arXiv subjects

Matthias A. Müller

Publications and source records attributed to Matthias A. Müller.

At least 37 records · Page 2Linked to original sources

arXiv2026

Distributed Model Predictive Control for Dynamic Cooperation of Multi-Agent Systems

We propose a distributed model predictive control (MPC) framework for coordinating heterogeneous, nonlinear multi-agent systems under individual and coupling constraints. The cooperative task is encoded as a shared objective function minimized collectively by the agents. Each agent optimizes an artificial reference as an intermediate step towards the cooperative objective, along with a control input to track it. We establish recursive feasibility, asymptotic stability, and transient performance bounds under suitable assumptions. The solution to the cooperative task is not predetermined but emerges from the optimized interactions of the agents. We demonstrate the framework on numerical examples inspired by satellite constellation control, collision-free narrow-passage traversal, and coordinated quadrotor flight.

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arXiv2026

Data-Driven Prediction and Control of Hammerstein-Wiener Systems with Implicit Gaussian Processes

This work investigates data-driven prediction and control of Hammerstein-Wiener systems using physics-informed Gaussian process (GP) models that encode the block-oriented model structure. Data-driven prediction algorithms have been developed for structured nonlinear systems based on Willems' fundamental lemma. However, existing frameworks do not apply to output nonlinearities in Wiener systems and rely on a finite-dimensional dictionary of basis functions for Hammerstein systems. In this work, an implicit predictor structure is considered, leveraging the linearity for the dynamical part of the model. This implicit function is learned by GP regression, utilizing carefully designed structured kernel functions from linear model parameters and GP priors for the nonlinearities. Virtual derivative points are added to the regression by expectation propagation to encode monotonicity information of the nonlinearities. The linear model parameters are estimated as hyperparameters by assuming a stable spline hyperprior. The implicit GP model provides explicit output prediction by optimizing selected optimality criteria. The implicit model is also applied to receding horizon control with the expected control cost and chance constraint satisfaction guarantee. Numerical results demonstrate that the proposed prediction and control algorithms are superior to black-box GP models without model structure knowledge.

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arXiv2026

Tuning the burn-in phase in training recurrent neural networks improves their performance

Training recurrent neural networks (RNNs) with standard backpropagation through time (BPTT) can be challenging, especially in the presence of long input sequences. A practical alternative to reduce computational and memory overhead is to perform BPTT repeatedly over shorter segments of the training data set, corresponding to truncated BPTT. In this paper, we examine the training of RNNs when using such a truncated learning approach for time series tasks. Specifically, we establish theoretical bounds on the accuracy and performance loss when optimizing over subsequences instead of the full data sequence. This reveals that the burn-in phase of the RNN is an important tuning knob in its training, with significant impact on the performance guarantees. We validate our theoretical results through experiments on standard benchmarks from the fields of system identification and time series forecasting. In all experiments, we observe a strong influence of the burn-in phase on the training process, and proper tuning can lead to a reduction of the prediction error on the training and test data of more than 60% in some cases.

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arXiv2026

Robust Control of Constrained Linear Systems using Online Convex Optimization and a Reference Governor

This article develops a control method for linear time-invariant systems subject to time-varying and a priori unknown cost functions, that satisfies state and input constraints, and is robust to exogenous disturbances. To this end, we combine the online convex optimization framework with a reference governor and a constraint tightening approach. The proposed framework guarantees recursive feasibility and robust constraint satisfaction. Its closed-loop performance is studied in terms of its dynamic regret, which is bounded linearly by the variation of the cost functions and the magnitude of the disturbances. The proposed method is illustrated by a numerical case study of a tracking control problem.

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arXiv2025

Inference in Latent Force Models Using Optimal State Estimation

Latent force models, a class of hybrid modeling approaches, integrate physical knowledge of system dynamics with a latent force - an unknown, unmeasurable input modeled as a Gaussian process. In this work, we introduce two optimal state estimation frameworks to reconstruct the latent forces and to estimate the states. In contrast to state-of-the-art approaches, the designed estimators enable the consideration of system-inherent constraints. Finally, the performance of the novel frameworks is investigated in several numerical examples. In particular, we demonstrate the performance of the new framework in a real-world biomedical example - the hypothalamic-pituitary-thyroid axis - using hormone measurements.

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arXiv2025

Nonlinear moving horizon estimation for robust state and parameter estimation -- extended version

We propose a moving horizon estimation scheme to estimate the states and the unknown constant parameters of general nonlinear uncertain discrete-time systems. The proposed framework and analysis explicitly do not involve the a priori verification of a particular excitation condition for the parameters. Instead, we use online information about the actual excitation of the parameters at any time during operation and ensure that the regularization term in the cost function is always automatically selected appropriately. This ensures that the state and parameter estimation error is bounded for all times, even if the parameters are never (or only rarely) excited during operation. Robust exponential stability of the state and parameter estimation error emerges under an additional uniform condition on the maximum duration of insufficient excitation. The theoretical results are illustrated by a numerical example.

