arXiv subjects

Stefan Streif

Publications and source records attributed to Stefan Streif.

At least 37 records · Page 2Linked to original sources

arXiv2024

Global Observability Analysis of a Growth Model for Insects Farming

The Hermetia illucens insects or the black soldier fly has been attracting a growing interest in the food and feed industry. For its high nutritional value on the one hand, and because it is an adequate species for insects in controlled environmental agriculture systems, on the other. Therefore, several models describing this larvae's behaviour have been developed in the literature. Due to the complex nature of living organisms, systems of controlled environment agriculture are characterised by their strong nonlinearities. In this paper, we present a three dimensional nonlinear model describing the black soldier fly dry biomass weight dynamic changes due to the temperature's influence. In practice, this biomass weight is not measured in real time. This becomes problematic for applying feedback control strategies that assume full information of the states. Thus, this work investigates the observability of the dry biomass of a Hermetia illucens farming batch. The instantaneous and global observability of the aforementioned model is proven by constructing an injective transformation between the state space and a higher dimensional space where the transformed states are observable.

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arXiv2024

Computer-assisted proofs for Lyapunov stability via Sums of Squares certificates and Constructive Analysis

We provide a computer-assisted approach to ensure that a given continuous or discrete-time polynomial system is (asymptotically) stable. Our framework relies on constructive analysis together with formally certified sums of squares Lyapunov functions. The crucial steps are formalized within of the proof assistant Minlog. We illustrate our approach with various examples issued from the control system literature.

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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.

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arXiv2024

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.

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arXiv2024

On constructive extractability of measurable selectors of set-valued maps

This paper investigates the possibility of constructive extraction of measurable selector from set-valued maps which may commonly arise in viability theory, optimal control, discontinuous systems etc. For instance, existence of solutions to certain differential inclusions, often requires iterative extraction of measurable selectors. Next, optimal controls are in general non-unique which naturally leads to an optimal set-valued function. Finally, a viable control law can be seen, in general, as a selector. It is known that selector theorems are non-constructive and so selectors cannot always be extracted. In this work, we analyze under which particular conditions selectors are constructively extractable. An algorithm is derived from the theorem and applied in a computational study with a three-wheel robot model.

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arXiv2023

A map-based model predictive control approach for train operation

Trains are a corner stone of public transport and play an important role in daily life. A challenging task in train operation is to avoid skidding and sliding during fast changes of traction conditions, which can, for example, occur due to changing weather conditions, crossings, tunnels or forest entries. The latter depends on local track conditions and can be recorded in a map together with other location-dependent information like speed limits and inclination. In this paper, a model predictive control (MPC) approach is developed. Thanks to the knowledge of future changes of traction conditions, the approach is able to avoid short-term skidding and sliding even under fast changes of traction conditions. In a first step, an optimal reference trajectory is determined by a multiple-shooting approach. In a second step, the reference trajectory is tracked by an MPC setup. The developed method is simulated along a track with fast-changing traction conditions for different scenarios, like changing weather conditions and unexpected delays. In all cases, skidding and sliding is avoided.

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arXiv2023

High-gain observer for the nitrification process including sensor dynamics

Fertilization is commonly used to increase harvests. The lack of knowledge of soil properties and the excessive use of fertilizers can result in overfertilization. Current sensor technology is able to measure the concentrations of some of the involved substances only at selected locations and depths. Point measurements of adjacent sensors in coarse sensor networks can be used to infer upon the state of nitrate concentrations in the sensor surroundings. For this purpose, a high gain observer is proposed. Models of the nitrification process as well as the measurement dynamics for the observer design are derived and discretized on a grid to obtain a system of ordinary differential equations. It is shown that the nonlinearities of the model can be bounded and how the observer gain can be computed via linear matrix inequalities. Furthermore, a model reduction is proposed, which allows the consideration of more grid points. A simulation study demonstrates the proposed approach.

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arXiv2023

Observability and Identifiability Analyses of Process Models for Agricultural Anaerobic Digestion Plants

Dynamic operation of anaerobic digestion plants requires advanced process monitoring and control. Different simplifications of the Anaerobic Digestion Model No. 1 (ADM1) have been proposed recently, which appear promising for model-based process automation and state estimation. As a fundamental requirement, observability and identifiability of these models are analyzed in this work, which was pursued through algebraic and geometric analysis. Manual algebraic assessment was successfull for small models such as the ADM1-R4 and simplified versions of the ADM1-R3, which were derived in this context. However, for larger model classes the algebraic approach showed to be insufficient. By contrast, the geometric approach, implemented in the STRIKE_GOLDD toolbox, allowed to show observability for more complex models (including ADM1-R4 and ADM1-R3), employing two independent algorithms. The present study lays the groundwork for state observer design, parameter estimation and advanced control resting upon ADM1-based models.

