This thesis deals with the problems of design and operation of process supply chains. Process supply chains face many challenges due to volatile market conditions, production and transportation delays, and stiff market competition, which ultimately affect their profitability. Supply chain management (SCM) is the process of managing the flow of materials and information within supply chain to optimize the SC performance. SCM is carried out using a hierarchical decision-making framework, where the top most layer looks at network design and the bottom-most layer deals with scheduling day-to-day activities. In this research, the systems engineering principles are applied to devise an improved methodology for supply chain optimization (SCO). First, we consider the design of supply chain in the presence of demand uncertainty. The representation of network topology plays an important role in deriving the optimal network design. In real practice, the shipping cost for transferring goods from one location to another is determined based on service time and quantity. More importantly, the cost associated with establishing a transportation linkage is relatively small for existing transportation infrastructure and can be changed if beneficial. The flexibility of changing the transportation routes is included in the network topology representation by the explicit inclusion of time limited transportation contract agreements. Further, the customer demand is volatile, and it is very difficult to predict accurately. To handle the demand uncertainty, a two-stage stochastic programming formulation is applied in the SC design approach. Next, we consider the problem of handling uncertainty in SC planning by applying a system engineering control principle, robust model predictive control (MPC). The uncertainty in model parameters (yield) and demand are captured by stochastic programming. In this approach, the planning activities are represented by a hybrid model with decisions governed by logical conditions/rulesets. An MPC based rolling horizon control framework is used to schedule the planning activities, where the SC performance is expressed using a multi-criterion objective comprising customer service and economics. The uncertainty in demand and yield are propagated by two mechanisms - an open-loop approach, and an approximate closed-loop strategy. Finally, we consider the problem of integration of SC planning and scheduling. Due to the use of different time scale models for planning and scheduling, the decision derived from the planning layer may result in infeasibility when those targets are implemented at the scheduling level, which ultimately affects the supply chain efficiency. To address this issue, we model tactical and operational planning activities using an integrated hybrid time modeling approach in which the first few planning periods are formulated using an operational planning model and the remaining time periods are modeled with a tactical planning model. The main rationale for formulating an integrated model is that customer demand forecast becomes less accurate for a future time, therefore making a detailed planning model unnecessary. A key benefit of using a hybrid modeling approach is that it avoids the problem of infeasibility encountered in the hierarchical decision framework, as well as the computational burden associated with the use of a detailed planning model over a long time horizon. We employ an MPC based rolling horizon framework as a tactical decision policy where the integrated model is used to predict the system behavior. / Thesis / Doctor of Philosophy (PhD)

<p dir="ltr">Personalized thermal controls are beneficial for occupant comfort and productivity in office buildings. Recent research efforts on learning personal thermal comfort support the integration of personalized preferences in optimal building control and further implementation in real buildings. This Thesis presents the development and field implementation of personal preference-based thermal control in real offices, emphasizing the role of model predictive control (MPC) and low-cost local sensing. Probabilistic thermal preference profiles, a low-cost thermal sensing network and a MPC framework were integrated into a centralized building management and control system. The customized, preference-based HVAC control implemented in the offices indicated the comfort benefits of monitoring local thermal conditions (vs wall thermostats) for different preference profiles and showed 28-35% energy savings with personalized MPC (vs personalized static setpoint control).