arXiv subjects

Frank Allgöwer

Publications and source records attributed to Frank Allgöwer.

At least 55 records · Page 3Linked to original sources

arXiv2025

A System Parameterization for Direct Data-Driven Estimator Synthesis

This paper introduces a novel parameterization to characterize unknown linear time-invariant systems using noisy data. The presented parameterization describes exactly the set of all systems consistent with the available data. We then derive verifiable conditions, when the consistency constraint reduces the set to the true system and when it does not have any impact. Furthermore, we demonstrate how to use this parameterization to perform a direct data-driven estimator synthesis with guarantees on the H_{\infty}-norm. Lastly, we conduct numerical experiments to compare our approach to existing methods.

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arXiv2025

Kernel-based error bounds of bilinear Koopman surrogate models for nonlinear data-driven control

We derive novel deterministic bounds on the approximation error of data-based bilinear surrogate models for unknown nonlinear systems. The surrogate models are constructed using kernel-based extended dynamic mode decomposition to approximate the Koopman operator in a reproducing kernel Hilbert space. Unlike previous methods that require restrictive assumptions on the invariance of the dictionary, our approach leverages kernel-based dictionaries that allow us to control the projection error via pointwise error bounds, overcoming a significant limitation of existing theoretical guarantees. The derived state- and input-dependent error bounds allow for direct integration into Koopman-based robust controller designs with closed-loop guarantees for the unknown nonlinear system. Numerical examples illustrate the effectiveness of the proposed framework.

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arXiv2025

Path-following model predictive control for autonomous e-scooters

In order to mitigate economical, ecological, and societal challenges in electric scooter (e-scooter) sharing systems, we develop an autonomous e-scooter prototype. Our vision is to design a fully autonomous prototype that can find its way to the next parking spot, high-demand area, or charging station. In this work, we propose a path-following model predictive control solution to enable localization and navigation in an urban environment with a provided path to follow. We design a closed-loop architecture that solves the localization and path following problem while allowing the e-scooter to maintain its balance with a previously developed reaction wheel mechanism. Our model predictive control approach facilitates state and input constraints, e.g., adhering to the path width, while remaining executable on a Raspberry Pi 5. We demonstrate the efficacy of our approach in a real-world experiment on our prototype.

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arXiv2025

A System Parametrization for Direct Data-Driven Analysis and Control with Error-in-Variables

In this paper, we present a new parametrization to perform direct data-driven analysis and controller synthesis for the error-in-variables case. To achieve this, we employ the Sherman-Morrison-Woodbury formula to transform the problem into a linear fractional transformation (LFT) with unknown measurement errors and disturbances as uncertainties. For bounded uncertainties, we apply robust control techniques to derive a guaranteed upper bound on the H2-norm of the unknown true system. To this end, a single semidefinite program (SDP) needs to be solved, with complexity that is independent of the amount of data. Furthermore, we exploit the signal-to-noise ratio to provide a data-dependent condition, that characterizes whether the proposed parametrization can be employed. The modular formulation allows to extend this framework to controller synthesis with different performance criteria, input-output settings, and various system properties. Finally, we validate the proposed approach through a numerical example.

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arXiv2025

Data-driven Estimator Synthesis with Instantaneous Noise

Data-driven controller design based on data informativity has gained popularity due to its straightforward applicability, while providing rigorous guarantees. However, applying this framework to the estimator synthesis problem introduces technical challenges, which can only be solved so far by adding restrictive assumptions. In this work, we remove these restrictions to improve performance guarantees. Moreover, our parameterization allows the integration of additional structural knowledge, such as bounds on parameters. Our findings are validated using numerical examples.

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arXiv2025

Bilinear Data-Driven Min-Max MPC: Designing Rational Controllers via Sum-of-squares Optimization

We propose a data-driven min-max model predictive control (MPC) scheme to control unknown discrete-time bilinear systems. Based on a sequence of noisy input-state data, we state a set-membership representation for the unknown system dynamics. Then, we derive a sum-of-squares (SOS) program that minimizes an upper bound on the worst-case cost over all bilinear systems consistent with the data. As a crucial technical ingredient, the SOS program involves a rational controller parameterization to improve feasibility and tractability. We prove that the resulting data-driven MPC scheme ensures closed-loop stability and constraint satisfaction for the unknown bilinear system. We demonstrate the practicality of the proposed scheme in a numerical example.

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arXiv2025

Multi-objective robust controller synthesis with integral quadratic constraints in discrete-time

This article presents a novel framework for the robust controller synthesis problem in discrete-time systems using dynamic Integral Quadratic Constraints (IQCs). We present an algorithm to minimize closed-loop performance measures such as the $\mathcal H_\infty$-norm, the energy-to-peak gain, the peak-to-peak gain, or a multi-objective mix thereof. While IQCs provide a powerful tool for modeling structured uncertainties and nonlinearities, existing synthesis methods are limited to the $\mathcal H_\infty$-norm, continuous-time systems, or special system structures. By minimizing the energy-to-peak and peak-to-peak gain, the proposed synthesis can be utilized to bound the peak of the output, which is crucial in many applications requiring robust constraint satisfaction, input-to-state stability, reachability analysis, or other pointwise-in-time bounds. Numerical examples demonstrate the robustness and performance of the controllers synthesized with the proposed algorithm.

