<p dir="ltr">At the cusp of scientific discovery and innovation, mankind's next greatest challenge lies in developing capabilities to enable human presence in deep space. This entails setting up space infrastructure, travel pathways, managing spacecraft traffic, and building up deep space operation logistics. Spacecrafts that are a part of the infrastructure must be able to perform myriad of operations and transfers such as rendezvous and docking, station-keeping, loitering, collision avoidance etc. In support of this endeavour, an investigation is done to analyze and recreate the solution space for fuel-optimal trajectories and control histories required for onboard trajectory design of inexpensive spacecraft transfers and operations. This study investigates close range rendezvous (CRR), nearby orbital transfer, collision avoidance, and long range transfer maneuvers for spacecrafts whose highly complex and nonlinear behavior is modelled using the circular restricted three-body problem (CR3BP) dynamics and to which a finite-burn maneuver is augmented to model low-propulsion maneuvers. In order to study the nonlinear solution space for such maneuvers, this investigation contributes new formulations of nonlinear programming (NLP) optimal control problems solved to minimize fuel consumption, and validated by traditional methods already in use. This investigation proposes a Feature Learning based Optimal Control Method (L-OCM) to learn the solution space and recreate results in real-time. The NLP problem is solved off-line for a range of initial conditions. The set of solutions is used to generate datasets with initial conditions as inputs and the identified features of the optimal control solution as outputs. These features are inherent to reconstructing the optimal control histories of the solution and are selected keeping onboard computational capabilities in mind. Deep Neural Networks (DNNs) are trained to map the complex, nonlinear relationship between the inputs and outputs, and then implemented to find on-line solutions to any initial condition. The L-OCM method provides fuel-optimal, real-time solutions that can be implemented by a spacecraft performing operations in cislunar space.</p>

Hyperthermia is a cancer treatment modality that raises cancerous tissue to cytotoxic temperature levels for roughly 30 to 45 minutes. Hyperthermia treatment planning refers to the use of computational models to optimize the heating protocol to be used in a hyperthermia treatment. This thesis presents a method to optimize a hyperthermia treatment heating protocol. An algorithm is developed which recovers a heating protocol that will cause a desired amount of thermal damage within a region of tissue. The optimization algorithm is validated experimentally on an albumen tissue phantom. The transient temperature distribution within the region is simulated using a two-dimensional, finite-difference model of the Pennes bioheat equation. The relationship between temperature and time is integrated to produce a damage field according to two different models; Henriques'' model and the thermal dose model (Moritz and Henriques (1947)), (Sapareto and Dewey (1984)). A minimization algorithm is developed which re duces the value of an objective function based on the squared difference between an optimal and calculated damage field. Either damage model can be used in the minimization algorithm. The adjoint problem in conjunction with the conjugate gradient method is used to minimize the objective function of the control problem. The flexibility of the minimization algorithm is proven experimentally and through a variety of simulations. With regards to the validation experiment, the optimal and recovered regions of permanent thermal damage are in good agreement for each test performed. A sensitivity analysis of the finite difference and damage models shows that the experimentally-obtained extent of damage is consistently within a tolerable error range. Excellent agreement between the optimal and recovered damage fields is also found in simulations of hyperthermia treatments on perfused tissue. A simplified and complex model of the human skin were created for use within the algorithm. Minimizations using both the Henriques'' model and the thermal dose model in the objective function are performed. The Henriques'' damage model was found to be more desirable for use in the minimization algorithm than the thermal dose model because it is less computationally intensive and includes a mechanism to predict the threshold of permanent thermal damage. The performance of the minimization algorithm was not hindered by adding complexity to the skin model. The method presented here for optimizing hyperthermia treatments is shown to be robust and merits further investigation using more complicated patient models. / Master of Science