</p><p dir="ltr">Regarding the practical limitations in collecting sufficient data from occupants to train their thermal comfort model, we present a Bayesian meta-learning approach for developing reliable, data-driven personalized thermal comfort models using limited data from individuals. A high-dimensional neural network was developed, considering general thermal comfort impact factors (environmental variables, clothing level and metabolic rate) as well as personal thermal characteristics (expressed as a vector of continuous latent variables) as model inputs. The model parameters in the neural network were trained with subsets of ASHRAE RP-884 database. The trained neural network is transferrable, so that the thermal preferences of new individuals can be predicted by inferring their personal thermal characteristics using limited data. The results show that the developed Bayesian meta-learning approach to infer personal thermal comfort performs better than existing methods, especially when using limited data.</p><p dir="ltr">Moreover, this Thesis also discusses the potential of balancing thermal comfort and energy cost by setting dynamic temperature constraints in personalized MPC. A co-simulation framework of EnergyPlus and MPC is constructed using EnergyPlus Python API. Dynamic temperature constraints are selected based on personal thermal profile, weather conditions and utility rate variations. The performance of the personalized MPC with dynamic constraints demonstrates a balance between thermal comfort and energy cost in cooling season.</p>

Stricter requirements on the reduction of Nitrogen Oxides (NOx) in the emissions of heavy-duty diesel vehicles drives development for more efficient aftertreatment systems. An ammonia covered catalyst is one of the most successful technologies in reducing NOx by converting it into the harmless byproducts water and nitrogen. The ammonia injection control is however difficult due to nonlinearities and the impact of external exhaust parameters. The ammonia coverage ratio depends heavily on the surface temperature of the catalyst and a rapid increase in surface temperature would lead to a rapid decrease in ammonia storage capabilities. If the storage capabilities decrease below the current level of stored ammonia, the excess ammonia will flow into the exhaust and convert to NOx, an undesired phenomenon due to the cost of and the pollution caused by the ammonia released, often referred to as ammonia slip. This issue is further amplified by the fact that the problem is asymmetric, that is injected ammonia cannot be actively removed but has to be reduced by the reaction with the NOx present in the exhaust. As such, it is very important to keep the level of ammonia storage ratio low enough to avoid slipping but at the same time sufficiently high to obtain a satisfactory NOx conversion efficiency. These two issues are the main reasons why feedback control has proven to be difficult to implement to solve the dosing problem. As one has to store a lot of ammonia in order to obtain a satisfactory conversion of NOx, one often cannot react to rapid temperature increases in the catalyst. As such, one often experiences a lot of ammonia slip during these scenarios. In this report it is shown that utilizing predicted parameters of the exhaust in a model predictive controller reduces the ammonia consumption by 38% while also improving the tracking of the NOx conversion reference by 5.5%. / Strängare krav på minskning av kväveoxider (NOx) i utsläpp från tunga dieselfordon driver utvecklingen för ett mer effektivt efterbehandlingssystem. En ammoniakbelagd katalysator är en av de mest framgångsrika tekniker för att minska NOx genom att omvandla det till de ofarliga biprodukterna vatten och kväve. Injeceringen av ammoniak är dock svår att reglera på grund av olinjär dynamik och påverkan av externa avgasparametrar. Täckningsgraden av ammoniak beror starkt på yttemperaturen hos katalysatorn, där en ökning av temperaturen skulle leda till en minskad lagringskapacitet av ammoniak. Om lagringskapaciteten minskar under nuvarande täckningsgraden av ammoniak kommer överskottet av ammoniak att frigöras och strömma ut ur katalysatorn tillsammans med avgaserna och omvandlas till NOx, ett oönskat fenomen på grund av kostnaden för och de föroreningar som orsakas av ammoniaken. Detta problem förvärras av det faktum att problemet är asymmetriskt, dvs injicerad ammoniak kan inte aktivt avlägsnas utan måste reduceras genom att reagera med de befintliga NOx som finns i avgaserna. Därav är det väldigt viktigt att täckningsgraden av ammoniak hålls tillräckligt lågt för att undvika att ammoniaken frigörs men samtidigt tillräckligt hög för att erhålla den önskade omvandlingen av NOx. Dessa två problem är de främsta anledningarna till att reglering med återkoppling har visat sig vara svårt att implementera för att lösa doseringsproblemet. Eftersom det krävs en hög täckningsgraden av ammoniak för att få en önskvärd omvandling av NOx hinner en ofta inte korrigera för snabba temperaturökningar i katalysatorn. Det frigörs därför mycket av den lagrade ammoniaken under dessa scenarier. I denna rapport demonstreras att användandet av predikterade avgasparametrar i en modell prediktiv kontroller minskar ammoniakförbrukningen med 38% samtidigt som den önskade NOx omvandlingen förbättrades med 5.5%.

