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Frank Allgöwer

Publications and source records attributed to Frank Allgöwer.

At least 19 recordsLinked to original sources
arXiv2026

Safety for Weakly-Hard Control Systems via Graph-Based Barrier Functions

Despite significant advancement in technology, communication and computational failures are still prevalent in safety-critical engineering applications. Often, networked control systems experience packet dropouts, leading to open-loop behavior that significantly affects the behavior of the system. Similarly, in real-time control applications, control tasks frequently experience computational overruns and thus occasionally no new actuator command is issued. This article addresses the safety verification and controller synthesis problem for a class of control systems subject to weakly-hard constraints, i.e., a set of window-based constraints where the number of failures are bounded within a given time horizon. The results are based on a new notion of graph-based barrier functions that are specifically tailored to the considered system class, offering a set of constraints whose satisfaction leads to safety guarantees despite such failures. Subsequent reformulations of the safety constraints are proposed to alleviate conservatism and improve computational tractability, and the resulting trade-offs are discussed. Finally, several numerical case studies including linear and polynomial systems demonstrate the effectiveness of the proposed approach.

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arXiv2026

Learning and Control Beyond Linearity: Towards a Non-asymptotic Theory for Bilinear Systems

This tutorial provides a unified view of the emerging area of bilinear learning and control. Using linear systems as a benchmark, it explains what fundamentally changes in the bilinear settings, how recent theory addresses finite-sample learning and control, and how these ideas connect to broader themes in nonlinear control, representation learning, and data-driven decision making. For learning, we emphasize tools that are particularly useful in the bilinear settings, such as one-sided Bernstein's inequality for dependent and heavy-tailed covariates, blocking arguments, and martingale concentration for input-dependent noise. We then apply these tools to obtain finite-sample learning guarantees for fully observed bilinear systems, partially observed bilinear systems, and linear systems with bilinear observations. For control, we discuss quadratic control from bilinear observations, where the classical separation principle fails, and review tractable approaches based on belief-space receding horizon control. We also cover stabilization of bilinear dynamics under state feedback using semi-definite programming, LMI relaxations, sum-of-squares methods, and Koopman-based lifting. We conclude by discussing connections to reinforcement learning and machine learning, and some open problems in combined learning and control of bilinear systems.

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arXiv2026

Comparing Controller Synthesis Methods with Deadline-Miss Awareness

This paper presents a comparative study of real-time controller design methods for dynamical control systems subject to deadline overruns. Numerous techniques have been proposed to handle missed deadlines, i.e., including models or information of possible deadline misses directly in the control design. These approaches substantially differ in their assumptions, supported execution semantics, required runtime information, and provided guarantees, making direct comparison challenging. We address this gap with a qualitative assessment of representative deadline-miss-aware control methods. We analyze the design space of such controllers and identify the critical assumptions on the real-time constraints, the control design criteria and implementation aspects. We expose how these different assumptions lead to the different trade-offs in applicability, and control performance and guarantees. We contribute a comparison tool enabling researchers to systematically benchmark new techniques against the state of the art. The study is supported by simulations on two case studies: a Furuta pendulum and an electric motor to illustrate the practical behavior of the different approaches under missed-deadline conditions.

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arXiv2026

Event-Triggered Discrete-Time Multivariable Extremum Seeking Systems

This paper introduces a discrete-time event-triggered extremum seeking framework for real-time optimization of multivariable nonlinear systems. In contrast to conventional discrete-time extremum seeking implementations that rely on periodic input updates, the proposed scheme updates the control action only when a state-dependent triggering condition is met, enabling aperiodic execution and substantial reduction of actuation and communication effort. The resulting closed-loop architecture reconciles two structurally different paradigms: the periodic excitation required for gradient recovery in extremum seeking and the aperiodic philosophy of event-triggered control. By combining discrete-time averaging arguments with Lyapunov-based analysis, we prove practical convergence of the system trajectories to a neighborhood of the unknown extremum and exponential stability of the corresponding average dynamics despite the loss of uniform sampling. The results show that appropriately designed triggering rules preserve the essential optimization mechanisms of classical extremum seeking while drastically reducing the number of input updates. Numerical simulations demonstrate that comparable optimization performance can be achieved with significantly fewer actuation events, highlighting the suitability of the method for resource-aware digital and networked control implementations.

