In this work we investigate the use of state-of-the-art tools for the regulation of complex, non-linear systems to improve the methodologies currently applied to trim comprehensive virtual prototypes of rotors and rotorcrafts. Among the several methods that have been proposed in the literature, the auto-pilot approach has the potential to solve trim problems efficiently even for the large and complex vehicle models of modern comprehensive finite element-based analysis codes. In this approach, the trim condition is obtained by adjusting the controls so as to virtually ``fly' the system to the final steady (periodic) flight condition. Published proportional auto-pilots show to work well in many practical instances. However, they cannot guarantee good performance and stability in all flight conditions of interest. Limit-cycle oscillations in control time histories are often observed in practice because of the non-linear nature of the problem and the difficulties in enforcing the constant-in-time condition for the controls. To address all the above areas of concern, in this research we propose a new auto-pilot, based on non-linear model-predictive control (NMPC). The formulation uses a non-linear reference model of the system augmented with an adaptive neural element, which identifies and corrects the mismatch between reduced model and controlled system. The methodology is tested on the wind-tunnel trim of a rotor multibody model and compared to an existing implementation of a classic auto-pilot. The proposed controller shows good performance without the need of a potentially very expensive tuning phase, which is required in classical auto-pilots. Moreover, model-predictive control provides a framework for guaranteeing stability of the non-linear closed-loop system, so it seems to be a viable approach for trimming complete rotorcraft comprehensive models in free-flight.

Simulation of maneuvers with multibody models of rotorcraft vehicles is an important research area due to its complexity. During the maneuvering flight, some important design limitations are encountered such as maximum loads and maximum turning rates near the proximity of the flight envelope. This increases the demand on high fidelity models in order to define appropriate controls to steer the model close to the desired trajectory while staying inside the boundaries. A framework based on the hierarchical decomposition of the problem is used for this study. The system should be capable of generating the track by itself based on the given criteria and also capable of piloting the model of the vehicle along this track. The generated track must be compatible with the dynamic characteristics of the vehicle. Defining the constraints for the maneuver is of crucial importance when the vehicle is operating close to its performance boundaries. In order to make the problem computationally feasible, two models of the same vehicle are used where the reduced model captures the coarse level flight dynamics, while the fine scale comprehensive model represents the plant. The problem is defined by introducing planning layer and control layer strategies. The planning layer stands for solving the optimal control problem for a specific maneuver of a reduced vehicle model. The control layer takes the resulting optimal trajectory as an optimal reference path, then tracks it by using a non-linear model predictive formulation and accordingly steers the multibody model. Reduced models for the planning and tracking layers are adapted by using neural network approach online to optimize the predictive capabilities of planner and tracker. Optimal neural network architecture is obtained to augment the reduced model in the best way. The methodology of adaptive learning rate is experimented with different strategies. Some useful training modes and algorithms are proposed for these type of applications. It is observed that the neural network increased the predictive capabilities of the reduced model in a robust way. The proposed framework is demonstrated on a maneuvering problem by studying an obstacle avoidance example with violent pull-up and pull-down.

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 has become a standard for most control strategies in modern process plants. It relies heavily on process models, which might not always be fundamentally available, but can be obtained from time series analysis. The first step in any control strategy is to identify or detect changes in the system, if present. The detection of such changes, known as dynamic changes, is the main objective of this study. In the literature a wide range of change detection methods has been developed and documented. Most of these methods assume some prior knowledge of the system, which is not the case in this study. Furthermore a large number of change detection methods based on process history data assume a linear relationship between process variables with some stochastic influence from the environment. These methods are well developed, but fail when applied to nonlinear dynamic systems, which is focused on in this study. A large number of the methods designed for nonlinear systems make use of statistics defined in phase space, which led to the method proposed in this study. The correlation dimension is an invariant measure defined in phase space that is sensitive to dynamic change in the system. The proposed method uses the correlation dimension as test statistic with and moving window approach to detect dynamic changes in nonlinear systems. The proposed method together with two dynamic change detection methods with different approaches was applied to simulated time series data. The first method considered was a change-point algorithm that is based on singular spectrum analysis. The second method applied to the data was mutual cross prediction, which utilises the prediction error from a multilayer perceptron network. After the proposed method was applied to the data the three methods’ performance were evaluated. Time series data were obtained from simulating three systems with mathematical equations and observing one real process, the electrochemical noise produced by a corroding system. The three simulated systems considered in this study are the Belousov-Zhabotinsky reaction, an autocatalytic process and a predatory-prey model. The time series obtained from observing a single variable was considered as the only information available from the systems. Before the change detection methods were applied to the time series data the phase spaces of the systems were reconstructed with time delay embedding. All three the methods were able to do identify the change in dynamics of the time series data. The change-point detection algorithm did however produce a haphazard behaviour of its detection statistic, which led to multiple false alarms being encountered. This behaviour was probably due to the distribution of the time series data not being normal. The haphazard behaviour reduces the ability of the method to detect changes, which is aggravated by the presence of chaos and instrumental or measurement noise. Mutual cross prediction is a very successful method of detecting dynamic changes and is quite robust against measurement noise. It did however require the training of a multilayer perceptron network and additional calculations that were time consuming. The proposed algorithm using the correlation dimension as test statistic with a moving window approach is very useful in detecting dynamic changes. It produced the best results on the systems considered in this study with quick and reliable detection of dynamic changes, even in then presence of some instrumental noise. The proposed method with the correlation dimension as test statistic was the only method applied to the real time series data. Here the method was successful in distinguishing between two different corrosion phenomena. The proposed method with the correlation dimension as test statistic appears to be a promising approach to the detection of dynamic change in nonlinear systems.

More stringent Euro 6 and LEV III emission standards will immediately begin execution on 2014 and 2015 respectively. Accurate air/fuel ratio control can effectively reduce vehicle emission. The simulation of engine dynamic system is a very powerful method for developing and analysing engine and engine controller. Currently, most engine air/fuel ratio control used look-up table combined with proportional and integral (PI) control and this is not robust to system uncertainty and time varying effects. This thesis first develops a simulation package for a port injection spark-ignition engine and this package include engine dynamics, vehicle dynamics as well as driving cycle selection module. The simulations results are very close to the data obtained from laboratory experiments. New controllers have been proposed to control air/fuel ratio in spark ignition engines to maximize the fuel economy while minimizing exhaust emissions. The PID control and fuzzy control methods have been combined into a fuzzy PID control and the effectiveness of this new controller has been demonstrated by simulation tests. A new neural network based predictive control is then designed for further performance improvements. It is based on the combination of inverse control and predictive control methods. The network is trained offline in which the control output is modified to compensate control errors. The simulation evaluations have shown that the new neural controller can greatly improve control air/fuel ratio performance. The test also revealed that the improved AFR control performance can effectively restrict engine harmful emissions into atmosphere, these reduce emissions are important to satisfy more stringent emission standards.

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