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In this thesis, we develop methods leading towards the distributed control of spatio-temporally constrained systems. Overall, we focus on two different approaches: a model predictive control approach and an approach based on ensuring set-invariance via control barrier functions. Developing a distributed control framework for spatio-temporally constrained systems is challenging since multiple subsystems are interconnected via time-varying state constraints. Often, such constraints are only implicitly given as logic formulas, for example in Signal Temporal Logic (STL). Our approach to dealing with spatio-temporal constraints is as follows. We aim at combining the computational efficiency of low-level feedback controllers with planning algorithms. Low-level feedback controllers shall ensure the satisfaction of parts of spatio-temporal constraints such as coupling state constraints or short term time-constraints. In contrast, planning algorithms account for those parts that require computationally intense planning operations. Powerful low-level controllers can simplify the planning task significantly. For this reason, the focus of this thesis is on the development of low level feedback controllers.  In the first part, we focus on handling coupling state constraints using a model predictive control (MPC) approach. Commonly, the distributed handling of coupling state constraints requires a sequential or iterative MPC scheme which however is computationally time-intense. We address this issue by employing consistency constraints to develop a parallelized distributed model predictive controller (DMPC). By using consistency constraints, each subsystem guarantees to its neighbors that its states stay within a particular neighborhood around a reference trajectory. Furthermore, we propose extensions to robust and iterative schemes. Building up on this, also systems with bounded dynamic couplings can be controlled. In the second part, we focus on methods for ensuring set-invariance. In particular, we focus on control barrier functions (CBF). We show how spatio-temporal constraints that comprise disjunctions (logic OR) can be encoded in non-smooth time-varying control barrier functions and how subgradients can be used to synthesize an efficient gradient-based controller. For these results, controllability assumptions must be invoked. To extend the results to systems with weaker controllability properties, we investigate the connection between controllability properties and the construction of CBFs. As a result, we propose a construction method for CBFs based on finite horizon predictions. The constructed CBF exhibits favorable properties for the extension of the previous results on encoding spatio-temporal constraints in CBFs to systems with weaker controllability properties. At last, we investigate with a case study how set-invariance methods can be used to implicitly coordinate systems subject to coupled state constraints. Our proposed method is fully decentralized and subsystems coordinate themselves purely via their actions and the adjustment of their individual constraints. In the end, we draw a conclusion and outline how the presented results contribute to the development of a distributed control framework for spatio-temporally constrained systems. / I den här avhandlingen utvecklar vi metoder som leder till distribuerad styrning av tillstånds-temporalt begränsade system. Vi följer två olika tillvägagångssätt: å ena sidan en modellprediktiv styrning och å andra sidan ett tillvägagångssätt som bygger på att säkerställa invarians i mängden via kontrollbarriärfunktioner. Det är en utmaning att utveckla ett ramverk för distribuerad styrning för tillstånds-temporalt begränsade system, eftersom flera delsystem är sammankopplade via sina tillståndsbegränsningar som varierar över tiden. Ofta ges sådana begränsningar endast implicit som logiska formler, till exempel i Signal Temporal Logic (STL).  Vår metod för att hantera tillstånds- och tidsmässiga begränsningar är följande. Vi strävar efter att kombinera beräkningseffektiviteten hos återkopplingsregulatorer på låg nivå med planeringsalgoritmer. Återkopplingsregulatorer på låg nivå skall säkerställa att delar av de tillstånds- och tidsmässiga begränsningarna uppfylls, t.ex. sammankopplande tillståndsbegränsningar eller kortsiktiga tidsbegränsningar, medan planeringsalgoritmerna tar hänsyn till de delar som kräver beräkningsintensiva planeringsoperationer. Kraftfulla styrsystem på låg nivå kan förenkla planeringsuppgiften avsevärt. Därför fokuserar vi i denna avhandlingen på utvecklingen av återkopplingsregulatorer på låg nivå.  I den första delen fokuserar vi på att hantera sammankopplande tillståndsbegränsningar för distribuerade system med hjälp av en modell prediktiv styrning (MPC). Vanligtvis kräver den distribuerade hanteringen av kopplingsbegränsningar ett sekventiellt eller iterativt MPC-system som dock är tidskrävande. Därför utvecklar vi en parallelliserad distribuerad modell prediktiv styrning (DMPC) baserad på konsistensbegränsningar. Därigenom garanterar ett delsystem till sina grannar att det håller sig inom ett visst område runt en referensbana. Den generiska formuleringen av vårt DMPC-system möjliggör flera realiseringar. En särskild realisering föreslås. Dessutom utvecklas utvidgningar till ett robust och iterativt system samt ett DMPC-system för system med begränsade dynamiska kopplingar. I den andra delen fokuserar vi på metoder för att säkerställa invariansen av mängder. Vi fokuserar särskilt på kontrollbarriärfunktioner (CBF). Vi visar hur tillstånds- och tidsmässiga begränsningar kan inkodas i icke-glatta