Autonomous navigation with high speed in rough terrain is one of the most challenging tasks for wheeled robots. To achieve mobility over this terrain, a high agility wheeled robot should adapt and react fast to optimally traverse this challenging environment. Therefore, this dissertation is geared towards the design and development of a novel reconfigurable wheeled robot paradigm for rough terrain applications. This research focuses on the design, modeling, analysis and control of the reconfigurable wheeled robot, TIGER, with an elastic actuated mechanism for improving the robot's dynamic stability on rough terrain by controlling the robot's ground clearance, body roll and pitch angles. The elastic actuated mechanism mainly consists of a linear actuator connected in series with a shock absorber. Four sets of the elastic actuated mechanism are used to create different robot configurations to adapt to the terrain. Three main aspects were considered in this research in order to extend the ability of the robot to effectively navigate in rough terrain. The first aspect focuses on designing an agile reconfigurable wheeled robot by including an elastic actuated mechanism for improving maneuverability, longitudinal/lateral stability, and rollover prevention. Robot agility, stability, and high speed have been considered during the design process. The new design provides different configuration modes. These configurations allow for controlling the robot's Center Of Mass (COM) height and optimally distribute the vertical force on each tire for enhancing the tractive efficiency, mobility and dynamic stability. The second aspect presents the robot kinematic and dynamic modeling and analysis. The robot dynamics model is represented with fourteen degrees of freedom (DOF), where the dynamic behaviors of the robot body, suspension system, forces and moments on the tires are included. The dynamic behavior is controlled using the linear actuators' position and speed as inputs to determine the resulting ground clearance, body roll, and pitch angles. Sensors are integrated onboard the robot to calculate the robot's states in real time for use in feedback control. The third aspect focuses on introducing a technique for estimating the robot state-space dynamic model and control the Elastic Actuated Mechanism (EAM) using only a noisy Inertial Measurement Unit (IMU) with COM position uncertainty. The simulation results show that the observer estimates the actual behavior of the robot with 95% accuracy and up to 20% COM uncertainty. The Root Mean Square (RMS) has been reduced by 21% for bounce, 51% for pitch and 50% for roll acceleration. / Ph. D. / Wheeled mobile robots are being used for rough terrain applications in the field of robotics as a practical solution to accomplish various tasks. Unfortunately, most of the wheeled robots are not able to perform high dynamically tasks with high speed in rough terrain due to complex suspension design, high power-to-weight ratio, high cost and complexity of controlling highly nonlinear model in real-time. Therefore, this dissertation is geared towards the design and development of a novel reconfigurable wheeled robot paradigm for rough terrain applications. This research focuses on the design, modeling, analysis and control of the reconfigurable wheeled robot, TIGER, with an elastic actuated mechanism for improving the robot’s dynamic stability on rough terrain by controlling the robot’s ground clearance, body roll and pitch angles. The elastic actuated mechanism mainly consists of a linear actuator connected in series with a shock absorber. Four sets of the elastic actuated mechanism are used to create different robot configurations to adapt to the terrain. Three main aspects were considered in this research in order to extend the ability of the robot to effectively navigate in rough terrain. The first aspect focuses on designing an agile reconfigurable wheeled robot by including an elastic actuated mechanism for improving maneuverability, longitudinal/lateral stability, and rollover prevention. Robot agility, stability, and high speed have been considered during the design process. The new design provides different configuration modes. These configurations allow for controlling the robot’s COM height and optimally distribute the vertical force on each tire for enhancing the tractive efficiency, mobility and dynamic stability. The second aspect presents the robot kinematic and dynamic modeling and analysis. The robot dynamics model is represented with fourteen degrees of freedom (DOF), where the dynamic behaviors of the robot body, suspension system, forces and moments on the tires are included. The dynamic behavior is controlled using the linear actuators’ position and speeds as inputs to determine the resulting ground clearance, body roll, and pitch angles. Sensors are integrated onboard the robot to calculate the robot’s states in real time for use in feedback control. The third aspect focuses on introducing a technique for estimating the robot state-space dynamic model and control the EAM using only a noisy IMU with COM position uncertainty. The simulation results show that the observer estimates the actual behavior of the robot with 95% accuracy and up to 20% COM uncertainty. The RMS has been reduced by 21% for bounce, 51% for pitch and 50% for roll acceleration.