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arXiv2025

On the Completeness and Ordering of Path-Complete Barrier Functions

This paper is concerned with path-complete barrier functions which offer a graph-based methodology for verifying safety properties in switched systems. The path-complete framework leverages algebraic (barrier functions) as well as combinatorial (graph) components to characterize a set of safety conditions for switched systems, thus offering high flexibility (two degrees of freedom) in searching for suitable safety certificates. In this paper, we do not propose any new safety criteria. Instead, we further investigate the role that the combinatorial component plays in the safety verification problem. First, we prove that path-completeness, which is a property on a graph that describes the switching sequences, is necessary to obtain a set of valid safety conditions. As a result, the path-complete framework is able to provide a complete characterization of safety conditions for switched systems. Furthermore, we provide a systematic methodology for comparing two path-complete graphs and the conservatism associated with the resulting safety conditions. Specifically, we prove that under some conditions, such as when there exists a simulation relation between two path-complete graphs, it is possible to conclude that one graph is always able to provide less conservative safety conditions than another, independent of the algebraic properties of the switched system and the template of the barrier function under consideration. Such a result paves the way for a systematic use of the path-complete framework with barrier functions, as one can then consistently choose the appropriate graph that provides less conservative safety conditions.

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arXiv2025

On discount functions for economic model predictive control without terminal conditions

In this paper, we investigate discounted economic model predictive control (E-MPC) schemes without terminal conditions in scenarios where the optimal operating behavior is a periodic orbit. For such a setting, it is known that a linearly discounted stage cost guarantees asymptotic stability of any arbitrarily small neighborhood of the optimal orbit if the prediction horizon is sufficiently long. However, in some examples very long prediction horizons are needed to achieve the desired performance. In this work, we extend these results by providing the same qualitative stability guarantees for a large class of discount functions. Numerical examples illustrate the influence of the discount function and show that with suitable discounting we can achieve significantly better performance than the linearly discounted E-MPC, even for short prediction horizons.

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arXiv2025

Data-Driven Min-Max MPC for Linear Systems: Robustness and Adaptation

Data-driven controllers design is an important research problem, in particular when data is corrupted by the noise. In this paper, we propose a data-driven min-max model predictive control (MPC) scheme using noisy input-state data for unknown linear time-invariant (LTI) system. The unknown system matrices are characterized by a set-membership representation using the noisy input-state data. Leveraging this representation, we derive an upper bound on the worst-case cost and determine the corresponding optimal state-feedback control law through a semidefinite program (SDP). We prove that the resulting closed-loop system is robustly stabilized and satisfies the input and state constraints. Further, we propose an adaptive data-driven min-max MPC scheme which exploits additional online input-state data to improve closed-loop performance. Numerical examples show the effectiveness of the proposed methods.

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arXiv2024

Decrypting Nonlinearity: Koopman Interpretation and Analysis of Cryptosystems

Public-key cryptosystems rely on computationally difficult problems for security, traditionally analyzed using number theory methods. In this paper, we introduce a novel perspective on cryptosystems by viewing the Diffie-Hellman key exchange and the Rivest-Shamir-Adleman cryptosystem as nonlinear dynamical systems. By applying Koopman theory, we transform these dynamical systems into higher-dimensional spaces and analytically derive equivalent purely linear systems. This formulation allows us to reconstruct the secret integers of the cryptosystems through straightforward manipulations, leveraging the tools available for linear systems analysis. Additionally, we establish an upper bound on the minimum lifting dimension required to achieve perfect accuracy. Our results on the required lifting dimension are in line with the intractability of brute-force attacks. To showcase the potential of our approach, we establish connections between our findings and existing results on algorithmic complexity. Furthermore, we extend this methodology to a data-driven context, where the Koopman representation is learned from data samples of the cryptosystems.

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arXiv2024

Lipschitz constant estimation for general neural network architectures using control tools

This paper is devoted to the estimation of the Lipschitz constant of general neural network architectures using semidefinite programming. For this purpose, we interpret neural networks as time-varying dynamical systems, where the $k$-th layer corresponds to the dynamics at time $k$. A key novelty with respect to prior work is that we use this interpretation to exploit the series interconnection structure of feedforward neural networks with a dynamic programming recursion. Nonlinearities, such as activation functions and nonlinear pooling layers, are handled with integral quadratic constraints. If the neural network contains signal processing layers (convolutional or state space model layers), we realize them as 1-D/2-D/N-D systems and exploit this structure as well. We distinguish ourselves from related work on Lipschitz constant estimation by more extensive structure exploitation (scalability) and a generalization to a large class of common neural network architectures. To show the versatility and computational advantages of our method, we apply it to different neural network architectures trained on MNIST and CIFAR-10.

