arXiv subjects

Timm Faulwasser

Publications and source records attributed to Timm Faulwasser.

At least 37 records · Page 2Linked to original sources

arXiv2025

Towards Stochastic (N-1)-Secure Redispatch

The intermittent nature of renewable power availability is one of the major sources of uncertainty in power systems. While markets can guarantee that the demand is covered by the available generation, transmission system operators have to often intervene via economic redispatch to ensure that the physical constraints of the network are satisfied. To account for uncertainty, the underlying optimal power flow (OPF) routines have to be modified. Recently, polynomial chaos expansion (PCE) has been suggested in the literature as a tool for stochastic OPF problems. However, the usage of PCE-based methods in security-constrained OPF for (N-1)-secure operations has not yet been explored. In this paper, we propose a procedure that iteratively solves a PCE-overloaded stochastic OPF problem by including line outage constraints until an (N-1)-secure solution is achieved. We demonstrate the efficacy of our method by comparing it with a Monte-Carlo simulation on a 118-bus example system.

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arXiv2025

Decentralized non-convex optimization via bi-level SQP and ADMM

Decentralized non-convex optimization is important in many problems of practical relevance. Existing decentralized methods, however, typically either lack convergence guarantees for general non-convex problems, or they suffer from a high subproblem complexity. We present a novel bi-level SQP method, where the inner quadratic problems are solved via ADMM. A decentralized stopping criterion from inexact Newton methods allows the early termination of ADMM as an inner algorithm to improve computational efficiency. The method has local convergence guarantees for non-convex problems. Moreover, it only solves sequences of Quadratic Programs, whereas many existing algorithms solve sequences of Nonlinear Programs. The method shows competitive numerical performance for an optimal power flow problem.

math.OC↗

arXiv2025

Decentralized Real-Time Iterations for Distributed NMPC

This article presents a Real-Time Iteration (RTI) scheme for distributed Nonlinear Model Predictive Control (NMPC). The scheme transfers the well-known RTI approach, a key enabler for many industrial real-time NMPC implementations, to the setting of cooperative distributed control. At each sampling instant, one outer iteration of a bi-level decentralized Sequential Quadratic Programming (dSQP) method is applied to a centralized optimal control problem. This ensures that real-time requirements are met and it facilitates cooperation between subsystems. Combining novel dSQP convergence results with RTI stability guarantees, we prove local exponential stability under standard assumptions on the MPC design with and without terminal constraints. The proposed scheme only requires neighbor-to-neighbor communication and avoids a central coordinator. A numerical example with coupled inverted pendulums demonstrates the efficacy of the approach.

math.OC↗

arXiv2025

Complexity Reduction for TSO-DSO Coordination: Flexibility Aggregation vs. Distributed Optimization

The increasing number of flexible devices and distributed energy resources in power grids renders the coordination of transmission and distribution systems increasingly complex. In this paper, we discuss and compare two different approaches to optimization-based complexity reduction: Flexibility aggregation via Approximate Dynamic Programming (ADP) and distributed optimization via the Alternating Direction Method of Multipliers (ADMM). Flexibility aggregation achieves near-optimal solutions with minimal communication. However, its performance depends on the quality of the approximation used. In contrast, ADMM attains results closer to the centralized solution but requires significantly more communication steps. We draw upon a case study combining different matpower benchmarks to compare both methods.

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arXiv2025

Towards Event-Triggered NMPC for Efficient 6G Communications: Experimental Results and Open Problems

Networked control systems enable real-time control and coordination of distributed systems, leveraging the low latency, high reliability, and massive connectivity offered by 5G and future 6G networks. Applications include autonomous vehicles, robotics, industrial automation, and smart grids. Despite networked control algorithms admitting nominal stability guarantees even in the presence of delays and packet dropouts, their practical performance still heavily depends on the specific characteristics and conditions of the underlying network. To achieve the desired performance while efficiently using communication resources, co-design of control and communication is pivotal. Although periodic schemes, where communication instances are fixed, can provide reliable control performance, unnecessary transmissions, when updates are not needed, result in inefficient usage of network resources. In this paper, we investigate the potential for co-design of model predictive control and network communication. To this end, we design and implement an event-triggered nonlinear model predictive controller for stabilizing a Furuta pendulum communicating over a tailored open radio access network 6G research platform. We analyze the control performance as well as network utilization under varying channel conditions and event-triggering criteria. Additionally, we analyze the network-induced delay pattern and its interaction with the event-triggered controller. Our results show that the event-triggered control scheme achieves similar performance to periodic control with reduced communication demand.

