Spacecraft relative motion modeling and control promises to enable or augment a wide range of missions for scientific research, military applications, and space situational awareness. This dissertation focuses on the development of novel, optimization-based, control design for some representative relative-motion-enabled missions. Spacecraft relative motion refers to two (or more) satellites in nearly identical orbits. We examine control design for relative configurations on the scale of meters (for the purposes of proximity operations) as well as on the scale of tens of kilometers (representative of science gathering missions). Realistic control design for satellites is limited by accurate modeling of the relative orbital perturbations as well as the highly constrained nature of most space systems. We present solutions to several types of optimal orbital maneuvers using a variety of different, realistic assumptions based on the maneuver objectives. Initially, we assume a perfectly circular orbit with a perfectly spherical Earth and analytically solve the under-actuated, minimum-energy, optimal transfer using techniques from optimal control and linear operator theory. The resulting open-loop control law is guaranteed to be a global optimum. Then, recognizing that very few, if any, orbits are truly circular, the optimal transfer problem is generalized to the elliptical linear and nonlinear systems which describe the relative motion. Solution of the minimum energy transfer for both the linear and nonlinear systems reveals that the resulting trajectories are nearly identical, implying that the nonlinearity has little effect on the relative motion. A continuous-time, nonlinear, sliding mode controller which tracks the linear trajectory in the presence of a higher fidelity orbit model shows that the closed-loop system is both asymptotically stable and robust to disturbances and un-modeled dynamics. Next, a novel method of computing discrete-time, multi-revolution, finite-thrust, fuel-optimal, relative orbit transfers near an elliptical, perturbed orbit is presented. The optimal control problem is based on the classical, continuous-time, fuel-optimization problem from calculus of variations, and we present the discrete-time analogue of this problem using a transcription-based method. The resulting linear program guarantees a global optimum in terms of fuel consumption, and we validate the results using classical impulsive orbit transfer theory. The new method is shown to converge to classical impulsive orbit transfer theory in the limit that the duration of the zero-order hold discretization approaches zero and the time horizon extends to infinity. Then the fuel/time optimal control problem is solved using a hybrid approach which uses a linear program to solve the fuel optimization, and a genetic algorithm to find the minimizing time-of-flight. The method developed in this work allows mission planners to determine the feasibility for realistic spacecraft and motion models. Proximity operations for robotic inspection have the potential to aid manned and unmanned systems in space situational awareness and contingency planning in the event of emergency. A potential limiting factor is the large number of constraints imposed on the inspector vehicle due to collision avoidance constraints and limited power and computational resources. We examine this problem and present a solution to the coupled orbit and attitude control problem using model predictive control. This control technique allows state and control constraints to be encoded as a mathematical program which is solved on-line. We present a new thruster constraint which models the minimum-impulse bit as a semi-continuous variable, resulting in a mixed-integer program. The new model, while computationally more expensive, is shown to be more fuel-efficient than a sub-optimal approximation. The result is a fuel efficient, trajectory tracking, model predictive controller with a linear-quadratic attitude regulator which tracks along a pre-computed ``safe'' trajectory in the presence of un-modeled dynamics on a higher fidelity orbital and attitude model. / Ph. D.

This thesis aims at investigating numerical methods through which the accuracy in landing of a Mars entry-descent-landing (EDL) vehicle can be improved. The methods investigated include the collocation method and model predictive control (MPC). The primary control variable utilized in this study is the bank angle of the spacecraft, which is the angle between the lift vector and the vertical direction. Modulating this vector affects the equations of system of equations and the seven state variables, namely altitude, velocity, latitude, longitude, flight path angle, heading angle and total time taken. An optimizer is implemented which utilizes the collocation method, through which the optimal bank angle is found at every discretized state along the trajectory which are equally separated through a definite timestep, which is a function of the end time state. A 3-sigma wind disturbance model is introduced to the system, as a function of the altitude, which introduces uncertainties to the system, resulting in a final state deviating from the targeted location. The trajectory is split into two parts, for better control of the vehicle during the end stages of flight. The MPC aims at reducing the end state deviation, through the implementation of a predictor-corrector algorithm that propagates the trajectory for a certain number of timesteps, followed by running the optimizer from the current disturbed state to the desired target location. At the end of this analysis, a new set of optimal bank angle are found, which account for the wind disturbances and navigates the EDL vehicle to the desired location. / M.S. / Landing on Mars has always been a process of following a set of predetermined instructions by the spacecraft, in order to reach a calculated landing target. This work aims to take the first steps towards autonomy in maneuvering the spacecraft, and finding a method by which the vehicle navigates itself towards the target. This work determines the optimal control scheme a Mars reentry vehicle must have through the atmosphere to reach the target location, and employs method through which the uncertainty in the final landing location is mitigated. A model predictive controller is employed which corrects the disturbed trajectory of the vehicle at certain timesteps, through which the previously calculated optimal control is changed so as to account for the disturbances. The control is achieved by means of changing the bank angle of the spacecraft, which in turn affects the lift and drag experienced by the vehicle. Through this work, a method has been demonstrated which reduces the uncertainty in final landing location, even with wind disturbances present.