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arXiv2024

Robust performance for switched systems with constrained switching and its application to weakly hard real-time control systems

Many cyber-physical systems can naturally be formulated as switched systems with constrained switching. This includes systems where one of the signals in the feedback loop may be lost. Possible sources for losses are shared or unreliable communication media in networked control systems, or signals which are discarded, e.g., when using a shared computation device such as a processor in real-time control applications. The use of switched systems with constrained switching is not limited to cyber-physical systems but, includes many other relevant applications such as power systems and modeling virus mutations. In this chapter, we introduce a framework for analyzing and designing controllers which guarantee robust quadratic performance for switched systems with constrained switching. The possible switching sequences are described by the language of a labeled graph where the labels are linked to the different subsystems. The subsystems are allowed to have different input and output dimensions, and their state-space representations can be affected by a broad class of uncertainties in a rational way. The proposed framework exploits ideas from dissipativity-based linear control theory to derive analysis and synthesis inequalities given by linear matrix inequalities. We demonstrate how the proposed framework can be applied to the design of controllers for uncertain weakly hard real-time control systems - a system class naturally appearing in networked and real-time control.

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arXiv2024

Data-Driven Min-Max MPC for LPV Systems with Unknown Scheduling Signal

This paper presents a data-driven min-max model predictive control (MPC) scheme for linear parameter-varying (LPV) systems. Contrary to existing data-driven LPV control approaches, we assume that the scheduling signal is unknown during offline data collection and online system operation. Assuming a quadratic matrix inequality (QMI) description for the scheduling signal, we develop a novel data-driven characterization of the consistent system matrices using only input-state data. The proposed data-driven min-max MPC minimizes a tractable upper bound on the worst-case cost over the consistent system matrices set and over all scheduling signals satisfying the QMI. The proposed approach guarantees recursive feasibility, closed-loop exponential stability and constraint satisfaction if it is feasible at the initial time. We demonstrate the effectiveness of the proposed method in simulation.

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arXiv2024

Data-driven MPC with terminal conditions in the Koopman framework

We investigate nonlinear model predictive control (MPC) with terminal conditions in the Koopman framework using extended dynamic mode decomposition (EDMD) to generate a data-based surrogate model for prediction and optimization. We rigorously show recursive feasibility and prove practical asymptotic stability w.r.t. the approximation accuracy. To this end, finite-data error bounds are employed. The construction of the terminal conditions is based on recently derived proportional error bounds to ensure the required Lyapunov decrease. Finally, we illustrate the effectiveness of the proposed data-driven predictive controller including the design procedure to construct the terminal region and controller.

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arXiv2024

Sequential learning and control: Targeted exploration for robust performance

We present a novel dual control strategy for uncertain linear systems based on targeted harmonic exploration and gain-scheduling with performance and excitation guarantees. In the proposed sequential approach, robust control is implemented after exploration with the main feature that the exploration is optimized with respect to the robust control performance. Specifically, we leverage recent results on finite excitation using spectral lines to determine a high probability lower bound on the resultant finite excitation of the exploration data. This provides an a priori upper bound on the remaining model uncertainty after exploration, which can further be leveraged in a gain-scheduling controller design that guarantees robust performance. This leads to a semidefinite program-based design which computes an exploration strategy with finite excitation bounds and minimal energy, and a gain-scheduled controller with probabilistic performance bounds that can be implemented after exploration. The effectiveness of our approach and its benefits over common random exploration strategies are demonstrated with an example of a system which is 'hard to learn'.

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arXiv2024

Towards targeted exploration for non-stochastic disturbances

We present a novel targeted exploration strategy for linear time-invariant systems without stochastic assumptions on the noise, i.e., without requiring independence or zero mean, allowing for deterministic model misspecifications. This work utilizes classical data-dependent uncertainty bounds on the least-squares parameter estimates in the presence of energy-bounded noise. We provide a sufficient condition on the exploration data that ensures a desired error bound on the estimated parameter. Using common approximations, we derive a semidefinite program to compute the optimal sinusoidal input excitation. Finally, we highlight the differences and commonalities between the developed non-stochastic targeted exploration strategy and conventional exploration strategies based on classical identification bounds through a numerical example.

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arXiv2024

State space representations of the Roesser type for convolutional layers

From the perspective of control theory, convolutional layers (of neural networks) are 2-D (or N-D) linear time-invariant dynamical systems. The usual representation of convolutional layers by the convolution kernel corresponds to the representation of a dynamical system by its impulse response. However, many analysis tools from control theory, e.g., involving linear matrix inequalities, require a state space representation. For this reason, we explicitly provide a state space representation of the Roesser type for 2-D convolutional layers with $c_\mathrm{in}r_1 + c_\mathrm{out}r_2$ states, where $c_\mathrm{in}$/$c_\mathrm{out}$ is the number of input/output channels of the layer and $r_1$/$r_2$ characterizes the width/length of the convolution kernel. This representation is shown to be minimal for $c_\mathrm{in} = c_\mathrm{out}$. We further construct state space representations for dilated, strided, and N-D convolutions.

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