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Jörg Raisch

Publications and source records attributed to Jörg Raisch.

At least 19 recordsLinked to original sources
arXiv2026

A Luenberger Observer for P-Time Event Graphs

P-Time Event Graphs (P-TEGs) are discrete event systems able to model synchronization and delay phenomena. They extend the modeling power of Timed Event Graphs (TEGs) by including not only lower-bound, but also upper-bound constraints on the sojourn times of tokens in places. In this work, we consider the problem of estimating the firing time of transitions in P-TEGs, assuming that only a subset of transitions can be directly observed. Building on the (now classical) Luenberger observer for TEGs, we design an algorithm that takes into account the additional restrictions posed by the upper-bound constraints of P-TEGs to obtain a more accurate firing time estimation.

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arXiv2026

Instability in Complex Oscillator Networks: Limitations and Potentials of Network Measures and Machine Learning

A central question of network science is how functional properties of systems emerge from their structure. For networked dynamical systems, structure is typically captured through network measures. We investigate the relationship between these measures and stability metrics across non-linear and linear oscillators, as well as real-world power grid topologies and dynamics. We find that this relationship is highly sensitive to the underlying ensemble: minor changes in the networks considered, such as going from mean degree 6 to mean degree 8, can invert the correlation between a network measure and stability. We also investigate network measures as inputs for machine learning, as well as Graph Neural Networks (GNNs) as predictors of stability. Both GNNs and the non-linear combination of many network measures can accurately predict stability within a given ensemble, yet both can fail when the ensemble changes. We conclude that neither approach reliably identifies the underlying structural causes of instability.

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arXiv2026

Over-the-Air Consensus-based Formation Control of Heterogeneous Agents: Communication-Rate and Geometry-Aware Convergence Guarantees

This paper investigates the formation control problem of heterogeneous, autonomous agents that communicate over a wireless multiple access channel. Instead of avoiding interference through orthogonal node-to-node transmissions, we exploit the superposition property of the wireless channel to compute, at each receiver, normalized convex combinations of simultaneously broadcast neighbor signals. At every communication instant, agents update their reference positions from these aggregates, and track the references in continuous time between updates. The only assumption on the agent dynamics is that each agent tracks constant reference positions exponentially, which accommodates a broad class of platforms. Under this assumption, we analyze the resulting jump-flow system under time-varying communication graphs and unknown channel coefficients. We derive a communication-rate based sufficient condition that guarantees convergence to a prescribed formation. We then provide a geometry-aware refinement showing how favorable tracking transients can relax the required condition. Simulations with unicycle agents illustrate the theoretical results and demonstrate a substantial reduction in the number of required orthogonal transmissions compared to interference-avoiding node-to-node communication protocols.

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arXiv2025

Controlled Invariance in Fully Actuated Max-plus Linear Systems with Precedence Semimodules

Given a max-plus linear system and a semimodule, the problem of computing the maximal controlled invariant subsemimodule is still open to this day. In this paper, we consider this problem for the specific class of fully actuated systems and constraints in the form of precedence semimodules. The assumption of full actuation corresponds to the existence of an input for each component of the system state. A precedence semimodule is the set of solutions of inequalities typically used to represent time-window constraints. We prove that, in this setting, it is possible to (i) compute the maximal controlled invariant subsemimodule and (ii) decide the convergence of a fixed-point algorithm introduced by R.D. Katz in strongly polynomial time.

math.OC↗
arXiv2025

Infinite precedence graphs for consistency verification in P-time event graphs

Precedence constraints are inequalities used to model time dependencies. In 1958, Gallai proved that a finite system of precedence constraints admits solutions if and only if the corresponding precedence graph does not contain positive-weight circuits. We show that this result extends naturally to the case of infinitely many constraints. We then analyze two specific classes of infinite precedence graphs -- $\mathbb{N}$-periodic and ultimately periodic graphs -- and prove that the existence of solutions of their related constraints can be verified in strongly polynomial time. The obtained algorithms find applications in P-time event graphs, which are a subclass of P-time Petri nets able to model production systems under cyclic schedules where tasks need to be performed within given time windows.

