arXiv subjects

Annika Eichler

Publications and source records attributed to Annika Eichler.

26 records · Page 2Linked to original sources

arXiv2022

Online Computation of Terminal Ingredients in Distributed Model Predictive Control for Reference Tracking

A distributed model predictive control scheme is developed for tracking piecewise constant references where the terminal set is reconfigured online, whereas the terminal controller is computed offline. Unlike many standard existing schemes, this scheme yields large feasible regions without performing offline centralized computations. Although the resulting optimal control problem (OCP) is a semidefinite program (SDP), an SDP scalability method based on diagonal dominance is used to approximate the derived SDP by a second-order cone program. The OCPs of the proposed scheme and its approximation are amenable to distributed optimization. Both schemes are evaluated using a power network example and compared to a scheme where the terminal controller is reconfigured online as well. It is found that fixing the terminal controller results in better performance, noticeable reduction in computational cost and similar feasible region compared to the case in which this controller is reconfigured online.

eess.SY↗

arXiv2022

Anomaly Detection at the European XFEL using a Parity Space based Method

A novel approach to detect anomalies in superconducting radio-frequency cavities is presented, based on the parity space method with the goal to detect quenches and distinguish them from other anomalies. The model-based parity space method relies on analytical redundancy and generates a residual signal computed from measurable RF waveforms. The residual is a sensitive indicator of deviation from the model and provides different signatures for different types of anomalies. This new method not only helps with detecting faults, but also provides a catalogue of unique signatures, based on the detected fault. The method was experimentally verified at the European X-ray Free Electron Laser (EuXFEL). Various types of anomalies incorrectly detected as quenches by the current quench detection system are analysed using this new approach.

physics.acc-ph↗

arXiv2021

Distributed Model Predictive Control with Reconfigurable Terminal Ingredients for Reference Tracking

Various efforts have been devoted to developing stabilizing distributed Model Predictive Control (MPC) schemes for tracking piecewise constant references. In these schemes, terminal sets are usually computed offline and used in the MPC online phase to guarantee recursive feasibility and asymptotic stability. Maximal invariant terminal sets do not necessarily respect the distributed structure of the network, hindering the distributed implementation of the controller. On the other hand, ellipsoidal terminal sets respect the distributed structure, but may lead to conservative schemes. In this paper, a novel distributed MPC scheme is proposed for reference tracking of networked dynamical systems where the terminal ingredients are reconfigured online depending on the closed-loop states to alleviate the aforementioned issues. The resulting non-convex infinite-dimensional problem is approximated using a quadratic program. The proposed scheme is tested in simulation where the proposed MPC problem is solved using distributed optimization.

eess.SY↗

arXiv2020

Multiperiod Stochastic Peak Shaving Using Storage

We present an online stochastic model predictive control framework for demand charge management for a grid-connected consumer with attached electrical energy storage. The consumer we consider must satisfy an inflexible but stochastic electricity demand, and also receives a stochastic electricity inflow. The optimization problem formulated solves a stochastic cost minimization problem, with given weather forecast scenarios converted into forecast demand and inflow. We introduce a novel weighting scheme to account for cases where the optimization horizon spans multiple demand charge periods. The optimization scheme is tested in a setting with building demand and photovoltaic array inflow data from a real office building. The simulation study allows us to compare various design and modeling alternatives, ultimately proposing a policy based on causal affine decision rules.

eess.SY↗

arXiv2020

Distributed Model Predictive Control with Asymmetric Adaptive Terminal Sets for the Regulation of Large-scale Systems