tidsvarierande kontrollbarriärfunktioner och hur subgradienter kan användas för att konstruera en effektiv gradientbaserad styrning. För dessa resultat måste antaganden om kontrollerbarhet åberopas. För att utvidga detta resultat till system med svagare kontrollerbarhetsegenskaper undersöker vi kopplingen mellan dynamiska systems kontrollerbarhetsegenskaper och konstruktionen av en CBF. Som ett resultat av detta föreslår vi en konstruktionsmetod för CBF:er som bygger på förutsägelser för ändliga horisonter. Den konstruerade CBF:n uppvisar gynnsamma egenskaper för att utvidga det tidigare resultatet om kodning av rums-temporala begränsningar i CBF:er till system med svagare kontrollerbarhetsegenskaper. Slutligen undersöker vi med hjälp av en fallstudie hur metoder för att säkerställa invariansen av mängder kan användas för att implicit samordna system som är kopplade via tillståndsbegränsningar. Vår föreslagna metod är helt decentraliserad och delsystemen samordnar sig själva endast via sina handlingar och justeringen av sina individuella begränsningar. Slutligen drar vi en slutsats och beskriver hur de presenterade resultaten bidrar till utvecklingen av ett ramverk för distribuerad styrning av tillstånds- och tidsmässigt begränsade system. / <p>QC 20230520</p>

The research on autonomous vehicles, and more specifically cooperation between autonomous vehicles, has become a prominent research field during the last cou- ple of decades. One example is the combination of an unmanned aerial vehicle (UAV) together with an unmanned ground vehicle (UGV). The benefits of this are that the two vehicles complement each other, where the UAV provides an aerial view and can reach areas where a ground vehicle can not. Furthermore, since the UAV has a limited range, the UGV can then serve as transport and recharge sta- tion for the UAV. This master thesis studies how model predictive control (MPC) can be used to land a UAV on a moving UGV.  A linear MPC is chosen, since previous work using this has shown promising results. The UAV is chosen to be controlled using commands in pitch, roll and climbing rate. The MPC is designed as a decoupled controller, with a separate horizontal and vertical controller. This allows for a spatial constraint to be im- plemented, which constrains the UAV from entering ground level before arriving above the UGV. It also constrains the UAV from potentially hitting protruding ob- jects on the UGV. The horizontal controller uses a simple planner, which guides the UAV to land on the UGV from behind.  The MPC is evaluated using a additive white Gaussian noise (AWGN) sen- sor error model with zero mean. The scenario used is that the UAV starts 50 m from the UGV, and the UGV starts driving in a given direction turning randomly. The MPC lands successfully in 100 % of the simulations for a wide range of tun- ings. The MPC maintains the same landing statistics with a delay in the sensor information of up to 500 ms. The AWGN could be increased while maintaining successful landings, however with significantly more retakes and longer landing times. Lower AWGN variance only slightly improves performance, suggesting that the MPC is quite robust towards high variance in the state estimation.  The MPC is also compared to a PID controller. The MPC has significantly shorter landing times. The PID has a more oscillatory control signal, however, the PID has a lower variance in landing positions, but a slightly less centered mean on the UGV. The overall results show that an MPC can be used to achieve a flexible controller that can be tuned and reformulated to fit the situation, and performs as good or better compared to a PID controller.  The hardware tests show promising results for the implementation of the MPC. The controller is not tuned and no system identification is done specifi- cally for the physical UAV, suggesting that the controller is robust for varying settings. Even though the UAV never lands on the UGV, the visual behavior and control signal plots suggest that it would be able to land. However, these tests are performed using global navigation satellite system state estimation on a sta- tionary UGV, therefore further tests need to be performed in more challenging scenarios.

The upward trends in renewable energy deployment in recent years brings new challengesto the development of electrical networks. Interconnected microgrids appear as a novelbottom-up approach to the production and integration of renewable energy.Using model predictive control (MPC), the energy management of several interconnectedmicrogrids is investigated. An optimisation problem is formulated and distributed ontothe individual units using the alternating direction method of multipliers (ADMM). Themicrogrids cooperate to reach a global optimum using neighbour-to-neighbour communications.The benefits of using distributed operation control for microgrids are analysed and a controlarchitecture is proposed. Two algorithms are implemented to solve the optimisationproblem and their advantages or differences are confronted. / Förnybara energikällor har ökat under senaste åren. Det innebär nya utmaningar förevolutionen av elektriska nät. Microgrids är en bottom-up ansats för produktion ochintegrering av förnybar energi.Energiförsörjning av flera sammankoppladeMicrogrids studeras in detta arbete genommodellbaserad prediktiv kontroll (MPC). Ett optimeringsproblem formuleras på de enskildaenheterna med Alternating DirectionMethod ofMultipliers (ADMM) och parallellberäkningar härledas.Microgrids samarbetar för att nå en global lösning av neighbourto-neighbour kommunikation.Distribuerad energiförsörjning av microgrids analyseras och två kontroll algorithmerutformas.