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arXiv2025

$\mathcal{H}_\infty$ Loop-shaping for Power Tracking Control of Wind Turbines

In this paper, we present an advanced wind turbine control scheme for power maximization as well as for active power control, which is designed using $\mathcal{H}_\infty$ loop-shaping. Our approach involves the synthesis of two separate controllers for two different operating modes. To ensure smooth transitions between these modes, we implement a bumpless transfer strategy that reduces transient effects. A comprehensive case study demonstrates the efficacy of our control scheme, showing significant improvements in power tracking accuracy and a reduction in mechanical wear. Moreover, our control strategy comes with robust stability guarantees.

eess.SY↗
arXiv2024

Robust LQ Optimal Control for Wind Turbine Power Tracking Operation

In this paper, a robust linear quadratic optimal control approach for accurate active power tracking of wind turbines is presented. For control synthesis, linear matrix inequalities are employed using an augmented wind turbine state model with uncertain parameters. The resulting controller ensures robust stability in different operating regions. In a case study, the novel approach is compared to existing controllers from literature. Simulations indicate that the controller improves power tracking accuracy while leading to similar mechanical wear as existing approaches.

eess.SY↗
arXiv2024

Model predictive control of wakes for wind farm power tracking

In this paper, a model predictive control scheme for wind farms is presented. Our approach considers wake dynamics including their influence on local wind conditions and allows to track a given power reference. In detail, a Gaussian wake model is used in combination with observation points that carry wind condition information. This allows to estimate the rotor effective wind speeds at downstream turbines based on which we deduce their power output. Through different approximation methods, the associated finite horizon nonlinear optimization problem is reformulated in a mixed-integer quadratically-constrained quadratic program fashion. By solving the reformulated problem online, optimal yaw angles and axial induction factors are found. Closed-loop simulations indicate good power tracking capabilities over a wide range of power setpoints while distributing wind turbine infeed evenly among all units. Additionally, the simulation results underline real time capabilities of our approach.

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arXiv2023

Consistency of P-time event graphs is decidable in polynomial time (extended version)

P-time event graphs are discrete event systems able to model cyclic production systems where tasks need to be performed within given time windows. Consistency is the property of admitting an infinite execution of such tasks that does not violate any temporal constraints. In this paper, we solve the long-standing problem of characterizing the decidability of consistency by showing that, assuming unary encoding of the initial marking, this property can be verified in strongly polynomial time. The proof is based on a reduction to the problem of detecting paths with infinite weight in infinite weighted digraphs called N-periodic graphs.

cs.LO↗
arXiv2023

Model Predictive Control of Wind Turbines with Piecewise-Affine Power Coefficient Approximation

In this paper, an offset-free bilinear model predictive control approach for wind turbines is presented. State-of-the-art controllers employ different control loops for pitch angle and generator torque which switch depending on wind conditions. In contrast, the presented controller is based on one unified control law that works for all wind conditions. The inherent nonlinearity of wind turbines is addressed through a piecewise-affine approximation of the power coefficient, which is modelled in a mixed-integer fashion. The presented controller is compared to a state-of-the-art baseline controller in a numerical case study using OpenFAST. Simulation results show that the presented controller ensures accurate reference power tracking. Additionally, damage equivalent loads are reduced for higher wind speeds.

eess.SY↗
arXiv2023

Switched max-plus linear-dual inequalities: cycle time analysis and applications

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by max-plus linear-dual inequalities (LDIs), i.e., systems of linear dynamical inequalities in the primal and dual operations of the max-plus algebra. We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operation, each corresponding to a set of LDIs, according to a sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the considered schedule is fixed and either periodic or intermittently periodic. We show that SLDIs can model a wide range of applications including single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose algorithms to compute: i. minimum and maximum cycle times for these processes, improving the time complexity of other existing approaches; ii. a complete trajectory of the robot including start-up and shut-down transients.