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arXiv2025

Online convex optimization for robust control of constrained dynamical systems

This article investigates the problem of controlling linear time-invariant systems subject to time-varying and a priori unknown cost functions, state and input constraints, and exogenous disturbances. We combine the online convex optimization framework with tools from robust model predictive control to propose an algorithm that is able to guarantee robust constraint satisfaction. The performance of the closed loop emerging from application of our framework is studied in terms of its dynamic regret, which is proven to be bounded linearly by the variation of the cost functions and the magnitude of the disturbances. We corroborate our theoretical findings and illustrate implementational aspects of the proposed algorithm by a numerical case study on a tracking control problem of an autonomous vehicle.

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arXiv2025

Data-driven stabilization of nonlinear systems via descriptor embedding

We introduce the notion of descriptor embedding for nonlinear systems and use it for the data-driven design of stabilizing controllers. Specifically, we provide sufficient data-dependent LMI conditions which, if feasible, return a stabilizing nonlinear controller of the form $u=K(x)Z(x)$ where $K(x)$ belongs to a polytope and $Z$ is a user-defined function. The proposed method is then extended to account for the presence of uncertainties and noisy data. Furthermore, a method to estimate the resulting region of attraction is given using only data. Simulation examples are used to illustrate the results and compare them to existing methods from the literature.

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arXiv2025

Optimal state estimation: Turnpike analysis and performance results

In this paper, we introduce turnpike arguments in the context of optimal state estimation. In particular, we show that the optimal solution of the state estimation problem involving all available past data serves as turnpike for the solutions of truncated problems involving only a subset of the data. We mathematically formalize this phenomenon and derive a sufficient condition that relies on a decaying sensitivity property of the underlying nonlinear program. As second contribution, we show how a specific turnpike property can be used to establish performance guarantees when approximating the optimal solution of the full problem by a sequence of truncated problems, and we show that the resulting performance (both averaged and non-averaged) is approximately optimal with error terms that can be made arbitrarily small by an appropriate choice of the horizon length. In addition, we discuss interesting implications of these results for the practically relevant case of moving horizon estimation and illustrate our results with a numerical example.

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arXiv2025

Local Observability of a Class of Feedforward Neural Networks

Beyond the traditional neural network training methods based on gradient descent and its variants, state estimation techniques have been proposed to determine a set of ideal weights from a control-theoretic perspective. Hence, the concept of observability becomes relevant in neural network training. In this paper, we investigate local observability of a class of two-layer feedforward neural networks~(FNNs) with rectified linear unit~(ReLU) activation functions. We analyze local observability of FNNs by evaluating an observability rank condition with respect to the weight matrix and the input sequence. First, we show that, in general, the weights of FNNs are not locally observable. Then, we provide sufficient conditions on the network structures and the weights that lead to local observability. Moreover, we propose an input design approach to render the weights distinguishable and show that this input also excites other weights inside a neighborhood. Finally, we validate our results through a numerical example.

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arXiv2025

Output-feedback model predictive control under dynamic uncertainties using integral quadratic constraints

In this work, we propose an output-feedback tube-based model predictive control (MPC) scheme for linear systems under dynamic uncertainties that are described via integral quadratic constraints (IQC). By leveraging IQCs, a large class of nonlinear and dynamic uncertainties can be addressed. We leverage recent IQC synthesis tools to design a dynamic controller and an estimator that are robust to these uncertainties and minimize the size of the resulting constraint tightening in the MPC. Thereby, we show that the robust estimation problem using IQCs with peak-to-peak performance can be convexified. We guarantee recursive feasibility, robust constraint satisfaction, and input-to-state stability of the resulting MPC scheme.

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arXiv2025

Moving horizon estimation for nonlinear systems with time-varying parameters

We propose a moving horizon estimation scheme for estimating the states and time-varying parameters of nonlinear systems. We consider the case where observability of the parameters depends on the excitation of the system and may be absent during operation, with the parameter dynamics fulfilling a weak incremental bounded-energy bounded-state property to ensure boundedness of the estimation error (with respect to the disturbance energy). The proposed estimation scheme involves a standard quadratic cost function with an adaptive regularization term depending on the current parameter observability. We develop robustness guarantees for the overall estimation error that are valid for all times, and that improve the more often the parameters are detected to be observable during operation. The theoretical results are illustrated by a simulation example.

