Cette thèse se développe sur deux fronts: nous nous concentrons sur les méthodes numériques des problèmes de contrôle optimal, en particulier sur le Principe de la Programmation Dynamique et sur le Model Predictive Control (MPC) et nous présentons des applications de techniques de contrôle en biologie. Dans la première partie, nous considérons l'approximation d'un problème de contrôle optimal avec horizon infini, qui combine une première étape, basée sur MPC permettant d'obtenir rapidement une bonne approximation de la trajectoire optimal, et une seconde étape, dans la quelle l¿équation de Bellman est résolue dans un voisinage de la trajectoire de référence. De cette façon, on peux réduire une grande partie de la taille du domaine dans lequel on résout l¿équation de Bellman et diminuer la complexité du calcul. Le deuxième sujet est le contrôle des méthodes Level Set: on considère un problème de contrôle optimal, dans lequel la dynamique est donnée par la propagation d'un graphe à une dimension, contrôlé par la vitesse normale. Un état finale est fixé, l'objectif étant de le rejoindre en minimisant une fonction coût appropriée. On utilise la programmation dynamique grâce à une réduction d'ordre de l'équation utilisant la Proper Orthogonal Decomposition. La deuxième partie est dédiée à l'application des méthodes de contrôle en biologie. On présente un modèle décrit par une équation aux dérivées partielles qui modélise l'évolution d'une population de cellules tumorales. On analyse les caractéristiques du modèle et on formule et résout numériquement un problème de contrôle optimal concernant ce modèle, où le contrôle représente la quantité du médicament administrée. / This thesis is divided in two parts: in the first part we focus on numerical methods for optimal control problems, in particular on the Dynamic Programming Principle and on Model Predictive Control (MPC), in the second part we present some applications of the control techniques in biology. In the first part of the thesis, we consider the approximation of an optimal control problem with an infinite horizon, which combines a first step based on MPC, to obtain a fast but rough approximation of the optimal trajectory and a second step where we solve the Bellman equation in a neighborhood of the reference trajectory. In this way, we can reduce the size of the domain in which the Bellman equation can be solved and so the computational complexity is reduced as well. The second topic of this thesis is the control of the Level Set methods: we consider an optimal control, in which the dynamics is given by the propagation of a one dimensional graph, which is controlled by the normal velocity. A final state is fixed and the aim is to reach the trajectory chosen as a target minimizing an appropriate cost functional. To apply the Dynamic Programming approach we firstly reduce the size of the system using the Proper Orthogonal Decomposition. The second part of the thesis is devoted to the application of control methods in biology. We present a model described by a partial differential equation that models the evolution of a population of tumor cells. We analyze the mathematical and biological features of the model. Then we formulate an optimal control problem for this model and we solve it numerically.

In this thesis, we first use the reachability theory to develop algorithms for state predictionunder delayed state or output measurements. We next develop control strategies forcollision avoidance and trajectory tracking of UAVs based on the devised algorithms andthe model predictive control theory. Finally, simulations results for collision avoidanceand trajectory tracking problems are presented, for different communication delays,using a UAV model with 6 degrees of freedom. / I denna avhandling använder vi först tillgänglighetsteorin för att utveckla algoritmerför tillståndsförutsägelse under fördröjda tillstånds- eller utgångsmätningar. Därefterutvecklar kontrollstrategier för undvikande av kollision och spårning av UAV: er baseradepå de planerade algoritmerna och modellen förutsägbar kontrollteori. Slutligenpresenteras simuleringsresultat för att undvika kollision och problem med spårningav banan, för olika kommunikationsförseningar, med en UAV-modell med 6 frihetsgrader.