The Hybrid Electric Vehicle Team (HEVT) of Virginia Tech is partaking in the 4-Year EcoCar Mobility Challenge organized by Argonne National Labs. The objective of this competition is to modify a stock 2019 traditional internal combustion engine Chevrolet Blazer and to transform the vehicle into a P4 hybrid. Due to the P4 Hybrid architecture, the HEVT vehicle has an internal combustion engine on the front axle and an electric motor on the rear axle. The goal of this competition is to create a vehicle that achieves better fuel economy and increases customer appeal. The general target market of hybrids is smaller vehicles. As a midsize sport utility vehicle (SUV), the Blazer offers a larger vehicle with the perk of better fuel economy. In the competition, the vehicle is assessed on the ability to integrate advanced vehicle technology, improve consumer appeal, and provide comfort for the passenger. The research of this paper is centered around the design of a full range longitudinal Adaptive Cruise Control (ACC) algorithm. Initially, research is conducted on various linear and nonlinear control strategies that provide the necessary functionality. Based on the ability to predict future time instances in an optimal method, the Model Predictive Control (MPC) algorithm is chosen and combined with other standard control strategies to create an ACC system. The main objective of this research is the implementation of Adaptive Cruise Control features that provide comfort and energy savings to the rider while maintaining safety as the priority. Rider comfort is achieved by placing constraints on acceleration and jerk. Lastly, a proper energy analysis is conducted to showcase the potential energy savings with the implementation of the Adaptive Cruise Control system. This implementation includes tuning the algorithm so that the best energy consumption at the wheel is achieved without compromising vehicle safety. The scope of this paper expands on current knowledge of Adaptive Cruise Control by using a simplified nonlinear vehicle system model in MATLAB to simulate different conditions. For each condition, comfort and energy consumption are analyzed. The city 505 simulation of a traditional ACC system show a 14% or 42 Wh/mi reduction in energy at the wheel. The city 505 simulation of the environmentally friendly ACC system show a 29% or 88 Wh/mi reduction in energy at the wheel. Furthermore, these simulations confirm that maximum acceleration and jerk are bounded. Specifically, peak jerk is reduced by 90% or 8 m/s3 during a jerky US06 drive cycle. The main objective of this analysis is to demonstrate that with proper implementation, this ACC system effectively reduces tractive energy consumption while improving rider comfort for any vehicle. / Master of Science / The Hybrid Electric Vehicle Team (HEVT) of Virginia Tech is partaking in the 4-Year EcoCar Mobility Challenge organized by Argonne National Labs. The objective of this competition is to modify a stock 2019 Chevrolet Blazer into a hybrid. This modification is accomplished by creating a vehicle that burns less gasoline and increases customer appeal. The general target market of hybrids is smaller vehicles. As a midsize sport utility vehicle (SUV), the Blazer offers a larger vehicle with the perk of better fuel economy. In the competition, the vehicle is assessed on the ability to integrate advanced technology, improve consumer appeal, and provide comfort for the passenger. The research of this paper is centered around the design of Adaptive Cruise Control (ACC). Initially, research is conducted on various control strategies that provide the necessary functionality. A controller that predicts future events is selected for the Adaptive Cruise Control. The main objective of this research is the implementation of Adaptive Cruise Control features that provide comfort and energy consumption savings to the rider while maintaining safety as the priority. Rider comfort is achieved by creating a smoother ride. Lastly, a proper energy analysis showcases the potential energy savings with the implementation of the Adaptive Cruise Control system. The scope of this paper expands on current knowledge of Adaptive Cruise Control by using a simplified vehicle model to simulate different conditions. The city simulations of a traditional ACC system show a 14% reduction in energy at the wheel. City simulations of the environmentally friendly Adaptive Cruise Controller show a 29% reduction in energy. Both of these simulations allow for comfortable ride. Specifically, maximum car jerk is reduced by 90%. The main objective of this analysis is to demonstrate that with proper implementation, this ACC system effectively reduces energy consumption at the wheel while improving rider comfort.