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arXiv2025

Online convex optimization for constrained control of nonlinear systems

This paper proposes a modular approach that combines the online convex optimization framework and reference governors to solve a constrained control problem featuring time-varying and a priori unknown cost functions. Compared to existing results, the proposed framework is uniquely applicable to nonlinear dynamical systems subject to state and input constraints. Furthermore, our method is general in the sense that we do not limit our analysis to a specific choice of online convex optimization algorithm or reference governor. We show that the dynamic regret of the proposed framework is bounded linearly in both the dynamic regret and the path length of the chosen online convex optimization algorithm, even though the online convex optimization algorithm does not account for the underlying dynamics. We prove that a linear bound with respect to the online convex optimization algorithm's dynamic regret is optimal, i.e., cannot be improved upon. Furthermore, for a standard class of online convex optimization algorithms, our proposed framework attains a bound on its dynamic regret that is linear only in the variation of the cost functions, which is known to be an optimal bound. Finally, we demonstrate implementation and flexibility of the proposed framework by comparing different combinations of online convex optimization algorithms and reference governors to control a nonlinear chemical reactor in a numerical experiment.

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arXiv2025

Gaussian Process-Based Nonlinear Moving Horizon Estimation

In this paper, we propose a novel Gaussian process-based moving horizon estimation (MHE) framework for unknown nonlinear systems. On the one hand, we approximate the system dynamics by the posterior means of the learned Gaussian processes (GPs). On the other hand, we exploit the posterior variances of the Gaussian processes to design the weighting matrices in the MHE cost function and account for the uncertainty in the learned system dynamics. The data collection and the tuning of the hyperparameters are done offline. We prove robust stability of the GP-based MHE scheme using a Lyapunov-based proof technique. Furthermore, as additional contribution, we derive a sufficient condition under which incremental input/output-to-state stability (a nonlinear detectability notion) is preserved when approximating the system dynamics using, e.g., machine learning techniques. Finally, we illustrate the performance of the GP-based MHE scheme in two simulation case studies and show how the chosen weighting matrices can lead to an improved performance compared to standard cost functions.

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arXiv2025

On sample-based functional observability of linear systems

Sample-based observability characterizes the ability to reconstruct the internal state of a dynamical system by using limited output information, i.e., when measurements are only infrequently and/or irregularly available. In this work, we investigate the concept of functional observability, which refers to the ability to infer a function of the system state from the outputs, within a samplebased framework. Here, we give necessary and sufficient conditions for a system to be sample-based functionally observable, and formulate conditions on the sampling schemes such that these are satisfied. Furthermore, we provide a numerical example, where we demonstrate the applicability of the obtained results.

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arXiv2025

Event-triggered moving horizon estimation for nonlinear systems

This work proposes an event-triggered moving horizon estimation (ET-MHE) scheme for general nonlinear systems. The key components of the proposed scheme are a novel event-triggering mechanism (ETM) and the suitable design of the MHE cost function. The main characteristic of our method is that the MHE's nonlinear optimization problem is only solved when the ETM triggers the transmission of measured data to the remote state estimator. If no event occurs, then the current state estimate results from an open-loop prediction using the system dynamics. Furthermore, we show robust global exponential stability of the ET-MHE under a suitable detectability condition. Finally, we illustrate the applicability of the proposed method in terms of a nonlinear benchmark example, where we achieved similar estimation performance compared to standard MHE using 86% less computational resources.

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arXiv2025

Sample-based nonlinear detectability for discrete-time systems

This paper introduces two sample-based formulations of incremental input/output-to-state stability (i-IOSS), a suitable detectability notion for general nonlinear systems. In this work we consider the case of limited output information, i.e., measurements are only infrequently and/or irregularly available. The output-dependent term of the sample-based i-IOSS bound is properly modified to yield a characterization for detectability in presence of incomplete output sequences. We provide both a non-timediscounted and a time-discounted formulation of samplebased i-IOSS. Furthermore, conditions for an i-IOSS system to be also sample-based i-IOSS are given and the relation between the two formulations of sample-based i-IOSS is shown.

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arXiv2025

Low-Rank Matrix Regression via Least-Angle Regression

Low-rank matrix regression is a fundamental problem in data science with various applications in systems and control. Nuclear norm regularization has been widely applied to solve this problem due to its convexity. However, it suffers from high computational complexity and the inability to directly specify the rank. This work introduces a novel framework for low-rank matrix regression that addresses both unstructured and Hankel matrices. By decomposing the low-rank matrix into rank-1 bases, the problem is reformulated as an infinite-dimensional sparse learning problem. The least-angle regression (LAR) algorithm is then employed to solve this problem efficiently. For unstructured matrices, a closed-form LAR solution is derived with equivalence to a normalized nuclear norm regularization problem. For Hankel matrices, a real-valued polynomial basis reformulation enables effective LAR implementation. Two numerical examples in network modeling and system realization demonstrate that the proposed approach significantly outperforms the nuclear norm method in terms of estimation accuracy and computational efficiency.

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