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arXiv2025

Towards an Optimal Control Perspective of ResNet Training

We propose a training formulation for ResNets reflecting an optimal control problem that is applicable for standard architectures and general loss functions. We suggest bridging both worlds via penalizing intermediate outputs of hidden states corresponding to stage cost terms in optimal control. For standard ResNets, we obtain intermediate outputs by propagating the state through the subsequent skip connections and the output layer. We demonstrate that our training dynamic biases the weights of the unnecessary deeper residual layers to vanish. This indicates the potential for a theory-grounded layer pruning strategy.

cs.LG↗

arXiv2025

Exact Time-Varying Turnpikes for Dynamic Operation of District Heating Networks

District heating networks (DHNs) are crucial for decarbonizing the heating sector. Yet, their efficient and reliable operation requires the coordination of multiple heat producers and the consideration of future demands. Predictive and optimization-based control is commonly used to address this task, but existing results for DHNs do not account for time-varying problem aspects. Since the turnpike phenomenon can serve as a basis for model predictive control design and analysis, this paper examines its role in DHN optimization by analyzing the underlying optimal control problem with time-varying prices and demands. That is, we derive conditions for the existence of a unique time-varying singular arc, which constitutes the time varying turnpike, and we provide its closed-form expression. Additionally, we present converse turnpike results showing a exact time-varying case implies strict dissipativity of the optimal control problem. A numerical example illustrates our findings.

math.OC↗

arXiv2025

Probabilistic Time Series Forecasting of Residential Loads -- A Copula Approach

Predicting the time series of future evolutions of renewable injections and demands is of utmost importance for the operation of power systems. However, the current state of the art is mostly focused on mean-value time series predictions and only very few methods provide probabilistic forecasts. In this paper, we rely on kernel density estimation and vine copulas to construct probabilistic models for individual load profiles of private households. Our approach allows the quantification of variability of individual energy consumption in general and of daily peak loads in particular. We draw upon an Australian distribution grid dataset to illustrate our findings. We generate synthetic loads that follow the distribution of the real data.

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arXiv2025

Large problems are not necessarily hard: A case study on distributed NMPC paying off

A key motivation in the development of Distributed Model Predictive Control (DMPC) is to accelerate centralized Model Predictive Control (MPC) for large-scale systems. DMPC has the prospect of scaling well by parallelizing computations among subsystems. However, communication delays may deteriorate the performance of decentralized optimization, if excessively many iterations are required per control step. Moreover, centralized solvers often exhibit faster asymptotic convergence rates and, by parallelizing costly linear algebra operations, they can also benefit from modern multicore computing architectures. On this canvas, we study the computational performance of cooperative DMPC for linear and nonlinear systems. To this end, we apply a tailored decentralized real-time iteration scheme to frequency control for power systems. DMPC scales well for the considered linear and nonlinear benchmarks, as the iteration number does not depend on the number of subsystems. Comparisons with multi-threaded centralized solvers demonstrate competitive performance of the proposed decentralized optimization algorithms.

math.OC↗

arXiv2025

Towards safe Bayesian optimization with Wiener kernel regression

Bayesian Optimization (BO) is a data-driven strategy for minimizing/maximizing black-box functions based on probabilistic surrogate models. In the presence of safety constraints, the performance of BO crucially relies on tight probabilistic error bounds related to the uncertainty surrounding the surrogate model. For the case of Gaussian Process surrogates and Gaussian measurement noise, we present a novel error bound based on the recently proposed Wiener kernel regression. We prove that under rather mild assumptions, the proposed error bound is tighter than bounds previously documented in the literature, leading to enlarged safety regions. We draw upon a numerical example to demonstrate the efficacy of the proposed error bound in safe BO.

stat.ML↗

arXiv2025

Turnpike and dissipativity in generalized discrete-time stochastic linear-quadratic optimal control

We investigate different turnpike phenomena of generalized discrete-time stochastic linear-quadratic optimal control problems. Our analysis is based on a novel strict dissipativity notion for such problems, in which a stationary stochastic process replaces the optimal steady state of the deterministic setting. We show that from this time-varying dissipativity notion, we can conclude turnpike behaviors concerning different objects like distributions, moments, or sample paths of the stochastic system and that the distributions of the stationary pair can be characterized by a stationary optimization problem. The analytical findings are illustrated by numerical simulations.

math.OC↗

arXiv2025

Cooperative distributed model predictive control for embedded systems: Experiments with hovercraft formations

This paper presents experiments for embedded cooperative distributed model predictive control applied to a team of hovercraft floating on an air hockey table. The hovercraft collectively solve a centralized optimal control problem in each sampling step via a stabilizing decentralized real-time iteration scheme using the alternating direction method of multipliers. The efficient implementation does not require a central coordinator, executes onboard the hovercraft, and facilitates sampling intervals in the millisecond range. The formation control experiments showcase the flexibility of the approach on scenarios with point-to-point transitions, trajectory tracking, collision avoidance, and moving obstacles.