This work is concerned with the construction of preconditioners for indefinite linear systems. The systems under investigation arise in the numerical solution of quadratic programming problems, for example in the form of Karush--Kuhn--Tucker (KKT) optimality conditions or in interior--point methods. Therefore, the system matrix is referred to as a KKT matrix. It is not the purpose of this thesis to investigate systems arising from general quadratic programming problems, but to study systems arising in linear quadratic control problems governed by partial differential equations. The KKT matrix is symmetric, nonsingular, and indefinite. For the solution of the linear systems generalizations of the conjugate gradient method, MINRES and SYMMLQ, are used. The performance of these iterative solution methods depends on the eigenvalue distribution of the matrix and of the cost of the multiplication of the system matrix with a vector. To increase the performance of these methods, one tries to transform the system to favorably change its eigenvalue distribution. This is called preconditioning and the nonsingular transformation matrices are called preconditioners. Since the overall performance of the iterative methods also depends on the cost of matrix--vector multiplications, the preconditioner has to be constructed so that it can be applied efficiently. The preconditioners designed in this thesis are positive definite and they maintain the symmetry of the system. For the construction of the preconditioners we strongly exploit the structure of the underlying system. The preconditioners are composed of preconditioners for the submatrices in the KKT system. Therefore, known efficient preconditioners can be readily adapted to this context. The derivation of the preconditioners is motivated by the properties of the KKT matrices arising in optimal control problems. An analysis of the preconditioners is given and various cases which are important for interior point methods are treated separately. The preconditioners are tested on a typical problem, a Neumann boundary control for an elliptic equation. In many important situations the preconditioners substantially reduce the number of iterations needed by the solvers. In some cases, it can even be shown that the number of iterations for the preconditioned system is independent of the refinement of the discretization of the partial differential equation. / Master of Science

The navigation and control of an autonomous vehicle is a highly complex task. Making a vehicle intelligent and able to operate "unmanned" requires extensive theoretical as well as practical knowledge. An autonomous vehicle must be able to make decisions and respond to situations completely on its own. Navigation and control serves as the major limitation of the overall performance, accuracy and robustness of an autonomous vehicle. This thesis will address this problem and propose a unique navigation and control scheme for an autonomous lawn mower (ALM). Navigation is a key aspect when designing an autonomous vehicle. An autonomous vehicle must be able to sense its location, navigate its way toward its destination, and avoid obstacles it encounters. Since this thesis attempts to automate the lawn mowing process, it will present a navigational algorithm that covers a bounded region in a systematic way, while avoiding obstacles. This algorithm has many applications including search and rescue, floor cleaning, and lawn mowing. Furthermore, the robustness and utility of this algorithm is demonstrated in a 3D simulation. This thesis will specifically study the dynamics of a two-wheeled differential drive vehicle. Using this dynamic model, various control techniques can then be applied to control the movement of the vehicle. This thesis will consider both open loop and closed loop control schemes. Optimal control, path following, and trajectory tracking are all considered, simulated, and evaluated as practical solutions for control of an ALM. To design and build an autonomous vehicle requires the integration of many sensors, actuators, and controllers. Software serves as the glue to fuse all these devices together. This thesis will suggest various sensors and actuators that could be used to physically implement an ALM. This thesis will also describe the operation of each sensor and actuator, present the software used to control the system, and discuss physical limitations and constraints that might be encountered while building an ALM. / Master of Science

The velocity tracking problem is motivated by the desire to match a desired target flow with a flow which can be controlled through time dependent distributed forces or time dependent boundary conditions. The flow model is the Navier-Stokes equations for a viscous incompressible fluid and different kinds of controls are studied. Optimal distributed and boundary controls minimizing a quadratic functional and an optimal bounded distributed control are investigated. The distributed optimal and the bounded control are compared with a linear feedback control. Here, a unified mathematical formulation, covering several specific classes of meaningful control problems in bounded domains, is presented with a complete and detailed analysis of all these time dependent optimal control velocity tracking problems. We concentrate not only on questions such as existence and necessary first order conditions but also on discretization and computational aspects. The first order necessary conditions are derived in the continuous, in the semidiscrete time approximation and in the fully finite element discrete case. This derivation is needed to obtain an accurate meaningful numerical algorithm with a satisfactory convergence rate. The gradient algorithm is used and several numerical computations are performed to compare and understand the limits imposed by the theory. Some computational aspects are discussed without which problems of any realistic size would remain intractable. / Ph. D.