In this paper, a novel distributed model predictive control (MPC) scheme with asymmetric adaptive terminal sets is developed for the regulation of large-scale systems with a distributed structure. Similar to typical MPC schemes, a structured Lyapunov matrix and a distributed terminal controller, respecting the distributed structure of the system, are computed offline. However, in this scheme, a distributed positively invariant terminal set is computed online and updated at each time instant taking into consideration the current state of the system. In particular, we consider ellipsoidal terminal sets as they are easy to compute for large-scale systems. The size and the center of these terminal sets, together with the predicted state and input trajectories, are considered as decision variables in the online phase. Determining the terminal set center online is found to be useful specifically in the presence of asymmetric constraints. Finally, a relaxation of the resulting online optimal control problem is provided. The efficacy of the proposed scheme is illustrated in simulation by comparing it to a recent distributed MPC scheme with adaptive terminal sets.

eess.SY↗

arXiv2020

Distributed Control Design for Heterogeneous Interconnected Systems

This paper presents scalable controller synthesis methods for heterogeneous and partially heterogeneous systems. First, heterogeneous systems composed of different subsystems that are interconnected over a directed graph are considered. Techniques from robust and gain-scheduled controller synthesis are employed, in particular the full-block S-procedure, to deal with the decentralized system part in a nominal condition and with the interconnection part in a multiplier condition. Under some structural assumptions, we can decompose the synthesis conditions into conditions that are the size of the individual subsystems. To solve these decomposed synthesis conditions that are coupled only over neighboring subsystems, we propose a distributed method based on the alternating direction method of multipliers. It only requires nearest-neighbor communication and no central coordination is needed. Then, a new classification of systems is introduced that consists of groups of homogeneous subsystems with different interconnection types. This classification includes heterogeneous systems as the most general and homogeneous systems as the most specific case. Based on this classification, we show how the interconnected system model and the decomposed synthesis conditions can be formulated in a more compact way. The computational scalability of the presented methods with respect to a growing number of subsystems and interconnections is analyzed, and the results are demonstrated in numerical examples.

eess.SY↗

arXiv2019

Two-Stage Dual Dynamic Programming with Application to Nonlinear Hydro Scheduling

We present an approximate method for solving nonlinear control problems over long time horizons, in which the full nonlinear model is preserved over an initial part of the horizon, while the remainder of the horizon is modeled using a linear relaxation. As this approximate problem may still be too large to solve directly, we present a Benders decomposition-based solution algorithm that iterates between solving the nonlinear and linear parts of the horizon. This extends the Dual Dynamic Programming approach commonly employed for optimization of linearized hydro power systems. We prove that the proposed algorithm converges after a finite number of iterations, even when the nonlinear initial stage problems are solved inexactly. We also bound the suboptimality of the split-horizon method with respect to the original nonlinear problem, in terms of the properties of a map between the linear and nonlinear state-input trajectories. We then apply this method to a case study concerning a multiple reservoir hydro system, approximating the nonlinear head effects in the second stage using McCormick envelopes. We demonstrate that near-optimal solutions can be obtained in a shrinking horizon setting when the full nonlinear model is used for only a short initial section of the horizon. For this example, the approach is shown to be more practical than both conventional dynamic programming and a multi-cell McCormick envelope approximation from literature.

math.OC↗

arXiv2018

Distributed Model Predictive Control for Linear Systems with Adaptive Terminal Sets

In this paper, we propose a distributed model predictive control (DMPC) scheme for linear time-invariant constrained systems which admit a separable structure. To exploit the merits of distributed computation algorithms, the stabilizing terminal controller, value function and invariant terminal set of the DMPC optimization problem need to respect the loosely coupled structure of the system. Although existing methods in the literature address this task, they typically decouple the synthesis of terminal controllers and value functions from the one of terminal sets. In addition, these approaches do not explicitly consider the effect of the current state of the system in the synthesis process. These limitations can lead the resulting DMPC scheme to poor performance since it may admit small or even empty terminal sets. Unlike other approaches, this paper presents a unified framework to encapsulate the synthesis of both the stabilizing terminal controller and invariant terminal set into the DMPC formulation. Conditions for Lyapunov stability and invariance are imposed in the synthesis problem in a way that allows the value function and invariant terminal set to admit the desired distributed structure. We illustrate the effectiveness of the proposed method on several examples including a benchmark spring-mass-damper problem.

math.OC↗