Networked control systems (NCSs) present many advantages such as easy installation and maintenance, flexible layouts and structures of components, and efficient allocation and distribution of resources. Consequently, they find potential applications in a variety of emerging industrial systems including multi-agent systems, power grids, tele-operations and cyber-physical systems. The study of NCSs with nonlinear dynamics (i.e., nonlinear NCSs) is a very significant yet challenging topic, and it not only widens application areas of NCSs in practice, but also extends the theoretical framework of NCSs with linear dynamics (i.e., linear NCSs). Numerous issues are required to be resolved towards a fully-fledged theory of industrial nonlinear NCS design. In this dissertation, three important problems of nonlinear NCSs are investigated: The robust filtering problem, the robust model predictive control (MPC) problem and the robust distributed MPC problem of large-scale nonlinear systems. In the robust filtering problem of nonlinear NCSs, the nonlinear system model is subject to uncertainties and external disturbances, and the measurements suffer from time delays governed by a Markov process. Utilizing the Lyapunov theory, the algebraic Hamilton-Jacobi inequality (HJI)-based sufficient conditions are established for designing the H_infty nonlinear filter. Moreover, the developed results are specialized for a special type of nonlinear systems, by presenting the HJI in terms of matrix inequalities. For the robust MPC problem of NCSs, three aspects are considered. Firstly, to reduce the computation and communication load, the networked MPC scheme with an efficient transmission and compensation strategy is proposed, for constrained nonlinear NCSs with disturbances and two-channel packet dropouts. A novel Lyapunov function is constructed to ensure the input-to-state practical stability (ISpS) of the closed-loop system. Secondly, to improve robustness, a networked min-max MPC scheme are developed, for constrained nonlinear NCSs subject to external disturbances, input and state constraints, and network-induced constraints. The ISpS of the resulting nonlinear NCS is established by constructing a new Lyapunov function. Finally, to deal with the issue of unavailability of system state, a robust output feedback MPC scheme is designed for constrained linear systems subject to periodical measurement losses and external disturbances. The rigorous feasibility and stability conditions are established. For the robust distributed MPC problem of large-scale nonlinear systems, three steps are taken to conduct the studies. In the first step, the issue of external disturbances is addressed. A robustness constraint is proposed to handle the external disturbances, based on which a novel robust distributed MPC algorithm is designed. The conditions for guaranteeing feasibility and stability are established, respectively. In the second step, the issue of communication delays are dealt with. By designing the waiting mechanism, a distributed MPC scheme is proposed, and the feasibility and stability conditions are established. In the third step, the robust distributed MPC problem for large-scale nonlinear systems subject to control input constraints, communication delays and external disturbances are studied. A dual-mode robust distributed MPC strategy is designed to deal with the communication delays and the external disturbances simultaneously, and the feasibility and the stability conditions are developed, accordingly. / Graduate / 0548 / 0544

Platooning is an interesting area which involve the possibility of decreasing the fuel consumption of heavy-duty vehicles. By reducing the inter-vehicle spacing in the platoon we can reduce air drag, which in turn reduces fuel consumption. Two fuel-efficient model predictive controllers for HDVs in a platoon has been formulated in this master thesis, both utilizing road grade preview information. The first controller is based on linear programming (LP) algorithms and the second on quadratic programming (QP). These two platooning controllers are compared with each other and with generic controllers from Scania. The LP controller proved to be more fuel-efficient than the QP controller, the Scania controllers are however more fuel-efficient than the LP controller.