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arXiv2026

Control-Oriented System Identification: Classical, Learning, and Physics-Informed Approaches

We survey classical, machine learning, and data-driven system identification approaches to learn control-relevant and physics-informed models of dynamical systems. Recently, machine learning approaches have enabled system identification from noisy, high-dimensional, and complex data. However, their utility is limited by their ability to provide provable guarantees on control-relevant properties. Meanwhile, control theory has identified several properties that are useful in analysis and control synthesis, such as dissipativity, monotonicity, energy conservation, and symmetry-preserving structures. We posit that merging system identification with such control-relevant or physics-informed properties can provide useful inductive bias, enhance explainability, enable control synthesis with provable guarantees, and improve sample complexity. We formulate system identification as an optimization problem where control-relevant properties can be enforced through direct parameterization (constraining the model structure to satisfy a desired property by construction), soft constraints (encouraging control-relevant properties through regularization or penalty terms), and hard constraints (imposing control-relevant properties as constraints in the optimization problem). Through this lens, we survey methods to learn physics-informed and control-relevant models spanning classical linear and nonlinear system identification, machine learning approaches, and direct identification through data-driven and behavioral representations. We also provide several expository examples that are accompanied by code and brief tutorials on a public Github repository. We also describe challenging directions for future research, including identification in networked, switched, and time-varying systems, experiment design, and bridging the gaps between data-driven, learning-based, and control-oriented approaches.

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arXiv2026

IMMPC: An Internal Model Based MPC for Rejecting Unknown Disturbances

Model predictive control (MPC) is a powerful control method that allows for the direct inclusion of state and input constraints into the controller design. However, errors in the model, e.g., caused by unknown disturbances, can lead to constraint violation, loss of feasibility, and deteriorate closed-loop performance. In this paper, we propose a new MPC scheme based on the internal model principle. This enables the MPC to reject unknown disturbances if the dynamics of the linear signal generator are known. We formulate the disturbance rejection problem as a stability problem to ensure feasibility, constraint satisfaction, and convergence to the optimal reachable output trajectory. The controller is validated on a fourtank system.

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arXiv2026

Data-Driven Robust MPC for Unknown Nonlinear Systems via Set-Membership Learning

Data-driven model predictive control (MPC) has become an attractive approach for controlling unknown systems, especially when data are corrupted by noise. However, most existing data-driven MPC methods focus on linear systems, and little attention has been given to nonlinear dynamics under disturbances. To fill this gap, we propose a robust data-driven min-max MPC scheme for unknown nonlinear systems with process disturbances. We represent the unknown nonlinear dynamics using vector fields built from a dictionary of basis functions, yielding an equivalent linear form with unknown matrices. These unknown matrices are characterized by a set-membership representation derived from noisy input-state data. Using this uncertainty description, we formulate a min-max MPC problem. Two online scenarios are studied: i) when state measurements are noise-free, and, ii) when they are corrupted by process disturbance. For each case, we derive a Lyapunov-based semidefinite program (SDP) to compute a stabilizing state-feedback controller. The resulting schemes are shown to guarantee recursive feasibility and either exponential or robust stability of the closed-loop system depending on whether there is process disturbance. Simulation studies on benchmark examples illustrate the effectiveness and competitive performance of the proposed approach compared to existing data-driven and model-based controllers.

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arXiv2026

Verifiable computations for dynamic encrypted control

Encrypted control can preserve the privacy of data and parameters while the necessary computations can be outsourced to a cloud server. To ensure the integrity of the received values from the cloud, i.e., that they have not been changed, however, strong assumptions or verification algorithms are needed. Previous methods require computationally expensive cryptographic protocols or are only applicable to static computations. In this paper, we present a novel type of verification algorithm for linear dynamic encrypted control. We utilize system-theoretic input-output properties of the controller for artificial challenge signals, which are processed in the cloud in parallel with the requested control input, to check the correctness of the results at the plant. This results in almost no additional computational load, wrong computations are revealed with high probability, and no replay attacks are possible.