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arXiv2023

Experimental verification of an online traction parameter identification method

Traction parameters, that characterize the ground-wheel contact dynamics, are the central factor in the energy efficiency of vehicles. To optimize fuel consumption, reduce wear of tires, increase productivity etc., knowledge of current traction parameters is unavoidable. Unfortunately, these parameters are difficult to measure and require expensive force and torque sensors. An alternative way is to use system identification to determine them. In this work, we validate such a method in field experiments with a mobile robot. The method is based on an adaptive Kalman filter. We show how it estimates the traction parameters online, during the motion on the field, and compare them to their values determined via a 6-directional force-torque sensor installed for verification. Data of adhesion slip ratio curves is recorded and compared to curves from literature for additional validation of the method. The results can establish a foundation for a number of optimal traction methods.

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arXiv2022

Modeling and optimal control of growth, energy, and resource dynamics of Hermetia illucens in mass production environment

Mass production of Hermetia illucens insect larvae is now being adopted in many countries and is taking an industrial production approach. Despite abundant literature on factors that affect larvae growth and the optimal static parameters identified in laboratory setup, for an industrial production process it is necessary to identify the trajectories such that the growth as well as the production process is optimal. To achieve this in this work, some of the important requirements and challenges involved thereof are identified and objectives of the automation process are formulated within a model based optimal control setup. Mechanistic models necessary for the optimization framework are derived as differential equations that describe the dynamic variation of resources (feed, water, O2 etc.), energy, and larval biomass. In addition, the elevated metabolic activity of larvae corresponding to the final instar development is identified and also modelled based on the observation from experiments. The mass and energy balance approach used in modelling enables the quantification and distinction of the mass and energy flux components in various levels (e.g. larvae body, growing medium, production environment, and external environment) while holding its applicability for both open and closed/reactor based production setups. Finally, the trajectories generated using the synthesized optimal controller are tested under different scenarios showcasing significant reduction in resource consumption compared to a fixed set-point operation of the production setup. Results presented in this work not only showcase the potential of the mechanistic models and their application in identifying the relevant process parameters (e.g. reactor properties such as volume, thermal conductivity, actuator capacities), but most importantly in optimizing the process dynamically and tuning the process objectives as desired.

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arXiv2022

Process Optimization of Black Soldier Fly Egg Production via Model Based Control

Black soldier fly (BSF) larvae (\textit{Hermetia illucens}) are a valuable protein source for manufacturing animal feed. To maximize their production, both the quantity and quality of their reproductive cycle, i.e. egg production during oviposition, must be increased. In artificial environments, flies often sit idle in cages without mating, depleting their energy reserves and resulting in lower egg production per female. By controlling environmental conditions such as temperature and light inside breeding cages, the flies may be stimulated in a way that improves egg output. However, this stimulation increases the energy demand of the process and may stress the flies, resulting in reduced egg production. Therefore, control must be applied in a careful way, which requires knowledge of the egg production cycle. In this work, a mathematical model describing the various fly life stages and their transition to the egg production process is developed. Relevant factors are identified and their effect on the fly life and egg production is mathematically described. Parameters are identified using data from literature and goodness of fit is evaluated. Using the model, an optimal control problem is formulated with the goal of minimizing the energy costs and increasing the egg production quantity. In Simulation, our approach showed 13\% higher output in shorter time at reduced energy costs compared to a (standard) constant setpoint approach. Optimal control could reach same amount of egg in 60~\% of time compared to standard scenario.

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arXiv2022

Predictive Control with Learning-Based Terminal Costs Using Approximate Value Iteration

Stability under model predictive control (MPC) schemes is frequently ensured by terminal ingredients. Employing a (control) Lyapunov function as the terminal cost constitutes a common choice. Learning-based methods may be used to construct the terminal cost by relating it to, for instance, an infinite-horizon optimal control problem in which the optimal cost is a Lyapunov function. Value iteration, an approximate dynamic programming (ADP) approach, refers to one particular cost approximation technique. In this work, we merge the results of terminally unconstrained predictive control and approximate value iteration to draw benefits from both fields. A prediction horizon is derived in dependence on different factors such as approximation-related errors to render the closed-loop asymptotically stable further allowing a suboptimality estimate in comparison to an infinite horizon optimal cost. The result extends recent studies on predictive control with ADP-based terminal costs, not requiring a local initial stabilizing controller. We compare this controller in simulation with other terminal cost options to show that the proposed approach leads to a shorter minimal horizon in comparison to previous results.

