京都大学 / 新制・課程博士 / 博士(情報学) / 甲第24263号 / 情博第807号 / 新制||情||136(附属図書館) / 京都大学大学院情報学研究科数理工学専攻 / (主査)准教授 加嶋 健司, 教授 太田 快人, 教授 山下 信雄 / 学位規則第4条第1項該当 / Doctor of Informatics / Kyoto University / DGAM

This thesis aims to produce a control strategy that minimizes the energy usage of the pumps in the sewer system of Växjö City. The pumps are located in a small number of pumping stations. These are connected by a network of pipes in a way that requires the control of the pumps to be coordinated, both within and between the pumping stations. A model of the system based on fluid mechanics is proposed and from this an optimization problem is constructed for the control problem. When the optimization problem is reformulated as a hierarchy of smaller problems these problems can be solved sequentially and the computational requirements are low. The resulting control strategy gives an optimal control at each flow rate to the waste water treatment plant, and the results show that an optimal control can yield significant energy savings. The control strategy is also shown to be stable with regards to errors in the model. / Detta arbete syftar till att beräkna en energieffektiv styrstrategi för pumpar i spillvattensystemet i Växjö stad. Pumparna finns i ett fåtal pumpstationer som är sammankopplade via ett rörsystem så att styrningen av pumparna behöver koordineras, både inom och mellan pumpstationerna. Utifrån en framtagen fysikalisk modell av systemet formuleras ett optimeringsproblem för att finna en energieffektiv styrning. Detta problem kan lösas på korta beräkningstider genom att det delas upp i en hierarki av mindre delproblem som löses sekventiellt. Den resulterande styrstrategin ger en optimal styrning för olika totala flöden i spillvattensystemet, och resultaten visar att en effektiv styrstrategi kan ge påtagliga besparingar i pumparnas energiförbrukning. Styrstrategin har även studerats gällande känslighet för viss osäkerhet i modellen och uppvisar stabilitet.

Cancer is a generic term for a large group of diseases where cells of the body lose their normal mechanisms for growth so that they grow in an uncontrolled way. One of the most common treatments of cancer is chemotherapy that aims to kill abnormal proliferating cells; however normal cells and other organs of the patients are also adversely affected. In practice, it¿s often difficult to maintain optimum chemotherapy doses that can maximise the abnormal cell killing as well as reducing side effects. The most chemotherapy drugs used in cancer treatment are toxic agents and usually have narrow therapeutic indices, dose levels in which these drugs significantly kill the cancerous cells are close to the levels which sometime cause harmful toxic side effects. To make the chemotherapeutic treatment effective, optimum drug scheduling is required to balance between the beneficial and toxic side effects of the cancer drugs. Conventional clinical methods very often fail to find drug doses that balance between these two due to their inherent conflicting nature. In this investigation, mathematical models for cancer chemotherapy are used to predict the number of tumour cells and control the tumour growth during treatment. A feedback control method is used so as to maintain certain level of drug concentrations at the tumour sites. Multi-objective Genetic Algorithm (MOGA) is then employed to find suitable solutions where drug resistances and drug concentrations are incorporated with cancer cell killing and toxic effects as design objectives. Several constraints and specific goal values were set for different design objectives in the optimisation process and a wide range of acceptable solutions were obtained trading off among different conflicting objectives. Abstract v In order to develop a multi-objective optimal control model, this study used proportional, integral and derivative (PID) and I-PD (modified PID with Integrator used as series) controllers based on Martin¿s growth model for optimum drug concentration to treat cancer. To the best of our knowledge, this is the first PID/I-PD based optimal chemotherapy control model used to investigate the cancer treatment. It has been observed that some solutions can reduce the cancer cells up to nearly 100% with much lower side effects and drug resistance during the whole period of treatment. The proposed strategy has been extended for more drugs and more design constraints and objectives. / Libyan Ministry of Higher Education

