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京都大学 / 新制・課程博士 / 博士(工学) / 甲第23888号 / 工博第4975号 / 新制||工||1777(附属図書館) / 京都大学大学院工学研究科航空宇宙工学専攻 / (主査)教授 藤本 健治, 教授 加納 学, 准教授 丸田 一郎, 教授 松野 文俊 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DGAM

The CO2 emissions from road vehicles must be reduced in order to avoid a 1.5 ◦C global warming. To reduce tailpipe emissions, a strong trend is to electrify powertrains to shift away from the use of fossil fuel. Among alternatives, the fuel cellhybrid electric vehicle (FCHEV) is seen as a promising configuration. With the high energy density of hydrogen propulsion systems, it is regarded viable for heavy-dutylong cycle hauling. The aim of this thesis is thus to explore optimal control of energy and thermal management systems of FCHEVs. With the intention of increasing knowledge of how to control FCHEVs for a driving mission, this thesis models an FCHEV powertrain for optimal control purposes. The developed model is used in conjunction with dynamic programming to find the hydrogen optimal control strategies of the energy and thermal management systems. Finally, a sensitivity analysis is performed, investigating how the fuel cell characteristics influence the control strategies. The results propose a feasible complete powertrain model for optimal control purposes and provides insight on how to optimally control the powertrain for various scenarios, minimizing hydrogen consumption. It is concluded that for demanding missions, the fuel cell should consistently provide the main power output and together with the battery handle power transients. For less demanding missions, the fuel cell should be controlled with an on/off strategy, switching between being atidle and working in its most efficient region. It is also concluded that integrated energy and thermal strategies for the fuel cell during a driving mission can increase fuel efficiency, with the optimal thermal strategy being dependent on the fuel cell’s characteristics.

The project considers the class of deterministic continuous-time optimal control problems (OCPs) with piecewise-affine (PWA) vector fields and polynomial data. The OCP is relaxed as an infinite-dimensional linear program (LP) over space of occupation measures. The LP is then written as a particular instance of the generalized moment problem which is then approached by an asymptotically converging hierarchy of linear matrix inequality (LMI) relaxations. The relaxed dual of the original LP gives a polynomial approximation of the value function along optimal trajectories. Based on this polynomial approximation, a novel suboptimal policy is developed to construct a state feedback in a sample-and-hold manner. The results show that the suboptimal policy succeeds in providing a stabilizing suboptimal state feedback law that drives the system relatively close to the optimal trajectories and respects the given constraints.

As vehicles become electrified and more intelligent in terms of sensing, actuation and processing; a number of interesting possibilities arise in controlling vehicle dynamics and driving behavior. Over-actuation with inwheel motors, all wheel steering and active camber is one such possibility, and can facilitate control combinations that push boundaries in energy consumption and safety. Optimal control can be used to investigate the best combinations of control inputs to an over-actuated system. In Part 1, a literature study is performed on the state of art in the field of optimal control, highlighting the strengths and weaknesses of different methods and their applicability to a vehicular system. Out of these methods, Dynamic Programming and Model Predictive Control are of particular interest. Prior work in overactuation, as well as control for reducing tire energy dissipation is studied, and utilized to frame the dynamics, constraints and objective of an optimal control problem. In Part 2, an optimal control problem representing the lateral dynamics of an over-actuated vehicle is formulated, and solved for different objectives using Dynamic Programming. Simulations are performed for standard driving maneuvers, performance parameters are defined, and a system design study is conducted. Objectives include minimizing tire cornering resistance (saving energy) and maintaining the reference vehicle trajectory (ensuring safety), and optimal combinations of input steering and camber angles are derived as a performance benchmark. Following this, Model Predictive Control is used to design an online controller that follows the optimal vehicle state, and studies are performed to assess the suitability of MPC to over-actuation. Simulation models are also expanded to include non-linear tires. Finally, vehicle implementation is considered on the KTH Research Concept Vehicle (RCV) and four vehicle-implementable control cases are presented. To conclude, this thesis project uses methods in optimal control to find candidate solutions to improve vehicle performance thanks to over-actuation. Extensive vehicle tests are needed for a clear indication of the energy saving achievable, but simulations show promising performance improvements for vehicles overactuated with all-wheel steering and active camber.

