arXiv subjects

Philipp Sauerteig

Publications and source records attributed to Philipp Sauerteig.

10 recordsLinked to original sources

arXiv2024

MPC without Terminal Ingredients Tailored to the SEIR Compartmental Epidemic Model

We consider the SEIR compartmental epidemic model subject to state and input constraints (a cap on the proportion of infectious individuals and limits on the allowed social distancing and quarantining measures, respectively). We present a tailored model predictive control (MPC) scheme without terminal conditions. We rigorously show recursive feasibility and asymptotic convergence of the MPC closed loop to the continuum of disease-free equilibrium points for suitably designed quadratic running cost and a sufficiently long prediction horizon (forecast window). Moreover, we establish the viability kernel (a.k.a. the admissible set) as a domain of attraction of the continuum of equilibria.

math.OC↗

arXiv2023

Deep Neural Network based Optimal Control of Greenhouses

Automatic control of greenhouse crop production is of great interest owing to the increasing energy and labor costs. In this work, we use two-level control, where the upper level generates suitable reference trajectories for states and control inputs based on day-ahead predictions. These references are tracked in the lower level using Nonlinear Model Predictive Control (NMPC). In order to apply NMPC, a model of the greenhouse dynamics is essential. However, the complex nature of the underlying model including discontinuities and nonlinearities results in intractable computational complexity and long sampling times. As a remedy, we employ NMPC as a data generator to learn the tracking control policy using deep neural networks. Then, the references are tracked using the trained Deep Neural Network (DNN) to reduce the computational burden. The efficiency of our approach under real-time disturbances is demonstrated by means of a simulation study.

eess.SY↗

arXiv2022

Bidirectional Optimisation for Load Shaping within Coupled Microgrids

We address the problem of load shaping within a network of coupled microgrids (MGs) in a bilevel optimisation framework. To this end, we consider the charging/discharging rates of residential energy storage devices within each MG on the lower level and the power exchange among neighbouring MGs on the upper level as optimisation variables. We improve a previously developed model such that the maximal amount of exchanged power does not depend on the power demand, thus, increasing the flexibility within the network, and adapt the corresponding bidirectional optimisation scheme accordingly. For efficiency, standard distributed optimisation routines are used for the optimisation on the lower level; the power exchange problem on the upper level is replaced by parallelisable small-scale quadratic programmings. We prove global convergence of the optimisation scheme and illustrate the potential of the approach in a numerical case study based on real-world data.

math.OC↗

arXiv2022

Model Predictive Control Tailored to Epidemic Models

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that in the MRPI all restrictions can be lifted without violating the infection cap, we choose a suitable subset of the MRPI to define terminal constraints in our MPC routine and show that the number of infected people decays exponentially within this set. Furthermore, under mild assumptions we prove existence of a uniform bound on the time required to reach this terminal region (without violating the infection cap) starting in the admissible set. The findings are substantiated based on a numerical case study.

math.OC↗

arXiv2021

How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the healthcare system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.

physics.soc-ph↗

arXiv2020

How much testing and social distancing is required to control COVID-19? Some insight based on an age-differentiated compartmental model

In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: 1) incubation time, 2) age-dependent symptom severity, and 3) testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social-distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.

math.OC↗

arXiv2020

Distributed Optimization using ALADIN for MPC in Smart Grids

This paper presents a distributed optimization algorithm tailored to solve optimization problems arising in smart grids. In detail, we propose a variant of the Augmented Lagrangian based Alternating Direction Inexact Newton (ALADIN) method, which comes along with global convergence guarantees for the considered class of linear-quadratic optimization problems. We establish local quadratic convergence of the proposed scheme and elaborate its advantages compared to the Alternating Direction Method of Multipliers (ADMM). In particular, we show that, at the cost of more communication, ALADIN requires fewer iterations to achieve the desired accuracy. Furthermore, it is numerically demonstrated that the number of iterations is independent of the number of subsystems. The effectiveness of the proposed scheme is illustrated by running both an ALADIN and an ADMM based model predictive controller on a benchmark case study.

eess.SY↗

arXiv2020

Distributed Control Enforcing Group Sparsity in Smart Grids

In modern smart grids, charging of local energy storage devices is coordinated on a residential level to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which reduces their lifetime. We enforce group sparsity by using an $\ell_{p,q}$-regularization on the control to counteract this phenomenon. This leads to a non-smooth convex optimization problem, for which we propose a tailored Alternating Direction Method of Multipliers algorithm. We elaborate further how to embed it in a Model Predictive Control framework. We show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving by numerical simulations.

eess.SY↗

arXiv2019

Surrogate Models in Bidirectional Optimization of Coupled Microgrids

The energy transition entails a rapid uptake of renewable energy sources. Besides physical changes within the grid infrastructure, energy storage devices and their smart operation are key measures to master the resulting challenges like, e.g., a highly fluctuating power generation. For the latter, optimization based control has demonstrated its potential on a microgrid level. However, if a network of coupled microgrids is considered, iterative optimization schemes including several communication rounds are typically used. Here, we propose to replace the optimization on the microgrid level by using surrogate models either derived from radial basis functions or neural networks to avoid this iterative procedure. We prove well-posedness of our approach and demonstrate its efficiency by numerical simulations based on real data provided by an Australian grid operator.

math.OC↗

arXiv2019

Towards multiobjective optimization and control of smart grids

The rapid uptake of renewable energy sources in the electricity grid leads to a demand in load shaping and flexibility. Energy storage devices such as batteries are a key element to provide solutions to these tasks. However, typically a trade-off between the performance related goal of load shaping and the objective of having flexibility in store for auxiliary services, which is for example linked to robustness and resilience of the grid, can be observed. We propose to make use of the concept of Pareto optimality in order to resolve this issue in a multiobjective framework. In particular, we analyse the Pareto frontier and quantify the trade-off between the non-aligned objectives to properly balance them.

math.OC↗