Model Predictive Control (MPC) is an optimization method used in a wide range of applications. However, in the housing sector its use is still limited. In this project, the possibilities of using an easily scalable MPC controller to optimize the heating of a building, is examined and evaluated. It is a combination of a Long Short Term Memory (LSTM) network for understanding the dynamics of the buildning in order to predict future indoor temperatures, and the probalistic technique Simulated Annealing (SA), used for solving the control problem. As an extension, predicted energy prices per hour are added, with the goal to lower the heating costs. The model is tested on a family house with eight rooms and centrally heated using gas. The results are promising, but ambiguous. The main reason for the uncertainties are the testing environment. / Model Predictive Control (MPC) är en optimeringsmetod som används inom många olika områden. Inom bostadssektorn är dock användningen fortfarande begränsad. I det här projektet undersöks möjligheten att använda en MPC kontroller för att optimera uppvärmningen av en byggnad, och om den enkelt kan appliceras på andra byggnader. Det är en kombination av ett long Short Term Memory (LSTM) nätverk för att förstå dynamiken av byggnaden med målet att förutse framtida inomhustemperaturer, och den probabilistiska metoden Simulated Annealing (SA) som används för att lösa kontrollproblemet. Ett tillägg till modellen är inkluderandet av energipriser för varje timme, där målet istället blir att minimera uppvärmningskostnaderna. Modellen testas på ett familjehus med åtta rum som är centralt uppvärmt genom gas. Resultaten är lovande, men tvetydiga. Huvudorsaken för osäkerheterna är testmiljön.

Trajectory planning constitutes an essential step for proper autonomous vehicles’performance. This work aims at defining and testing a stochastic approach providingsafe, length-optimal and comfortable trajectories accounting for road, model anddisturbance uncertainties. A Stochastic Model Predictive Control (SMPC) problemis formulated using a Linear Parameter Varying Bicycle Model, state-probabilisticconstraints and input constraints. The SMPC is transformed into a tractable quadraticoptimisation problem after assuming independent and gaussian uncertainties.The proposed trajectory planning methodology is intended to be implemented onlinein a Receding Horizon fashion in a real vehicle. Results are presented after computersimulatedtests have been carried out to study the influence of model uncertaintiesand SMPC parameters on the planned and executed trajectories in standard drivingsituations. Particularly, road crosswind is modelled, its effect on vehicles withdifferent steering characteristics is studied and it is considered for improved trajectoryplanning. The approach constitutes a promising method to provide robust trajectoriesto unmodeled errors reaching an equilibrium between conservativeness and quality ofthe solution. / Banplanering utgör ett väsentligt steg för riktiga autonoma fordons prestanda.Syftet med detta arbete är att definiera och testa stokastiska strategier som gersäkra, optimala och bekväma banor som tar hänsyn till vägen, modelbrus ochosäkerheter. En stokastisk Model Predictive Control (SMPC) problem är formuleratmed hjälp av Linear Parameter Varying Bicycle Model, tillstånds-sannolikhetsbivillkoroch inmatningsbivillkor. SMPC transformeras till ett lätthanterlig kvadratiskoptimeringsproblem efter oberoende gaussfördelade osäkerheter antagits.Den föreslagna banplaneringsmetoden är avsedd att implementeras online meden Receding Horizon för ett riktigt fordon. Resultatet är presenterat efterdatorsimulerade experiment har blivit genomförda för att studera påverkan avmodelosäkerheter och SMPC parametrar på den planerade och genomförda banorför standard körsituationer. I synnerhet, är sidovind modellerat, dens effekt påfordon med olika styrkaraktäristik är studerad och är tagen hänsyn till för förbättradbanplanering. Tillvägagångssättet utgör en lovande metod för att tillhandahållarobusta banor för icke-model fel som når en jämvikt mellan konservativitet och kvalitethos lösningen.

This paper presents the mathematical modeling and the design of an optimal pressure tracking controller for an often used setup in pneumatic applications. Two pneumatic chambers are connected with a pneumatic tube. The pressure in the second chamber is to be controlled using two switching valves connected to the first chamber and based on the pressure measurement in the first chamber. The optimal control problem is formulated and solved using the MPC framework. The designed controller shows good tracking quality, while fulfilling hard constraints, like maintaining the pressure below a given upper bound.