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arXiv2026

Koopman meets input-output data: Data-driven output-feedback control of nonlinear systems with closed-loop guarantees

Data-driven control of nonlinear systems from input-output measurements remains a fundamental challenge, as existing approaches with rigorous closed-loop guarantees predominantly require access to full state measurements. In this paper, we address this gap by proposing a data-driven output-feedback controller design method for nonlinear systems that provides provable closed-loop guarantees while operating solely on measured input-output data. Our approach combines Koopman operator theory with an extended state representation of the nonlinear system constructed from input-output trajectories. This allows us to obtain a bilinear surrogate model directly from data, on which robust state-feedback design methods can be applied. By exploiting the observability of the underlying nonlinear system, we establish exponential stability of the extended state, which in turn implies exponential convergence of the original system state to the origin. Finally, we validate our theoretical findings in numerical simulations.

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arXiv2026

Data-Driven Min-Max MPC with Integral Quadratic Constraints

Data-driven control of nonlinear systems with rigorous guarantees is a challenging control problem. Integral quadratic constraints (IQCs) provide a powerful framework for modeling nonlinearities. This paper presents a data-driven min-max model predictive control (MPC) synthesis method for unknown systems subject to (nonlinear) uncertainties using the IQC framework. The unknown system matrices are characterized by a set-membership representation using the input-state data and the knowledge of the IQCs. We derive two semidefinite programs (SDPs) that minimize an upper bound on the worst-case cost over all possible system dynamics and uncertainties. By iteratively solving these SDPs, the proposed state-feedback control law is obtained. We further prove that the resulting closed-loop system is exponentially stable and satisfies the input and state constraints. A numerical example demonstrates the validity of the proposed method.

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arXiv2026

A Koopman Set-Membership Approach for Nonlinear Data-Driven Control with Stability Guarantees

This paper proposes a data-driven controller design method for unknown nonlinear systems based on a Koopman bilinear realization. Using Koopman operator theory, the nonlinear system can be represented as a bilinear discrete-time system with a residual error term. The residual error is proportionally bounded by the norm of the lifted state and input, while the system matrices of the bilinear model are unknown. Assuming that bounds on the residual error are available, the unknown system matrices are characterized via a set-membership representation using the collected input-state data pairs of the nonlinear system. A data-driven controller design method is proposed to ensure stability for all bilinear systems within this set-membership description and for all admissible residual errors. More specifically, we design a rational state-feedback controller that stabilizes the bilinear model with residual error and, consequently, the original nonlinear system, by solving a sum-of-squares (SOS) program. The effectiveness of the proposed approach is demonstrated through numerical examples.

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arXiv2026

Beyond Bounded Noise: Stochastic Set-Membership Estimation for Nonlinear Systems

In this paper, we derive a novel procedure for set-membership estimation of dynamical systems affected by stochastic noise with unbounded support. Employing a bound on the sample covariance matrix, we are able to provide a finite- sample uncertainty set containing the true system parameters with high probability. Our approach can be natively applied to a wide class of nonlinear systems affected by sub-Gaussian noise. Our analysis provides conditions under which the proposed uncertainty set converges to the true system parameters and establishes an upper bound on the convergence rate. The proposed uncertainty set can be used directly for robust controller synthesis with probabilistic stability and performance guarantees. Concluding numerical examples demonstrate the advantages of the proposed formulation over established approaches.

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arXiv2026

Beyond Asymptotics: Targeted exploration with finite-sample guarantees

In this paper, we introduce a targeted exploration strategy for the non-asymptotic, finite-time case. The proposed strategy is applicable to uncertain linear time-invariant systems subject to sub-Gaussian disturbances. As the main result, the proposed approach provides a priori guarantees, ensuring that the optimized exploration inputs achieve a desired accuracy of the model parameters. The technical derivation of the strategy (i) leverages existing non-asymptotic identification bounds with self-normalized martingales, (ii) utilizes spectral lines to predict the effect of sinusoidal excitation, and (iii) effectively accounts for spectral transient error and parametric uncertainty. A numerical example illustrates how the finite exploration time influence the required exploration energy.

