifications Guaranteeing System Dynamics Specifications

Complex mechatronic systems are typically composed of interconnected modules, often developed by independent teams. This development process challenges the verification of system specifications before all modules are integrated. To address this challenge, a modular redesign framework is proposed in this paper. Herein, first, allowed changes in the dynamics (represented by frequency response functions (FRFs)) of the redesigned system are defined with respect to the original system model, which already satisfies system specifications. Second, these allowed changes in the overall system dynamics (or system redesign specifications) are automatically translated to dynamics (FRF) specifications on module level that, when satisfied, guarantee overall system dynamics (FRF) specifications. This modularity in specification management supports local analysis and verification of module design changes, enabling design teams to work in parallel without the need to iteratively rebuild the system model to check fulfilment of system FRF specifications. A modular redesign process results that shortens time-to-market and decreases redesign costs. The framework's effectiveness is demonstrated through three examples of increasing complexity, highlighting its potential to enable modular mechatronic system (re)design.

eess.SY↗

arXiv2024

Reduced-order Modeling of Modular, Position-dependent Systems with Translating Interfaces

Many complex mechatronic systems consist of multiple interconnected dynamical subsystems, which are designed, developed, analyzed, and manufactured by multiple independent teams. To support such a design approach, a modular model framework is needed to reduce computational complexity and, at the same time, enable multiple teams to develop and analyze the subsystems in parallel. In such a modular framework, the subsystem models are typically interconnected by means of a static interconnection structure. However, many complex dynamical systems exhibit position-dependent behavior (e.g., induced by translating interfaces) which cannot be not captured by such static interconnection models. In this paper, a modular model framework is proposed, which allows to construct an interconnected system model, which captures the position-dependent behavior of systems with translating interfaces, such as linear guide rails, through a position-dependent interconnection structure. Additionally, this framework allows to apply model reduction on subsystem level, enabling a more effective reduction approach, tailored to the specific requirements of each subsystem. Furthermore, we show the effectiveness of this framework on an industrial wire bonder. Here, we show that including a position-dependent model of the interconnection structure 1) enables to accurately model the dynamics of a system over the operating range of the system and, 2) modular model reduction methods can be used to obtain a computationally efficient interconnected system model with guaranteed accuracy specifications.

eess.SY↗

arXiv2023

Passivity-Preserving, Balancing-Based Model Reduction for Interconnected Systems

This paper proposes a balancing-based model reduction approach for an interconnection of passive dynamic subsystems. This approach preserves the passivity and stability of both the subsystems and the interconnected system. Hereto, one Linear Matrix Inequality (LMI) per subsystem and a single Lyapunov equation for the entire interconnected system needs to be solved, the latter of which warrants the relevance of the reduction of the subsystems for the accurate reduction of the interconnected system, while preserving the modularity of the reduction approach. In a numerical example from structural dynamics, the presented approach displays superior accuracy with respect to an approach in which the individual subsystems are reduced independently.

eess.SY↗

arXiv2023

Stochastic Optimization of Large-Scale Parametrized Dynamical Systems

Many relevant problems in the area of systems and control, such as controller synthesis, observer design and model reduction, can be viewed as optimization problems involving dynamical systems: for instance, maximizing performance in the synthesis setting or minimizing error in the reduction setting. When the involved dynamics are large-scale (e.g., high-dimensional semi-discretizations of partial differential equations), the optimization becomes computationally infeasible. Existing methods in literature lack computational scalability or solve an approximation of the problem (thereby losing guarantees with respect to the original problem). In this paper, we propose a novel method that circumvents these issues. The method is an extension of Stochastic Gradient Descent (SGD) which is widely used in the context of large-scale machine learning problems. The proposed SGD scheme minimizes the $\mathcal{H}_2$ norm of a (differentiable) parametrized dynamical system, and we prove that the scheme is guaranteed to preserve stability with high probability under boundedness conditions on the step size. Conditioned on the stability preservation, we also obtain probabilistic convergence guarantees to local minimizers. The method is also applicable to problems involving non-realizable dynamics as it only requires frequency-domain input-output samples. We demonstrate the potential of the approach on two numerical examples: fixed-order observer design for a large-scale thermal model and controller tuning for an infinite-dimensional system.