Model predictive control (MPC) has gained great acceptance in the industry since it was developed and first applied about 25 years ago [1]. It has established its place mainly in the advanced control community. Traditionally, MPC configurations are developed and commissioned by control experts. MPC implementations have usually been only worthwhile to apply on processes that promise large profit increase in return for the large cost of implementation. Thus the scale of MPC applications in terms of number of inputs and outputs has usually been large. This is the main reason why MPC has not made its way into low-level loop control. In recent years, academia and control system vendors have made efforts to broaden the range of MPC applications. Single loop MPC and multiple PID strategy replacements for processes that are difficult to control with PID controllers have become available and easier to implement. Such processes include deadtime-dominant processes, override strategies, decoupling networks, and more. MPC controllers generally have more "knobs" that can be adjusted to gain optimum performance than PID. To solve this problem, general PID replacement MPC controllers have been suggested. Such controllers include forward modeling controller (FMC)[2], constraint LQ control[3] and adaptive controllers like ADCO[4]. These controllers are meant to combine the benefits of predictive control performance and the convenience of only few (more or less intuitive) tuning parameters. However, up until today, MPC controllers generally have only succeeded in industrial environments where PID control was performing poorly or was too difficult to implement or maintain. Many papers and field reports [5] from control experts show that PID control still performs better for a significant number of processes. This is on top of the fact that PID controllers are cheaper and faster to deploy than MPC controllers. Consequently, MPC controllers have actually replaced only a small fraction of PID controllers. This research shows that deficiencies in the feedback control capabilities of MPC controllers are one reason for the performance gap between PID and MPC. By adopting knowledge from PID and other proven feedback control algorithms, such as statistical process control (SPC) and Fuzzy logic, this research aims to find algorithms that demonstrate better feedback control performance than methods commonly used today in model predictive controllers. Initially, the research focused on single input single output (SISO) processes. It is important to ensure that the new feedback control strategy is implemented in a way that does not degrade the control functionality that makes MPC superior to PID in multiple input multiple output (MIMO) processes. / text

This thesis presents the development of self adaptive flight controller for an unmanned helicopter system under hovering manoeuvre. The neural network (NN) based model predictive control (MPC) approach is utilised in this work. We use this controller due to its ability to handle system constraints and the time varying nature of the helicopter dynamics. The non-linear NN based MPC controller is known to produce slow solution convergence due to high computation demand in the optimisation process. To solve this problem, the automatic flight controller system is designed using the NN based approximate predictive control (NNAPC) approach that relies on extraction of linear models from the non-linear NN model at each time step. The sequence of control input is generated using the prediction from the linearised model and the optimisation routine of MPC subject to the imposed hard constraints. In this project, the optimisation of the MPC objective criterion is implemented using simple and fast computation of the Hildreth's Quadratic Programming (QP) procedure. The system identification of the helicopter dynamics is typically performed using the time regression network (NNARX) with the input variables. Their time lags are fed into a static feed-forward network such as the multi-layered perceptron (MLP) network. NN based modelling that uses the NNARX structure to represent a dynamical system usually requires a priori knowledge about the model order of the system. Low model order assumption generally leads to deterioration of model prediction accuracy. Furthermore, massive amount of weights in the standard NNARX model can result in an increased NN training time and limit the application of the NNARX model in a real-time application. In this thesis, three types of NN architectures are considered to represent the time regression network: the multi-layered perceptron (MLP), the hybrid multi-layered perceptron (HMLP) and the modified Elman network. The latter two architectures are introduced to improve the training time and the convergence rate of the NN model. The model structures for the proposed architecture are selected using the proposed Lipschitz coefficient and k-cross validation methods to determine the best network configuration that guarantees good generalisation performance for model prediction. Most NN based modelling techniques attempt to model the time varying dynamics of a helicopter system using the off-line modelling approach which are incapable of representing the entire operating points of the flight envelope very well. Past research works attempt to update the NN model during flight using the mini-batch Levenberg-Marquardt (LM) training. However, due to the limited processing power available in the real-time processor, such approaches can only be employed to relatively small networks and they are limited to model uncoupled helicopter dynamics. In order to accommodate the time-varying properties of helicopter dynamics which change frequently during flight, a recursive Gauss-Newton (rGN) algorithm is developed to properly track the dynamics of the system under consideration. It is found that the predicted response from the off-line trained neural network model is suitable for modelling the UAS helicopter dynamics correctly. The model structure of the MLP network can be identified correctly using the proposed validation methods. Further comparison with model structure selection from previous studies shows that the identified model structure using the proposed validation methods offers improvements in terms of generalisation error. Moreover, the minimum number of neurons to be included in the model can be easily determined using the proposed cross validation method. The HMLP and modified Elman networks are proposed in this work to reduce the total number of weights used in the standard MLP network. Reduction in the total number of weights in the network structure contributes significantly to the reduction in the computation time needed to train the NN model. Based on the validation test results, the model structure of the HMLP and modified Elman networks are found to be much smaller than the standard MLP network. Although the total number of weights for both of the HMLP and modified Elman networks are lower than the MLP network, the prediction performance of both of the NN models are on par with the prediction quality of the MLP network. The identification results further indicate that the rGN algorithm is more adaptive to the changes in dynamic properties, although the generalisation error of repeated rGN is slightly higher than the off-line LM method. The rGN method is found capable of producing satisfactory prediction accuracy even though the model structure is not accurately defined. The recursive method presented here in this work is suitable to model the UAS helicopter in real time within the control sampling time and computational resource constraints. Moreover, the implementation of proposed network architectures such as the HMLP and modified Elman networks is found to improve the learning rate of NN prediction. These positive findings inspire the implementation of the real time recursive learning of NN models for the proposed MPC controller. The proposed system identification and hovering control of the unmanned helicopter system are validated in a 6 degree of freedom (DOF) safety test rig. The experimental results confirm the effectiveness and the robustness of the proposed controller under disturbances and parameter changes of the dynamic system.