In recreational boating, docking is one of the most stressful and accident prone situations. Due to the loss of maneuverability at low speeds, it is a procedure that requires experience. There are mainly two problems when it comes to autonomous docking of a boat, these are identifying a berth’s position as well as keeping the boat on its intended path and correcting any deviations. Autonomous docking in recreational boating is still quite uncommon, with companies still exploring different solutions. This thesis proposes a Model Predictive Control (MPC) system combined with Pulsed Coherent Radar technology, equipped on an under-actuated boat model, to achieve autonomous docking. A major part of this thesis was to evaluate the amount and placement of radar sensors, as well as determining whether these are suitable in a water environment. In order to test this, the sensors were placed alongside the hull of the boat. It was found that the placement of sensors had a bigger impact than the amount when it came to correctly detecting the position of a berth. Once the placement of sensors and the berth position algorithmhad been done, a closed-loop MPC was used. This controller got constant feedback of the boat’s position relative the berth, in order to calculate the thruster control inputs for the next time step. The developed autonomous docking system was then implemented on the boat which was tested in a swimming pool. The optimal radar configuration combined withMPC, made it possible to successfully dock a boat autonomously without any modification to the berth. / För fritidsbåtlivet är tilläggning en av demest stressfulla och olycksbenägna situationerna. På grund av förlust av manövrering vid låga hastigheter är det en procedur som kräver erfarenhet. Det finns främst två problem när det kommer till autonom tilläggning, det är att identifiera positionen av en brygga såväl som att hålla båten på den avsedda kursen och rätta till små avvikelser. Autonom tilläggning för fritidsbåtlivet är fortfarande rätt ovanligt och företag utforskar fortfarande olika lösningar. Denna avhandling föreslår ett Modellprediktivt Reglersystem (MPC) kombinerat med Pulserad Koherent Radarteknik som är utrustad på en underaktuerad båtmodell för att uppnå autonom tilläggning. En stor del av avhandlingen var att utvärdera antalet och placeringen av radarsensorer, såväl som att fastställa om dessa är lämpliga att användas i en vattenmiljö. För att undersöka detta placerades sensorerna längs med båtens skrov. Det konstaterades att placeringen av sensorer hade en större påverkan än mängden när det kom till att läsa av positionen av bryggan korrekt. När placeringen av sensorer och bryggpositionsalgoritmen var klar användes MPC med återkoppling. Denna regulator fick konstant återkoppling av båtens position relativt bryggan för att räkna ut styrsignal till motorerna för nästa tidssteg. Den utvecklade autonoma tilläggningen var sedan implementerad på båten som testades i en pool. Den optimala radarplaceringen kombinerat med MPC gjorde det möjligt att med framgång kunna lägga till båten autonomt utan modifiering av bryggan.

Formation flying of satellites describes a mission in which a set of satellites arrange their position with respect to one another. In this paper, satellite formation flying guidance and control algorithms are investigated in terms of required velocity increment Delta-v, and tracking error for a Chief/Deputy satellite system. Different control methods covering continuous and impulsive laws are implemented and tested for Low Earth Orbit (LEO). Sliding Mode, Feedback Linearization and Model Predictive Controllers are compared to an Impulsive Feedback Law which tracks the mean orbital element differences. Sliding Mode and Feedback Linearization controllers use the same dynamic model which includes Earth Oblateness perturbations. On the other hand, Model Predictive Control with Multi-Objective Cost Function is based on the Clohessy–Wiltshire equations, which do not account for any perturbation and do not cover the eccentricity of the orbit. The comparison was done for two different missions both including Earth Oblateness effects only. A relative orbit mission, which was based on the Prisma Satellite Mission and a rendezvous mission, was implemented. The reference trajectory for the controllers was generated with Yamanaka and Ankersen’s state transition matrix, while a separate method was used for the Impulsive Law. In both of the missions, it was observed that the implemented Impulsive Law outperformed in terms of Delta-v, 1.2 to 3.5 times smaller than the continuous control approaches, while the continuous controllers had a smaller tracking error, 2 to 8.3 times less, both in terms of root mean square error and maximum error in the steady state. Finally, this study shows that the tracking error and Delta-v has inversely proportional relationship. / Formationsflygning av satelliter innebär att en grupp satelliter flyger tillsammans och anpassar sina relativa lägen i förhållande till varandra. I detta examensarbete studerades regleralgoritmer för formationsflygande satelliter med fokus på bränsleförbrukning och positionsavvikelse genom ”Chief &amp; Deputy”-metoden. Olika reglermetoder har studerats, t.ex. Sliding Mode- och Feedback Linearization-reglering för formationsflygningsfall i låg jordbana med J2-störning samt en Model Predictive-reglering för fall med relativ rörelse baserad på Clohessy-Wiltshire-ekvationerna. Vidare studerades en reglermetod baserad på impulsframdrivning. De fyra reglermetoderna implementerades på två olika rymduppdrag. Först ett uppdrag baserat på Prisma-satelliterna för två satelliter i relativ omloppsbana och sedan ett Rendezvous-uppdrag. Referensbanan för alla reglermetoder, utom för implusmetoden, har tagits fram med hjälp av Yamanakas och Ankersens tillståndsmatris. Resultaten visar att den implementerade impulsmetoden presterar bättre med avseende på bränsleförbrukning, medan de kontinuerliga reglermetoderna producerade mindre relativ positionsavvikelse, både med avseende på kvadratiskt medelvärde och maximalt värde.