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arXiv2022

Critical Clearing Time Estimates of Power Grid Faults via a Set-Based Method

This paper is concerned with estimating critical clearing times in the transient stability problem of power grids without extensive time-domain simulations. We consider a highdimensional post-fault system (the grid after the fault is cleared) which we decouple into many smaller subsystems. Then, for each subsystem, we find the so-called safety sets and simulate the faulted system once to deduce the so-called safe and unsafe critical clearing times, which specify the intervals of time over which the fault may remain active before safety is compromised. We demonstrate the approach with a numerical example involving the IEEE 14 bus system.

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arXiv2022

Approximate infinite-horizon predictive control

Predictive control is frequently used for control problems involving constraints. Being an optimization based technique utilizing a user specified so-called stage cost, performance properties, i.e., bounds on the infinite horizon accumulated stage cost, aside closed-loop stability are of interest. To achieve good performance and to influence the region of attraction associated with the prediction horizon, the terminal cost of the predictive controller's optimization objective is a key design factor. Approximate dynamic programming refers to one particular approximation paradigm that pursues iterative cost adaptation over a state domain. Troubled by approximation errors, the associated approximate optimal controller is, in general, not necessarily stabilizing nor is its performance quantifiable on the entire approximation domain. Using a parametric terminal cost trained via approximate dynamic programming, a stabilizing predictive controller is proposed whose performance can directly be related to cost approximation errors. The controller further ensures closed-loop asymptotic stability beyond the training domain of the approximate optimal controller associated to the terminal cost.

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arXiv2022

A stabilizing reinforcement learning approach for sampled systems with partially unknown models

Reinforcement learning is commonly associated with training of reward-maximizing (or cost-minimizing) agents, in other words, controllers. It can be applied in model-free or model-based fashion, using a priori or online collected system data to train involved parametric architectures. In general, online reinforcement learning does not guarantee closed loop stability unless special measures are taken, for instance, through learning constraints or tailored training rules. Particularly promising are hybrids of reinforcement learning with "classical" control approaches. In this work, we suggest a method to guarantee practical stability of the system-controller closed loop in a purely online learning setting, i.e., without offline training. Moreover, we assume only partial knowledge of the system model. To achieve the claimed results, we employ techniques of classical adaptive control. The implementation of the overall control scheme is provided explicitly in a digital, sampled setting. That is, the controller receives the state of the system and computes the control action at discrete, specifically, equidistant moments in time. The method is tested in adaptive traction control and cruise control where it proved to significantly reduce the cost.

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arXiv2022

Generating a robustly stabilizable class of nonlinear systems for the converse optimality problem

Converse optimality theory addresses an optimal control problem conversely where the system is unknown and the value function is chosen. Previous work treated this problem both in continuous and discrete time and non-extensively considered disturbances. In this paper, the converse optimality theory is extended to the class of affine systems with disturbances in continuous time while considering norm constraints on both control inputs and disturbances. The admissibility theorem and the design of the internal dynamics model are generalized in this context. A robust stabilizability condition is added for the initial converse optimality probelm using inverse optimality tool: the robust control Lyapunov function. A design for nonlinear class of systems that are both robustly stabilizable and globally asymptotically stable in open loop is obtained. A case study illustrates the presented theory.

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arXiv2022

Performance bounds of adaptive MPC with bounded parameter uncertainties

Model predictive control is a control approach that minimizes a stage cost over a predicted system trajectory based on a model of the system and is capable of handling state and input constraints. For uncertain models, robust or adaptive methods can be used. Because the system model is used to calculate the control law, the closed-loop behavior of the system and thus its performance, measured by the sum of the stage costs, are related to the model used. If it is adapted online, a performance bound is difficult to obtain and thus the impact of model adaptation is mostly unknown. This work provides a (worst-case) performance bound for a linear adaptive predictive control scheme with a specific model parameter estimation. The proposed bound is expressed in terms of quantities such as the initial system parameter error and the constraint set, among others and can be calculated a priori. The results are discussed in a numerical example.

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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.

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