In the thesis, two different model predictive control (MPC) strategies are investigated for linear systems with uncertainty in the presence of constraints: namely robust MPC and stochastic MPC. Firstly, a Youla Parameter is integrated into an efficient robust MPC algorithm. It is demonstrated that even in the constrained cases, the use of the Youla Parameter can desensitize the costs to the effect of uncertainty while not affecting the nominal performance, and hence it strengthens the robustness of the MPC strategy. Since the controller u = K x + c can offer many advantages and is used across the thesis, the work provides two solutions to the problem when the unconstrained nominal LQ-optimal feedback K cannot stabilise the whole class of system models. The work develops two stochastic tube approaches to account for probabilistic constraints. By using a semi closed-loop paradigm, the nominal and the error dynamics are analyzed separately, and this makes it possible to compute the tube scalings offline. First, ellipsoidal tubes are considered. The evolution for the tube scalings is simplified to be affine and using Markov Chain model, the probabilistic tube scalings can be calculated to tighten the constraints on the nominal. The online algorithm can be formulated into a quadratic programming (QP) problem and the MPC strategy is closed-loop stable. Following that, a direct way to compute the tube scalings is studied. It makes use of the information on the distribution of the uncertainty explicitly. The tubes do not take a particular shape but are defined implicitly by tightened constraints. This stochastic MPC strategy leads to a non-conservative performance in the sense that the probability of constraint violation can be as large as is allowed. It also ensures the recursive feasibility and closed-loop stability, and is extended to the output feedback case.

Growing concerns about the environmental impact of fossil fuel energy and improvements in both the cost and performance of wind turbine technologies has spurred a sharp expansion in wind energy generation. However, both the increasing size of wind farms and the increased contribution of wind energy to the overall electricity generation market has created new challenges. As wind farms grow in size and power density, the aerodynamic wake interactions that occur between neighboring turbines become increasingly important in characterizing the unsteady turbine loads and power output of the farm. Turbine wake interactions also impact variability of farm power generation, acting either to increase variability or decrease variability depending on the wind farm control algorithm. In this dissertation, both the unsteady vortex wake loading and the effect of wake interaction on farm power variability are investigated in order to better understand the fundamental physics that govern these processes and to better control wind farm operations to mitigate negative effects of wake interaction. The first part of the dissertation examines the effect of wake interactions between neighboring turbines on the variability in power output of a wind farm, demonstrating that turbine wake interactions can have a beneficial effect on reducing wind farm variability if the farm is properly controlled. In order to balance multiple objectives, such as maximizing farm power generation while reducing power variability, a model predictive control (MPC) technique with a novel farm power variability minimization objective function is utilized. The controller operation is influenced by a number of different time scales, including the MPC time horizon, the delay time between turbines, and the fluctuation time scales inherent in the incident wind. In the current research, a non-linear MPC technique is developed and used to investigate the effect of three time scales on wind farm operation and on variability in farm power output. The goal of the proposed controller is to explore the behavior of an "ideal" farm-level MPC controller with different wind, delay and horizon time scales and to examine the reduction of system power variability that is possible in such a controller by effective use of wake interactions. The second part of the dissertation addresses the unsteady vortex loading on a downstream turbine caused by the interaction of the turbine blades with coherent vortex structures found within the upstream turbine wake. Periodic, stochastic, and transient loads all have an impact on the lifetime of the wind turbine blades and drivetrain. Vortex cutting (or vortex chopping) is a type of stochastic load that is commonly observed when a propeller or blade passes through a vortex structure and the blade width is of the same order of magnitude as the vortex core diameter. A series of Navier-Stokes simulations of vortex cutting with and without axial flow are presented. The goal of this research is to better understand the challenging physics of vortex cutting by the blade rotor, as well as to develop a simple, physics-based, validated expression to characterize the unsteady force induced by vortex