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arXiv2023

Switched max-plus linear-dual inequalities for makespan minimization: the case study of an industrial bakery shop

In this paper, an industrial bakery shop is modeled by switched max-plus linear-dual inequalities (SLDIs). SLDIs are timed discrete event systems suitable for describing flow shops with time-window constraints and switching operating modes, where each mode corresponds to a job type. We consider the scheduling problem of minimizing the makespan of the shop, and we show that the application of methods based on the max-plus algebra leads to a faster solution compared to standard techniques. The results of the paper are general, in the sense that they can be applied to any permutation flow shop with time-window constraints.

math.OC↗
arXiv2023

Federated Learning in Wireless Networks via Over-the-Air Computations

In a multi-agent system, agents can cooperatively learn a model from data by exchanging their estimated model parameters, without the need to exchange the locally available data used by the agents. This strategy, often called federated learning, is mainly employed for two reasons: (i) improving resource-efficiency by avoiding to share potentially large datasets and (ii) guaranteeing privacy of local agents' data. Efficiency can be further increased by adopting a beyond-5G communication strategy that goes under the name of Over-the-Air Computation. This strategy exploits the interference property of the wireless channel. Standard communication schemes prevent interference by enabling transmissions of signals from different agents at distinct time or frequency slots, which is not required with Over-the-Air Computation, thus saving resources. In this case, the received signal is a weighted sum of transmitted signals, with unknown weights (fading channel coefficients). State of the art papers in the field aim at reconstructing those unknown coefficients. In contrast, the approach presented here does not require reconstructing channel coefficients by complex encoding-decoding schemes. This improves both efficiency and privacy.

cs.LG↗
arXiv2022

LQ Optimal Control for Power Tracking Operation of Wind Turbines

In this paper, an approach for active power control of individual wind turbines is presented. State-of-the-art controllers typically employ separate control loops for torque and pitch control. In contrast, we use a multivariable control approach. In detail, active power control is achieved by using reference trajectories for generator speed, generator torque, and pitch angle such that a desired power demand is met if weather conditions allow. Then, a linear quadratic (LQ) optimal controller is used for reference tracking. In an OpenFAST simulation environment, the controller is compared to a state-of-the-art approach. The simulations show a similar active power tracking performance, while the LQ optimal controller results in lower mechanical wear. Moreover, the presented approach exhibits good reference tracking and by improving the reference trajectory generation further performance increases can be expected.

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arXiv2022

Weak consistency of P-time event graphs

P-time event graphs (P-TEGs) are event graphs where the residence time of tokens in places is bounded by specified time windows. In this paper, we define a new property of PTEGs, called weak consistency. In weakly consistent P-TEGs, the amount of times a transition can fire before the first violation of a time constraint can be made as large as desired. We show the practical implications of this property and, based on previous results in graph theory, we formulate an algorithm of strongly polynomial time complexity that verifies it. From this algorithm, it is possible to determine, in pseudo-polynomial time, the maximum number of firings before the first constraint violation in a P-TEG.

eess.SY↗
arXiv2022

Switched Max-Plus Linear-Dual Inequalities: Application in Scheduling of Multi-Product Processing Networks

P-time event graphs are discrete event systems suitable for modeling processes in which tasks must be executed in predefined time windows. Their dynamics can be represented by systems of linear dynamical inequalities in the max-plus algebra and its dual, the min-plus algebra, referred to as max-plus linear-dual inequalities (LDIs). We define a new class of models called switched LDIs (SLDIs), which allow to switch between different modes of operations, each corresponding to an LDI, according to an infinite sequence of modes called schedule. In this paper, we focus on the analysis of SLDIs when the schedule is fixed and periodic. We show that SLDIs can model single-robot multi-product processing networks, in which every product has different processing requirements and corresponds to a specific mode of operation. Based on the analysis of SLDIs, we propose an algorithm to compute minimum and maximum cycle times for these processes that improves the time complexity of other existing approaches.

eess.SY↗
arXiv2021

Probabilistic Behavioral Distance and Tuning - Reducing and aggregating complex systems

Given a complex system with a given interface to the rest of the world, what does it mean for a the system to behave close to a simpler specification describing the behavior at the interface? We give several definitions for useful notions of distances between a complex system and a specification by combining a behavioral and probabilistic perspective. These distances can be used to tune a complex system to a specification. We show that our approach can successfully tune non-linear networked systems to behave like much smaller networks, allowing us to aggregate large sub-networks into one or two effective nodes. Finally, we discuss similarities and differences between our approach and $H_\infty$ model reduction.

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