arXiv subjects

Christoph Mark

Publications and source records attributed to Christoph Mark.

11 recordsLinked to original sources

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

Uncertainty Quantification Methods for Optimal Excitation Design in Parameter Identification

Parameter identification is crucial in virtual engineering processes, yet determining appropriate system excitations for identifying specific parameters remains challenging. In practice, extensive experimental programs often fail to generate data with sufficient information content for reliable parameter estimation. This work presents a systematic approach for deriving optimal excitations by maximizing the global sensitivity of target parameters across the space of possible excitation functions. To address the computational challenge of sensitivity evaluation during optimization, we develop two complementary approaches based on uncertainty quantification (UQ) methods. For systems with known mathematical structure, we present an intrusive polynomial chaos expansion (PCE) method that constructs deterministic surrogate models, enabling rapid sensitivity computation. For black-box models where intrusive approaches are not feasible, we introduce a novel non-intrusive method based on optimal transport theory, specifically using Wasserstein distances to quantify sensitivity measures without requiring knowledge of internal system dynamics. Both methods significantly reduce computational costs, making optimal excitation design practical for complex engineering systems. We demonstrate the effectiveness of both approaches on vehicle dynamics models, showing substantial improvements in parameter identification capability. The benefit for parameter identification is further validated experimentally on a test vehicle and compared to the state of the art.

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arXiv2023

Distributionally robust model predictive control for wind farms

In this paper, we develop a distributionally robust model predictive control framework for the control of wind farms with the goal of power tracking and mechanical stress reduction of the individual wind turbines. We introduce an ARMA model to predict the turbulent wind speed, where we merely assume that the residuals are sub-Gaussian noise with statistics contained in an moment-based ambiguity set. We employ a recently developed distributionally model predictive control scheme to ensure constraint satisfaction and recursive feasibility of the control algorithm. The effectiveness of the approach is demonstrated on a practical example of five wind turbines in a row.

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arXiv2022

Recursively feasible Data-driven Distributionally Robust Model Predictive Control with additive disturbances

In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly interpolated initial state constraint in combination with a simplified affine disturbance feedback policy. We consider a moment-based ambiguity set with data-driven radius for the second moment of the disturbance, where we derive a minimum number of samples in order to ensure user-given confidence bounds on the chance constraints and closed-loop performance. The paper closes with a numerical example, highlighting the performance gain and chance constraint satisfaction based on different sample sizes.

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arXiv2021

Data-driven Distributionally Robust MPC: An indirect feedback approach

This paper presents a distributionally robust stochastic model predictive control (SMPC) approach for linear discrete-time systems subject to unbounded and correlated additive disturbances. We consider hard input constraints and state chance constraints, which are approximated as distributionally robust (DR) Conditional Value-at-Risk (CVaR) constraints over a Wasserstein ambiguity set. The computational complexity is reduced by resorting to a tube-based MPC scheme with indirect feedback, such that the error scenarios can be sampled offline. Recursive feasibility is guaranteed by softening the CVaR constraint. The approach is demonstrated on a four-room temperature control example.

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arXiv2021

Stochastic Model Predictive Control for tracking of distributed linear systems with additive uncertainty

In this paper, we propose a chance constrained stochastic model predictive control scheme for reference tracking of distributed linear time-invariant systems with additive stochastic uncertainty. The chance constraints are reformulated analytically based on mean-variance information, where we design suitable Probabilistic Reachable Sets for constraint tightening. Furthermore, the chance constraints are proven to be satisfied in closed-loop operation. The design of an invariant set for tracking complements the controller and ensures convergence to arbitrary admissible reference points, while a conditional initialization scheme provides the fundamental property of recursive feasibility. The paper closes with a numerical example, highlighting the convergence to changing output references and empirical constraint satisfaction.

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arXiv2020

Stochastic MPC with Distributionally Robust Chance Constraints

In this paper we discuss distributional robustness in the context of stochastic model predictive control (SMPC) for linear time-invariant systems. We derive a simple approximation of the MPC problem under an additive zero-mean i.i.d. noise with quadratic cost. Due to the lack of distributional information, chance constraints are enforced as distributionally robust (DR) chance constraints, which we opt to unify with the concept of probabilistic reachable sets (PRS). For Wasserstein ambiguity sets, we propose a simple convex optimization problem to compute the DR-PRS based on finitely many disturbance samples. The paper closes with a numerical example of a double integrator system, highlighting the reliability of the DR-PRS w.r.t. the Wasserstein set and performance of the resulting SMPC.