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arXiv2026

The Cesàro Value Iteration

In this paper, we consider undiscouted infinite-horizon optimal control for deterministic systems with an uncountable state and input space. We specifically address the case when the classic value iteration does not converge. For such systems, we use the Ces`aro mean to define the infinite-horizon optimal control problem and the corresponding infinite-horizon value function. Moreover, for this value function, we introduce the Cesàro value iteration and prove its convergence for the special case of systems with periodic optimal operating behavior. For this instance, we also show that the Cesàro value function recovers the undiscounted infinite-horizon optimal cost, if the latter is well-defined.

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arXiv2026

On stability and non-averaged performance of economic MPC with terminal conditions for optimal periodic operation

Operation at steady state is often not optimal when optimizing over an economic cost objective. In many cases, periodic operation yields better performance. Therefore, we derive asymptotic stability guarantees of an economic model predictive control scheme with terminal conditions for systems with optimal periodic operation for a more general setup than existing methods can handle. Moreover, we establish a non-averaged closed-loop performance bound by defining the closed-loop cost via a Cesàro summation instead of ordinary summation. Such a non-averaged performance bound provides new insights for systems with periodic optimal operation.

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arXiv2026

LipKernel: Lipschitz-Bounded Convolutional Neural Networks via Dissipative Layers

We propose a novel layer-wise parameterization for convolutional neural networks (CNNs) that includes built-in robustness guarantees by enforcing a prescribed Lipschitz bound. Each layer in our parameterization is designed to satisfy a linear matrix inequality (LMI), which in turn implies dissipativity with respect to a specific supply rate. Collectively, these layer-wise LMIs ensure Lipschitz boundedness for the input-output mapping of the neural network, yielding a more expressive parameterization than through spectral bounds or orthogonal layers. Our new method LipKernel directly parameterizes dissipative convolution kernels using a 2-D Roesser-type state space model. This means that the convolutional layers are given in standard form after training and can be evaluated without computational overhead. In numerical experiments, we show that the run-time using our method is orders of magnitude faster than state-of-the-art Lipschitz-bounded networks that parameterize convolutions in the Fourier domain, making our approach particularly attractive for improving the robustness of learning-based real-time perception or control in robotics, autonomous vehicles, or automation systems. We focus on CNNs, and in contrast to previous works, our approach accommodates a wide variety of layers typically used in CNNs, including 1-D and 2-D convolutional layers, maximum and average pooling layers, as well as strided and dilated convolutions and zero padding. However, our approach naturally extends beyond CNNs as we can incorporate any layer that is incrementally dissipative.

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arXiv2026

Robust IMMPC: An Offset-free MPC for Rejecting Unknown Disturbances

Output regulation is the problem of finding a control input to asymptotically track reference trajectories and reject disturbances. This can be addressed by using the internal model principle to embed a model of the disturbance in the controller. In this work, we present a Model Predictive Control scheme to achieve offset-free control. To do so, we extend Internal Model MPC to general bounded disturbances that must not be generated by the disturbance model. We show recursive feasibility, constraint satisfaction, and provide convergence conditions for the optimal reachable output. The proposed controller is validated on a four-tank system.

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arXiv2026

Discrete-Time Event-Triggered Extremum Seeking

This paper proposes a discrete-time event-triggered extremum seeking control scheme for real-time optimization of nonlinear systems. Unlike conventional discrete-time implementations relying on periodic updates, the proposed approach updates the control input only when a state-dependent triggering condition is satisfied, reducing unnecessary actuation and communication. The resulting closed-loop system combines extremum seeking with an event-triggering mechanism that adaptively determines the input update instants. Using discrete-time averaging and Lyapunov analysis, we establish practical convergence of the trajectories to a neighborhood of the unknown extremum point and show exponential stability of the associated average dynamics. The proposed method preserves the optimization capability of classical extremum seeking while significantly reducing the number of input updates. Simulation results illustrate the effectiveness of the approach for resource-aware real-time optimization.

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