math.OC↗

arXiv2023

Uncertainty Learning for LTI Systems with Stability Guarantees

We present a framework for learning of modeling uncertainties in Linear Time Invariant (LTI) systems. We propose a methodology to extend the dynamics of an LTI (without uncertainty) with an uncertainty model, based on measured data, to improve the predictive capacity of the model in the input-output sense. The proposed framework guarantees stability of the extended model. To achieve this, two semi-definite programs are provided that allow obtaining optimal uncertainty model parameters, given state and uncertainty data. To obtain this data from available input-output trajectory data, we introduce a filter in which an internal model of uncertainty is proposed. This filter is also designed via a semi-definite program with guaranteed robustness with respect to uncertainty model mismatches, disturbances, and noise. Numerical simulations are presented to illustrate the effectiveness and practicality of the proposed methodology in improving model accuracy, while warranting model stability.

eess.SY↗

arXiv2023

Mode Selection for Component Mode Synthesis with Guaranteed Assembly Accuracy

In this work, a modular approach is introduced to select the most important eigenmodes for each component of a composed structural dynamics system to obtain the required accuracy of the reduced-order assembly model. To enable the use of models of complex (structural) dynamical systems in engineering practice, e.g., in a design, optimization and/or control context, the complexity of the models needs to be reduced. When the model consist of an assembly of multiple interconnected structural components, component mode synthesis is often the preferred model reduction method. The standard approach to component mode synthesis for such system is to select the eigenmodes of a component that are most important to accurately model the dynamic behavior of this component in a certain frequency range of interest. However, often, a more relevant goal is to obtain, in this frequency range, an accurate model of the assembly. In the proposed approach, accuracy requirements on the level of the assembly are translated to accuracy requirements on component level, by employing techniques from the field of systems and control. With these component-level requirements, the eigenmodes that are most important to accurately model the dynamic behavior of the assembly can be selected in a modular fashion. We demonstrate with two structural dynamics benchmark systems that this method based on assembly accuracy allows for a computationally efficient selection of eigenmodes that 1) guarantees satisfaction of the assembly accuracy requirements and 2) results in most cases in reduced-order models of significantly lower order with respect to the industrial standard approach in which component eigenmodes are selected using a frequency criterion.

eess.SY↗

arXiv2023

Overcoming the Fear of the Dark: Occlusion-Aware Model-Predictive Planning for Automated Vehicles Using Risk Fields

As vehicle automation advances, motion planning algorithms face escalating challenges in achieving safe and efficient navigation. Existing Advanced Driver Assistance Systems (ADAS) primarily focus on basic tasks, leaving unexpected scenarios for human intervention, which can be error-prone. Motion planning approaches for higher levels of automation in the state-of-the-art are primarily oriented toward the use of risk- or anti-collision constraints, using over-approximates of the shapes and sizes of other road users to prevent collisions. These methods however suffer from conservative behavior and the risk of infeasibility in high-risk initial conditions. In contrast, our work introduces a novel multi-objective trajectory generation approach. We propose an innovative method for constructing risk fields that accommodates diverse entity shapes and sizes, which allows us to also account for the presence of potentially occluded objects. This methodology is integrated into an occlusion-aware trajectory generator, enabling dynamic and safe maneuvering through intricate environments while anticipating (potentially hidden) road users and traveling along the infrastructure toward a specific goal. Through theoretical underpinnings and simulations, we validate the effectiveness of our approach. This paper bridges crucial gaps in motion planning for automated vehicles, offering a pathway toward safer and more adaptable autonomous navigation in complex urban contexts.

cs.RO↗

arXiv2023

Privacy-Preserving Anomaly Detection in Stochastic Dynamical Systems: Synthesis of Optimal Gaussian Mechanisms

We present a framework for designing distorting mechanisms that allow remotely operating anomaly detectors while preserving privacy. We consider the problem setting in which a remote station seeks to identify anomalies using system input-output signals transmitted over communication networks. However, disclosing true data of the system operation is not desired as it can be used to infer private information -- modeled here as a system private output. To prevent accurate estimation of private outputs by adversaries, we pass original signals through distorting (privacy-preserving) mechanisms and send the distorted data to the remote station (which inevitably leads to degraded monitoring performance). We formulate the design of these mechanisms as a privacy-utility trade-off problem. We cast the synthesis of dependent Gaussian mechanisms as the solution of a convex program where we seek to maximize privacy quantified using information-theoretic metrics (mutual information and differential entropy) over a finite window of realizations while guaranteeing a bound on monitoring performance degradation.

eess.SY↗