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arXiv2020

Detecting long-range interactions between migrating cells

Chemotaxis enables cells to systematically approach distant targets that emit a diffusible guiding substance. However, the visual observation of an encounter between a cell and a target does not necessarily indicate the presence of a chemotactic approach mechanism, as even a blindly migrating cell can come across a target by chance. To distinguish between the chemotactic approach and blind migration, we present an objective method that is based on the analysis of time-lapse recorded cell migration trajectories. First, we validate our method with simulated data, demonstrating that it reliably detects the presence or absence of remote cell-cell interactions. In a second step, we apply the method to data from three-dimensional collagen gels, interspersed with highly migratory natural killer (NK) cells that were derived from two different human donors. We find for one of the donors an attractive interaction between the NK cells, pointing to a cooperative behavior of these immune cells. When adding nearly stationary K562 tumor cells to the system, we find a repulsive interaction between K562 and NK cells for one of the donors. By contrast, we find attractive interactions between NK cells and an IL-15-secreting variant of K562 tumor cells. We therefore speculate that NK cells find wild-type tumor cells only by chance, but are programmed to leave a target quickly after a close encounter. We provide a freely available Python implementation of our p-value method that can serve as a general tool for detecting long-range interactions in collective systems of self-driven agents.

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arXiv2020

A stochastic output-feedback MPC scheme for distributed systems

In this paper, we present a novel stochastic output-feedback MPC scheme for distributed systems with additive process and measurement noise. The chance constraints are treated with the concept of probabilistic reachable sets, which, under an unimodality assumption on the disturbance distributions are guaranteed to be satisfied in closed-loop. By conditioning the initial state of the optimization problem on feasibility, the fundamental property of recursive feasibility is ensured. Closed-loop chance constraint satisfaction, recursive feasibility and convergence to an asymptotic average cost bound are proven. The paper closes with a numerical example of three interconnected subsystems, highlighting the chance constraint satisfaction and average cost compared to a centralized setting.

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arXiv2019

A stochastic MPC scheme for distributed systems with multiplicative uncertainty

This paper presents a Distributed Stochastic Model Predictive Control algorithm for networks of linear systems with multiplicative uncertainties and local chance constraints on the states and control inputs. The chance constraints are approximated via Cantelli's inequality by means of expected value and covariance. The cooperative control algorithm is based on the distributed Alternating Direction Method of Multipliers, which renders the controller fully distributedly implementable, recursively feasible and ensures point-wise convergence of the states. The aforementioned properties are guaranteed through a properly selected distributed invariant set and distributed terminal constraints for the mean and covariance. The paper closes with an example highlighting the chance constraint satisfaction, numerical properties and scalability of our approach.

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arXiv2014

Bayesian inference of time varying parameters in autoregressive processes

In the autoregressive process of first order AR(1), a homogeneous correlated time series $u_t$ is recursively constructed as $u_t = q\; u_{t-1} + σ\;ε_t$, using random Gaussian deviates $ε_t$ and fixed values for the correlation coefficient $q$ and for the noise amplitude $σ$. To model temporally heterogeneous time series, the coefficients $q_t$ and $σ_t$ can be regarded as time-dependend variables by themselves, leading to the time-varying autoregressive processes TVAR(1). We assume here that the time series $u_t$ is known and attempt to infer the temporal evolution of the 'superstatistical' parameters $q_t$ and $σ_t$. We present a sequential Bayesian method of inference, which is conceptually related to the Hidden Markov model, but takes into account the direct statistical dependence of successively measured variables $u_t$. The method requires almost no prior knowledge about the temporal dynamics of $q_t$ and $σ_t$ and can handle gradual and abrupt changes of these superparameters simultaneously. We compare our method with a Maximum Likelihood estimate based on a sliding window and show that it is superior for a wide range of window sizes.

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