The control and optimization of chemical plants is a major area of research as it has the potential to improve both economic output and plant safety. It is often prudent to separate control and optimization tasks of varying complexities and time scales, creating a hierarchical control structure. Within this structure, it is beneficial for one control layer to be able to account for the effects of other layers. A clear example of this, and the basis of this work, is closed-loop dynamic real-time optimization (CL-DRTO), in which an economic optimization method considers both the plant behavior and the effects of an underlying model predictive controller (MPC). This technique can be expanded on to allow its use and methods to be employed in a greater diversity of applications, particularly unstable and uncertain plant environments. First, this work seeks to improve on existing robust MPC techniques, which incorporate plant uncertainty via direct multi-scenario modelling, by also including future MPC behavior through the use of the CL modelling technique of CL-DRTO. This allows the CL robust MPC to account for how future MPC executions will be affected by uncertain plant behavior. Second, Lyapunov MPC (LMPC) is a generally nonconvex technique which focuses on effective control of plants which exhibit open-loop unstable behavior. A new convex LMPC formulation is presented here which can be readily embedded into a CL-DRTO scheme. Next, uncertainty handling is incorporated directly into a CL-DRTO via a robust multi-scenario method to allow for the economic optimization to take uncertain plant behavior into account while also modelling MPC behavior under plant uncertainty. Finally, the robust CL-DRTO method is computationally expensive, so a decomposition method which separates the robust CL-DRTO into its respective scenario subproblems is developed to improve computation time, especially for large optimization problems. / Thesis / Doctor of Philosophy (PhD) / It is common for control and optimization of chemical plants to be performed in a multi-layered hierarchy. The ability to predict the behavior of other layers or the future behavior of the same layer can improve overall plant performance. This thesis presents optimization and control frameworks which use this concept to more effectively control and economically optimize chemical plants which are subject to uncertain behavior or instability. The strategy is shown, in a series of simulated case studies, to effectively control chemical plants with uncertain behavior, control and optimize unstable plant systems, and economically optimize uncertain chemical plants. One of the drawbacks of these strategies is the relatively large computation time required to solve the optimization problems. Therefore, for uncertain systems, the problem is separated into smaller pieces which are then coordinated towards a single solution. This results in reduced computation time.

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, after a comprehensive literature review on different conventional and predictive torque control strategies for switched reluctance motor (SRM) drives, two online methods and one offline multi-objective optimization-based method are proposed to extend the operating speed range of finite control set model predictive torque control (FCS-MPTC) for SRM by adaptively controlling the commutation angles in the entire speed range. Furthermore, a method is proposed to minimize the steady state torque tracking error of FCS-MPTC for SRM drives. The incapability of the conventional FCS-MPTC in controlling the commutation angles, which is considered as one of the main drawbacks of the conventional FCS-MPTC, limits its application for high-speed torque control of SRM drives. The phase turn-off angle is always selected to be close to the aligned position with the conventional FCS-MPTC regardless of the operating speed. However, commutation angle advancement is required for high-speed torque control of SRM drives to limit the negative phase torque resulting from the current tail after the turn-off angle in the generating region. Excessive negative torque with the conventional FCS-MPTC at higher speeds can result in a degraded performance with high rms current, low average torque, high torque ripple, and reduced efficiency. The phase turn-off angle can be adaptively controlled as speed changes with the first online commutation angle control strategy proposed in this thesis. This method is based on predicting the free-wheeling phase current in an extended time interval which is much bigger than the prediction horizon of FCS-MPTC. The second online turn-off angle control method is also proposed by improving the optimality condition defined for determining the optimal turn-off angle. The optimality condition is determined by calculating the work done by the conducting phase after the phase is turned off. The weighting factor of the objective function of FCS-MPTC is kept constant with both proposed online methods. An offline multi-objective optimization-based strategy is proposed to determine the globally optimal turn-off angle and the weighting factor in the entire operating torque and speed ranges. The effectiveness of both proposed online methods and the offline commutation angle control strategy is verified using simulations and experimental results. The results are also compared to the conventional FCS-MPTC and the indirect average torque control with optimized conduction angles which is considered as one of the main conventional torque control strategies for SRM drives. In order to minimize the torque tracking error as a result of either parameter uncertainties or tracking multiple objectives with a single objective function with weighting factors, a method is proposed which is based on updating the reference torque at each sample time by calculating the average torque tracking error in the previous sample times. The validity of the proposed method is verified using simulations. / Thesis / Doctor of Philosophy (PhD)

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.