Inflatable robots with pneumatic actuation are naturally lightweight and compliant. Both of these characteristics make a robot of this type better suited for human environments where unintentional impacts will occur. The dynamics of an inflatable robot are complex and dynamic models that explicitly allow variable stiffness control have not been well developed. In this thesis, a dynamic model was developed for an antagonistic, pneumatically actuated joint with inflatable links.The antagonistic nature of the joint allows for the control of two states, primarily joint position and stiffness. First a model was developed to describe the position states. The model was used with model predictive control (MPC) and linear quadratic control (LQR) to control a single degree of freedom platform to within 3° of a desired angle. Control was extended to multiple degrees of freedom for a pick and place task where the pick was successful ten out of ten times and the place was successful eight out of ten times.Based on a torque model for the joint which accounts for pressure states that was developed in collaboration with other members of the Robotics and Dynamics Lab at Brigham Young University, the model was extended to account for the joint stiffness. The model accounting for position, stiffness, and pressure states was fit to data collected from the actual joint and stiffness estimation was validated by stiffness measurements.Using the stiffness model, sliding mode control (SMC) and MPC methods were used to control both stiffness and position simultaneously. Using SMC, the joint stiffness was controlled to within 3 Nm/rad of a desired trajectory at steady state and the position was controlled to within 2° of a desired position trajectory at steady state. Using MPC,the joint stiffness was controlled to within 1 Nm/rad of a desired trajectory at steady state and the position was controlled to within 2° of a desired position trajectory at steady state. Stiffness control was extended to multiple degrees of freedom using MPC where each joint was treated as independent and uncoupled. Controlling stiffness reduced the end effecter deflection by 50% from an applied load when high stiffness (50 Nm/rad) was used rather than low stiffness (35 Nm/rad).This thesis gives a state space dynamic model for an inflatable, pneumatically actuated joint and shows that the model can be used for accurate and repeatable position and stiffness control with stiffness having a significant effect.

For accurate prediction of tsunami wave propagation, information on the system of PDEs modelling its evolution and full initial and/or boundary data is required. However the latter is not generally fully available, and so the primary objective becomes to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme based on the calculus of variations, the purpose of which is to optimise some distorted form of the initial condition to give a prediction closer to the exact initial data. We considered two possible forms of distortion, by adding noise to our initial wave, and by rescaling the wave amplitude. Multiple cases were analysed, with observations measured at different points in our spatial domain, as well as variations in the number of observation points. We found that the error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken. In the linear case, since the wave form simply translates a fixed form, multiple measurement points did not necessarily provide more information. In the nonlinear case, because the waveform changes shape as it translates, adding more measurement points provides more information about the dynamics and the wave shape. This is reflected in the fact that in the nonlinear case adding more points gave a bigger decrease in error, and much closer convergence of the optimised guess for our initial condition to the exact initial wave profile. / Thesis / Master of Science (MSc) / In ocean wave modelling, information on the system dynamics and full initial and/or boundary data is required. When the latter is not fully available the primary objective is to find an optimal estimate of these conditions, using available information. Data Assimilation is a methodology used to optimally integrate observed measurements into a mathematical model, to generate a better estimate of some control parameter, such as the initial condition of the wave, or the sea floor bathymetry. In this study, we considered the shallow water equations in both linear and non-linear form as an approximation for ocean wave propagation, and derived a data assimilation scheme to optimise some distorted form of the initial condition to generate predictions converging to the exact initial data. The error between measurements and observation data was sufficiently minimised across all cases. A relationship was found between the number of measurement points and the error, dependent on the choice of where measurements were taken.

High-amplitude freestream turbulence and surface roughness elements can excite a laminar boundary-layer flow sufficiently enough to cause streamwise-oriented vortices to develop. These vortices resemble elongated streaks having alternate spanwise variations of the streamwise velocity. Following the transient growth phase, the fully developed vortex structures downstream undergo an inviscid secondary instability mechanism and, ultimately, transition to turbulence. This mechanism becomes much more complicated in high-speed boundary layer flows due to compressibility and thermal effects, which become more significant for higher Mach numbers. In this research, we formulate and test an optimal control algorithm to suppress the growth rate of the aforementioned streamwise vortex system. The derivation of the optimal control algorithm follows two stages. In the first stage, to optimize the computational cost of the analysis, the study develops an efficient numerical algorithm based on the nonlinear boundary region equations (NBREs), a reduced form of the compressible Navier-Stokes equations in a high-Reynolds-number asymptotic framework. The NBREs algorithm results agree well with direct numerical simulation (DNS) results. The numerical simulations are substantially less computationally costly than a full DNS and have a more rigorous theoretical foundation than parabolized stability equation (PSE) based models. The substantial reduction in computational time required to predict the full development of a G\"{o}rtler vortex system in high-speed flows allows investigation into feedback control in reasonable total computational time, which is the focus of the second part of the study. In the second stage, the method of Lagrange multipliers is utilized -- via an appropriate transformation of the original constrained optimization problem into an unconstrained form -- to obtain the adjoint compressible boundary-region equations (ACBREs) and corresponding optimality conditions, which constitute the basis of the optimal control approach. Numerical solutions for high-supersonic and hypersonic flows reveal a significant decrease in the kinetic energy and wall shear stress for all configurations considered. Streamwise velocity contour plots illustrate the qualitative effect of the optimal control iterations, demonstrating a significant decrease in the amplitude of the primary vortex instabilities.