Connected and Automated Vehicles (CAVs) have the potential to revolutionize transportation efficiency and safety through collaborative behavior. This dissertation explores the challenges and opportunities associated with achieving socially optimal cooperative maneuvers, using the problem of cooperative lane-changing to showcase the significance of cooperativeness. Cooperative lane-changing serves as an ideal testbed for examining decentralized optimal control, interactions with uncooperative vehicles, accommodating diverse human driving preferences, and integrating planning and execution processes. Initially, the research focuses on scenarios where all vehicles are cooperative CAVs, leveraging their communication and coordination capabilities. Decentralized optimal control problems are formulated to minimize energy consumption, travel time, and traffic disruption during sequential cooperative lane changes, balancing individual vehicle objectives with system-level goals. The dissertation then extends the analysis to mixed-traffic scenarios involving uncooperative human-driven vehicles (HDVs). A novel approach is developed to ensure safety assurance, combining optimal control with Control Barrier Functions (CBFs) and fixed-time convergence (FxT-OCBF). Robust methods for handling disturbances from uncooperative vehicles are introduced, enhancing the resilience and dependability of cooperative lane-changing maneuvers. An innovative online learning framework is presented to address the complexities of CAVs interacting with HDVs exhibiting diverse driving preferences. Safety preferences are characterized using parameterized CBFs, and an extended Kalman filter dynamically adjusts control parameters based on observed interactions, enabling real-time adaptation to evolving human behaviors. The proposed methodologies bridge the gap between high-level planning and low-level control execution, facilitating safe and near-optimal cooperative maneuvers. Comprehensive analysis demonstrates improved traffic throughput, reduced energy consumption, and enhanced safety compared to non-cooperative or reactive approaches. This research lays the foundation for deploying CAV technologies that prioritize social optimality while addressing uncertainties in mixed-traffic settings, ultimately paving the way for safer and more efficient transportation systems. / 2025-03-11T00:00:00Z

Simulation modeling is important for resource management and operational strategy within the industry. Optimation AB specializes in modeling and simulation of complex systems using Dymola, but also offers solutions for decision support by solving simplified optimal control problems (OCPs). Since simulation models can be exported as functional mock-up units (FMUs), interfacing the underlying equations, this thesis explores the use of FMUs to formulate and solve OCPs in Python, proposing a workflow based on the softwares CasADi, Rockit and IPOPT. Test cases of increasing complexity, including a cogeneration plant OCP, were employed to evaluate the workflow. Promising results were obtained for simplified models, though scaling, initial guesses and solver settings require further consideration. Collocation demonstrated the fastest convergence time and overall robustness. It could be concluded that integrating FMUs into OCPs is feasible, although complex models require modifications. This suggest that creating simplified component libraries in Dymola, tailored for optimization, could improve method implementation and re-usability.