The maneuverability and freedom provided by unmanned aerial vehicles (UAVs) make these an interesting choice for transporting objects in settings such as search and rescue operations, construction, and smart factories. A commonly proposed method of transport is by using cables attached between each UAV and the payload. However, the geometrical constraints posed by these attachments typically result in a system with highly complex dynamics. Although not an issue for conventional PID control schemes, these complex dynamics make the direct application of model predictive controllers (MPCs) infeasible for real-time usage. For this reason, much of the previous work has focused on treating the payload as a disturbance, thereby losing the ability to predict its effect on the UAVs. Contrary to this, this thesis presents an MPC that both captures the dynamics of the payload, and is capable of real-time usage. This is made possible by a parametrized linearization of the original system, and results in greatly improved performance compared to the disturbance model approach. The controller is derived for a system with two UAVs that transport a bar-like payload and verified both in simulations and physical experiments. The resulting control system is able track a multitude of setpoints, including rotations of both payload and UAVs, as well as lateral translations. Furthermore, it is able to attenuate external disturbances well, and dampens and prevents oscillations more efficiently when compared to the disturbance based approach. The resulting MPC solving time is on the order of milliseconds. Additionally, an initial attempt to decentralize the system is made, and the resulting controller experimentally tested on the UAV–bar system, resulting in a lower MPC solving time (2:5 times faster on average), but worsened performance in terms of position tracking of the bar. / Den manövrerbarhet och frihet som möjliggörs av användandet utav obemannade luftfarkoster (drönare) gör dessa till tämligen intressanta kandidater för lasttransport inom områden såsom sök- och räddningsuppdrag, byggnadskonstruktion och s.k. smarta fabriker. En vanligen förespråkad transportmetod består utav att förse systemet med kablar som fästs mellan last och drönare. De geometriska restriktioner som denna lastkoppling innebär resulterar emellertid ofta i system med väldigt komplicerad dynamik och interaktionskrafter. Även om detta inte innebär något problem för konventionella PID reglersystem så omöjliggör detta det direkta applicerandet utav modellprediktiv reglering (MPC) för realtidsbruk. Av denna anledning har tidigare verk fokuserat på att behandla lasten och dess inverkan på drönarna som en störning, men med detta därmed förlorat möjligheten att förutspå dess effekt på drönarna. I kontrast till detta, kommer det i detta verk att presenteras en MPC som både fångar lastens dynamik och är snabb nog för realtidsanvändning. Detta görs möjligt utav en parametriserad linjärisering utav originalsystemet och ger märkbart bättre resultat än den störningbaserade modellen. Reglersystemet appliceras på ett system bestående utav två drönare och en stång-liknande last och resultatet verifieras både i form av numeriska simuleringar och fysiska experiment. Det resulterande systemet klarar av både rotationer utav last och drönare samt translationer i alla riktningar. Dessutom är systemet kapabelt att hantera externa störningar och både dämpar och förhindrar oscillationer bättre i jämförelse med reglersystem baserat på störningsmodeller. Lösningstiden för MPC-regulatorn är i storleksordningen millisekunder. Utöver detta görs ett initialt försök i att decentralisera tidigare nämnda MPC och det resulterande reglersystemet utvärderas experimentellt på samma drönarsystem som tidigare. Detta resulterar i en lägre lösningstid (2.5 ggr snabbare i genomsnitt), men även i försämrad prestanda med avseende på reglering av stångens position.