Electromagnetism and optimal control stand out as a topics that feature impactful applications in modern engineering, as well as challenging theoretical aspects of mathematical analysis. Within this context, a major role is played by the search of necessary and sufficient conditions characterizing optimal solutions, as they are functional to numerical algorithms aiming to approximate such solutions. In this thesis, three standalone topics in optimization sharing the underlying framework of Maxwell-related PDEs are discussed. First, I present an optimal control problem driven by a quasi-linear magneto-static obstacle problem featuring first-order differential state constraints. The non-linearity allows to suitably model electromagnetic waves in the presence of ferromagnetic materials, while the first-order obstacle is relevant for applications in the field of magnetic shielding. Existence theory and the derivation of an optimality system are addressed with an approximation technique based on a relaxation-penalization of the variational inequality. Second, I analyze an eddy current problem controlled through a dipole type source, i.e. a Dirac mass with fixed position and variable intensity: well-posedness of the state equation through a fundamental solution (of a curl curl - Id operator) approach and first order conditions are dealt with. To conclude, I discuss the computation of the topological derivative for shape functionals constrained to low-frequency electromagnetic problems (closely related to the eddy current model), with respect to the inclusion/removal of conducting material; the results are obtained using a Lagrangian approach and in particular the so-called averaged adjoint method. This approach requires the study of the asymptotic behavior of the solutions of some problems defined in the whole space, and the introduction and consequent analysis of appropriate function spaces.

Traffic congestion is a central problem in transportation systems, especially in urban areas. The rapid development of Connected and Automated Vehicles (CAVs) and new traffic infrastructure technologies provides a promising solution to solve this problem. This work focuses on the safety-critical optimal control of CAVs in autonomous traffic systems. The dissertation starts with the roundabout problem of controlling CAVs travelling through a roundabout so as to jointly minimize their travel time, energy consumption, and centrifugal discomfort while providing speed-dependent safety guarantees. A systematic approach is developed to determine the safety constraints for each CAV dynamically. The joint optimal control and control barrier function (OCBF) controller is applied, where the unconstrained optimal control solution is derived which is subsequently optimally tracked by a real-time controller while guaranteeing the satisfaction of all safety constraints. Secondly, the dissertation deals with the feasibility problem of OCBF. The feasibility problem arises when the control bounds conflict with the Control Barrier Function (CBF) constraints and is solved by adding a single feasibility constraint to the Quadratic Problem (QP) in the OCBF controller to derive the feasibility guaranteed OCBF. The feasibility guaranteed OCBF is applied in the merging control problem which provably guarantees the feasibility of all QPs derived from the OCBF controller. Thirdly, the dissertation deals with the performance loss of OCBF due to the improperly selected reference trajectory which deviates largely from the complete optimal solution especially when the vehicle limitations are tight. A neural network is used to learn the control policy from data retrieved by offline calculation from the complete optimal solutions. Tracking the learnt reference trajectory with CBF outperforms OCBF in simulation experiments. Finally, a hierarchical framework of modular control zones (CZ) is proposed to extend the safety-critical optimal control of CAV from a single CZ to a traffic network. The hierarchical modular CZ framework is developed consisting of a lower-level OCBF controller and a higher-level feedback flow controller to coordinate adjacent CZs which outperforms a direct extension of the OCBF framework to multiple CZs without any flow control in simulation.