<p dir="ltr">This thesis presents a comprehensive exploration of advanced optimization strategies for addressing mixed-integer optimal control problems (MIOCPs) in aerospace applications, emphasizing the enhancement of convergence robustness, computational efficiency, and accuracy. The research develops a broad spectrum of optimization methodologies, including multi-phase approaches, parallel computing, reinforcement learning (RL), and distributed algorithms, to tackle complex MIOCPs characterized by highly nonlinear dynamics, intricate constraints, and discrete control variables.</p><p dir="ltr">Through discretization and reformulation, MIOCPs are transformed into general quadratically constrained quadratic programming (QCQP) problems, which are then equivalently converted into rank-one constrained semidefinite programs problems. To address these, iterative algorithms are developed specifically for solving such problems. Initially, two iterative search methods are introduced to achieve convergence: one is a hybrid alternating direction method of multipliers (ADMM) designed for large-scale QCQP problems, and the other is an iterative second-order cone programming (SOCP) algorithm developed to achieve global convergence. Moreover, to facilitate the convergence of these iterative algorithms and to enhance their solution quality, a multi-phase strategy is proposed. This strategy integrates with both the iterative ADMM and SOCP algorithms to optimize the solving of QCQP problems, improving both the convergence rate and the optimality of the solutions. To validate the effectiveness and improved computational performance of the proposed multi-phase iterative algorithms, the proposed algorithms were applied to several aerospace optimization problems, including six-degree-of-freedom (6-DoF) entry trajectory optimization, fuel-optimal powered descent, and multi-point precision landing challenges in a human-Mars mission. Theoretical analyses of convergence properties along with simulation results have been conducted, demonstrating the efficiency, robustness, and enhanced convergence rate of the optimization framework.</p><p dir="ltr">However, the iteration based multi-phase algorithms primarily guarantee only local optima for QCQP problems. This research introduces a novel approach that integrates a distributed framework with stochastic search techniques to overcome this limitation. By leveraging multiple initial guesses for collaborative communication among computation nodes, this method not only accelerates convergence but also enhances the exploration of the solution space in QCQP problems. Additionally, this strategy extends to tackle general nonlinear programming (NLP) problems, effectively steering optimization toward more globally promising directions. Numerical simulations and theoretical proofs validate these improvements, marking significant advancements in solving complex optimization challenges.</p><p dir="ltr">Following the use of multiple agents in QCQP problems, this research expand this advantage to address more general rank-constrained semidefinite programs (RCSPs). This research developed a method that decomposes matrices into smaller submatrices for parallel processing by multiple agents within a distributed framework. This approach significantly enhances computational efficiency and has been validated in applications such as image denoising, showcasing substantial improvements in both efficiency and effectiveness.</p><p dir="ltr">Moreover, to address uncertainties in applications, a learning-based algorithm for QCQPs with dynamic parameters is developed. This method creates high-performing initial guesses to enhance iterative algorithms, specifically applied to the iterative rank minimization (IRM) algorithm. Empirical evaluations show that the RL-guided IRM algorithm outperforms the original, delivering faster convergence and improved optimality, effectively managing the challenges of dynamic parameters.</p><p dir="ltr">In summary, this thesis introduces advanced optimization strategies that significantly enhance the resolution of MIOCPs and extends these methodologies to more general issues like NLP and RCSP. By integrating multi-phase approaches, parallel computing, distributed techniques, and learning methods, it improves computational efficiency, convergence, and solution quality. The effectiveness of these methods has been empirically validated and theoretically confirmed, representing substantial progress in the field of optimization.</p>

In this thesis, an optimal multivariable current control method is presented for the highspeed permanent magnet synchronous motor (HS-PMSM). The HS-PMSMs have growing applications in the industry. One of their major challenges is the low switching to fundamental frequency ratio (SFR). At high speed and low SFR, the control time delays including the digital, the PWM, and sensor delays become more pronounced and lead to oscillations and even instabilities. A well-known method for delay compensation is to advance the phase angle of control input for a known amount. In practice, the exact delay is unknown, and mismatch in the compensating angle causes deteriorating effect on the system. In the proposed method, the digital and PWM delays are modelled and integrated with an optimal multivariable controller. This method improves the stability margin and achievable speed margin compared to the traditional phase advancing delay compensation (PADC) method. Combining the proposed delay modeling and the PADC method further improves the response, as the uncertain sensor delays can be compensated greatly. Besides the delay, the cross-coupling between ���� axis affects the dynamic performance of the machine. The proposed multivariable approach considers and directly addresses the coupling. Dynamic performance of the PMSM with the proposed method is thoroughly compared with the conventional delay compensation method. The proposed method is validated through extensive simulation studies on a 2 kW high-speed machine.