Le craquage catalytique à lit fluidisé (FCC) est l'un des procédés les plus importants au sein d'une raffinerie moderne et joue un rôle économique primordial. Le fonctionnement du FCC pose des problèmes d'opération liés à sa complexité. L'étude a porté sur la simulation du FCC, sa commande prédictive multivariable et l'estimation de paramètres-clés. Après une revue de la littérature sur les FCC et les différentes approches de modélisation ainsi que des cinétiques de craquage, un modèle du FCC qui intègre les dynamiques importantes a été choisi pour les besoins de la commande prédictive. La simulation du riser a été effectuée pour différents modèles de craquage et a montré de grandes disparités entre modèles, créant une difficulté à définir un modèle général de riser pour les FCC. Outre le nombre de groupes considérés, les différences concernent la chaleur de réaction globale, les lois de formation de coke sur le catalyseur et la désactivation de ce dernier. Des algorithmes de commande prédictive linéaire et non linéaire basée sur le modèle ont été utilisés pour commander le FCC en tenant compte de sa nature multivariable et des contraintes imposées aux variables manipulées. Les sorties commandées, température en haut du riser et température du régénérateur ont été maintenues proches des consignes, tant en régulation qu'en poursuite, tout en respectant les contraintes portant sur les deux variables manipulées, le débit de catalyseur régénéré et le débit d'air entrant dans le régénérateur. Une commande à trois entrées manipulées, incluant le débit d'alimentation, a également été testée avec succès. La commande prédictive linéaire avec observateur a fourni des résultats encore meilleurs que la commande linéaire quadratique. La commande prédictive non linéaire a été testée mais présente des problèmes pour une implantation en temps réel. L'estimation du coke sur le catalyseur a été réalisée par le filtre de Kalman étendu, mais les erreurs d'estimation sont importantes, probablement à cause du choix insuffisant des mesures effectuées. L'ensemble de l'étude a montré que la commande avancée prédictive du FCC est performante et doit être recommandée, mais peut encore être améliorée en particulier par son réglage et l'estimation des états / Fluid catalytic cracking (FCC) is one of the most important processes in a modern refinery and is of essential economic importance. The FCC operation presents difficulties related to its complexity. The study was related to its simulation, multivariable control and estimation of key parameters. After a litterature review of the FCC, the different approaches of modelling and cracking kinetics, a FCC model that takes into account the important dynamics was chosen for model predictive control purposes. The riser simulation was carried out for different cracking models and shows great differences between these models, which makes it difficult to define a general riser model for the FCC. Besides the number of lumps, differences deal with the global heat of reaction, the coke formation laws and its deactivation functions. Linear and nonlinear model predictive algorithms were used for FCC control taking into account its multivariable nature and the constraints imposed on the manipulated variables. The controlled outputs, temperature at the riser top and temperature in the regenerator were maintained close to their respective set points in regulation and tracking modes while respecting the constraints on the two manipulated variable, the flow rate of regenerated catalyst and the flow rate of air entering the regenerator. A control with three manipulated variables including the feed flow rate was also successfully tested. Linear predictive control with an observer gave better results than linear quadratic control. Nonlinear predictive control was tested but presents problems for real time implementation. The estimation of coke on the catalyst was carried out using extended Kalman filter, but the estimation errors are important, probably due to an insufficient choice of measurements. The overall study showed that advanced predictive control of the FCC is efficient and must be recommended, but it can still be improved upon particularly by its tuning and state estimation