With the recent advances in the field of unmanned aerial vehicles, many applications have been identified. In tasks that require high-payload-to-weight ratios, flight times in the order of days, reduced noise and/or hovering capabilities, lighter-than-air vehicles present themselves as a competitive platform compared to fixed-wing and rotor based vehicles. The limiting factor in their widespread use in autonomous applications comes from the complexity of the control task. The so-called airships are highly-susceptible to aerodynamic forces and pose complex nonlinear system dynamics that complicate their modeling and control. Model-free control lends itself well as a solution to this type of problem, as it derives its control policies using input-output data, and can therefore learn complex dynamics and handle uncertain or unknown parameters and disturbances. In this work, two multi-input multi-output algorithms are presented on the basis of optimal control theory. Leveraging results from reinforcement learning, a single layer, partially connected neural network is formulated as a value function appropriator in accordance with Weierstrass higher-order approximation theorem. The so-called critic-network is updated using gradient descent methods on the mean-squared error of the temporal difference equation. In the single-network controller, the control policy is formulated as a closed form equation that is parameterized on the weights of the critic-network. A second controller is proposed that uses a second single-layer partially connected neural network, the actor-network, to calculate the control action. The actor-network is also updated using gradient descent on the squared error of the temporal difference equation. The controllers are employed in a highly realistic simulation airship model in nominal conditions and in the presence of external disturbances in the form of turbulent wind. To verify the validity and test the sensitivity of the algorithms to design parameters (the initialization of certain terms), ablation studies are carried out with multiple initial parameters. Both of the proposed algorithms are able to track the desired waypoints in both the nominal and disturbed flight tests. Furthermore, the performance of the controllers is compared to a modern, state-of-the-art multi-input multi-output controller. The two proposed controllers outperform the comparison controller in all but one flight test, with up to four fold reduction in the integral absolute error and integral time absolute error metrics. On top of the quantitative improvements seen in the proposed controllers, both controllers demonstrate a reduction in system oscillation and actuator chattering with respect to the comparison algorithm.

Identification and characterization of a target object included within a surrounding medium is of interest in a variety of fields ranging from medical imaging and diagnostics, to counter-mine operations in military environments. The work described in this document applies a new approach to this problem through the development of Dynamic Interrogation, whereby physical stimuli are combined with imaging techniques to identify physical properties of a target inclusion. Interaction with physical systems in the real world brings with it a number of challenges, namely the stochastic nature of physical systems which adds complexity and uncertainty to any analysis or manipulation performed. In the field of optimal control, stochastic systems are well-studied. However, most approaches from literature seek to minimize the mean cost value of the system. An alternative approach found in literature is to minimize the variance of the cost function while constraining the mean cost to some selected value. This approach is known as Minimal Cost Variance control, and has been demonstrated to regulate finite continuous-time systems while minimizing the cost variance. In this work, we expand this technique to develop a new optimal control methodology suitable for robotic tracking applications. The unknown nature of the interrogation target provides an opportunity to leverage techniques from Model Predictive Control approaches to further improve the performance of the Dynamic Interrogation system. As a result, the developed novel control focuses on utilizing a minimal cost variance approach within the framework of model predictive control to optimize the performance of a Dynamic Interrogation system and facilitate implementation in an online architecture. To do this, we first develop the solution to the continuous-time, full-state feedback tracking MCV control problem which enables stochastic systems track a-priori state trajectories while minimizing the cost variance of the system. Next, we extend the tracking MCV solution to the discrete-time case to facilitate implementation in online architectures and to integrate with architectures from the field of model predictive control, most of which are implemented in discrete time. Finally, we derive the full Model Predictive Minimal Cost Variance (MPMCV) control and provide example implementations to physical systems. In addition to the optimal control work, this dissertation includes the development and structure of Dynamic Interrogation as implemented by robotic systems. The initial application for development of a Dynamic Interrogation approach focuses on tumor detection and characterization within biological tissue by implementation of recently developed imaging techniques to robotic manipulation utilizing novel optimal control approaches. This dissertation presents a nominal architecture for implementation of Dynamic Interrogation on the Baxter research robot, a platform developed specifically for applications in close proximity to humans. Additionally, the development of a Tactile Imagining sensor designed for integration with the robotic platform is presented. The integrated sensor system was then installed and tested on the Baxter robot within a laboratory environment, and experimentation done to verify the abilities and performance of the full system on phantom tissue analogs. The work concludes with experimental results from this implementation and a discussion of future work. / Electrical and Computer Engineering