cs.RO↗

arXiv2025

A Polynomial Chaos Approach to Stochastic LQ Optimal Control: Error Bounds and Infinite-Horizon Results

The stochastic linear--quadratic regulator problem subject to Gaussian disturbances is well known and usually addressed via a moment-based reformulation. Here, we leverage polynomial chaos expansions, which model random variables via series expansions in a suitable $\mathcal{L}^2$ probability space, to tackle the non-Gaussian case. We present the optimal solutions for finite and infinite horizons and we analyze the infinite-horizon asymptotics. We show that the limit of the optimal state-input trajectory is the unique solution to a corresponding stochastic stationary optimization problem in the sense of probability measures. Moreover, we provide a constructive error analysis for finite-dimensional polynomial chaos approximations of the optimal solutions and of the optimal stationary pair in non-Gaussian settings. A numerical example illustrates our findings.

math.OC↗

arXiv2025

Towards Data-Driven Multi-Stage OPF

The operation of large-scale power systems is usually scheduled ahead via numerical optimization. However, this requires models of grid topology, line parameters, and bus specifications. Classic approaches first identify the network topology, i.e., the graph of interconnections and the associated impedances. The power generation schedules are then computed by solving a multi-stage optimal power flow (OPF) problem built around the model. In this paper, we explore the prospect of data-driven approaches to multi-stage optimal power flow. Specifically, we leverage recent findings from systems and control to bypass the identification step and to construct the optimization problem directly from data. We illustrate the performance of our method on a 118-bus system and compare it with the classical identification-based approach.

eess.SY↗

arXiv2024

Tutorial Problems for Nonsmooth Dynamics and Optimal Control: Ski Jumping and Accelerating a Bike Without Pedaling

Nonsmooth phenomena, such as abrupt changes, impacts, and switching behaviors, frequently arise in real-world systems and present significant challenges for traditional optimal control methods, which typically assume smoothness and differentiability. These phenomena introduce numerical challenges in both simulation and optimization, highlighting the need for specialized solution methods. Although various applications and test problems have been documented in the literature, many are either overly simplified, excessively complex, or narrowly focused on specific domains. On this canvas, this paper proposes two novel tutorial problems that are both conceptually accessible and allow for further scaling of problem difficulty. The first problem features a simple ski jump model, characterized by state-dependent jumps and sliding motion on impact surfaces. This system does not involve control inputs and serves as a testbed for simulating nonsmooth dynamics. The second problem considers optimal control of a special type of bicycle model. This problem is inspired by practical techniques observed in BMX riding and mountain biking, where riders accelerate their bike without pedaling by strategically shifting their center of mass in response to the track's slope.

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arXiv2024

On Data-Driven Stochastic Output-Feedback Predictive Control

The fundamental lemma by Jan C. Willems and co-authors enables the representation of all input-output trajectories of a linear time-invariant system by measured input-output data. This result has proven to be pivotal for data-driven control. Building on a stochastic variant of the fundamental lemma, this paper presents a data-driven output-feedback predictive control scheme for stochastic Linear Time-Invariant (LTI) systems. The considered LTI systems are subject to non-Gaussian disturbances about which only information about their first two moments is known. Leveraging polynomial chaos expansions, the proposed scheme is centered around a data-driven stochastic Optimal Control Problem (OCP). Through tailored online design of initial conditions, we provide sufficient conditions for the recursive feasibility of the proposed output-feedback scheme based on a data-driven design of the terminal ingredients of the OCP. Furthermore, we provide a robustness analysis of the closed-loop performance. A numerical example illustrates the efficacy of the proposed scheme.

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arXiv2024

Optimal control of port-Hamiltonian systems: energy, entropy, and exergy

We consider irreversible and coupled reversible-irreversible nonlinear port-Hamiltonian systems and the respective sets of thermodynamic equilibria. In particular, we are concerned with optimal state transitions and output stabilization on finite-time horizons. We analyze a class of optimal control problems, where the performance functional can be interpreted as a linear combination of energy supply, entropy generation, or exergy supply. Our results establish the integral turnpike property towards the set of thermodynamic equilibria providing a rigorous connection of optimal system trajectories to optimal steady states. Throughout the paper, we illustrate our findings by means of two examples: a network of heat exchangers and a gas-piston system.

math.OC↗

arXiv2024

Exploring the Links between the Fundamental Lemma and Kernel Regression

Generalizations and variations of the fundamental lemma by Willems et al. are an active topic of recent research. In this note, we explore and formalize the links between kernel regression and some known nonlinear extensions of the fundamental lemma. Applying a transformation to the usual linear equation in Hankel matrices, we arrive at an alternative implicit kernel representation of the system trajectories while keeping the requirements on persistency of excitation. We show that this representation is equivalent to the solution of a specific kernel regression problem. We explore the possible structures of the underlying kernel as well as the system classes to which they correspond.

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