This dissertation is concerned with three problems within the field of optimization for agent--based systems. Firstly, the inverse optimal control problem is investigated for the single-agent system. Given a dynamic process, the goal is to recover the quadratic cost function from the observation of optimal control sequences. Such estimation could then help us develop a better understanding of the physical system and reproduce a similar optimal controller in other applications. Next, problems of optimization over networked systems are considered. A novel differential game approach is proposed for the optimal intrinsic formation control of multi-agent systems. As for the credit scoring problem, an optimal filtering framework is utilized to recursively improve the scoring accuracy based on dynamic network information. In paper A, the problem of finite horizon inverse optimal control problem is investigated, where the linear quadratic (LQ) cost function is required to be estimated from the optimal feedback controller. Although the infinite-horizon inverse LQ problem is well-studied with numerous results, the finite-horizon case is still an open problem. To the best of our knowledge, we propose the first complete result of the necessary and sufficient condition for the existence of corresponding LQ cost functions. Under feasible cases, the analytic expression of the whole solution space is derived and the equivalence of weighting matrices is discussed. For infeasible problems, an infinite dimensional convex problem is formulated to obtain a best-fit approximate solution with minimal control residual, where the optimality condition is solved under a static quadratic programming framework to facilitate the computation. In paper B, the optimal formation control problem of a multi-agent system is studied. The foraging behavior of N agents is modeled as a finite-horizon non-cooperative differential game under local information, and its Nash equilibrium is studied. The collaborative swarming behaviour derived from non-cooperative individual actions also sheds new light on understanding such phenomenon in the nature. The proposed framework has a tutorial meaning since a systematic approach for formation control is proposed, where the desired formation can be obtained by only intrinsically adjusting individual costs and network topology. In contrast to most of the existing methodologies based on regulating formation errors to the pre-defined pattern, the proposed method does not need to involve any information of the desired pattern beforehand. We refer to this type of formation control as intrinsic formation control. Patterns of regular polygons, antipodal formations and Platonic solids can be achieved as Nash equilibria of the game while inter-agent collisions are naturally avoided. Paper C considers the credit scoring problem by incorporating dynamic network information, where the advantages of such incorporation are investigated in two scenarios. Firstly, when the scoring publishment is merely individual--dependent, an optimal Bayesian filter is designed for risk prediction, where network observations are utilized to provide a reference for the bank on future financial decisions. Furthermore, a recursive Bayes estimator is proposed to improve the accuracy of score publishment by incorporating the dynamic network topology as well. It is shown that under the proposed evolution framework, the designed estimator has a higher precision than all the efficient estimators, and the mean square errors are strictly smaller than the Cramér-Rao lower bound for clients within a certain range of scores. / I denna avhandling behandlas tre problem inom optimering för agentbaserade system. Inledningsvis undersöks problemet rörande invers optimal styrning för ett system med en agent. Målet är att, givet en dynamisk process, återskapa den kvadratiska kostnadsfunktionen från observationer av sekvenser av optimal styrning. En sådan uppskattning kan ge ökad förståelse av det underliggande fysikaliska systemet, samt vara behjälplig vid konstruktion av en liknande optimal regulator för andra tillämpningar. Vidare betraktas problem rörande optimering över nätverkssystem. Ett nytt angreppssätt, baserat på differentialspel, föreslås för optimal intrinsisk formationsstyrning av system med fler agenter. För kreditutvärderingsproblemet utnyttjas ett filtreringsramverk för att rekursivt förbättra kreditvärderingens noggrannhet baserat på dynamisk nätverksinformation. I artikel A undersöks problemet med invers optimal styrning med ändlig tidshorisont, där den linjärkvadratiska (LQ) kostnadsfunktionen måste uppskattas från den optimala återkopplingsregulatorn. Trots att det inversa LQ-problemet med oändlig tidshorisont är välstuderat och med flertalet resultat, är fallet med ändlig tidshorisont fortfarande ett öppet problem. Så vitt vi vet presenterar vi det första kompletta resultatet med både tillräckliga och nödvändiga villkor för existens av en motsvarande LQ-kostnadsfunktion. I fallet med lösbara problem härleds ett analytiskt uttryck för hela lösningsrummet och frågan om ekvivalens med viktmatriser behandlas. För de olösbara problemen formuleras ett oändligtdimensionellt konvext optimeringsproblem för att hitta den bästa approximativa lösningen med den minsta styrresidualen. För att underlätta beräkningarna löses optimalitetsvillkoren i ett ramverk för statisk kvadratisk programmering. I artikel B studeras problemet rörande optimal formationsstyrning av ett multiagentsystem. Agenternas svärmbeteende modelleras som ett icke-kooperativt differentialspel med ändlig tidshorisont och enbart lokal information. Vi studerar detta spels Nashjämvikt. Att, ur icke-kooperativa individuella handlingar, härleda ett kollaborativt svärmbeteende kastar nytt ljus på vår förståelse av sådana, i naturen förekommande, fenomen. Det föreslagna ramverket är vägledande i den meningen att det är ett systematiskt tillvägagångssätt för formationsstyrning, där den önskade formeringen kan erhållas genom att endast inbördes justera individuella kostnader samt nätverkstopologin. I motstat till de flesta befintliga metoder, vilka baseras på att reglera felet i formeringen relativt det fördefinierade mönstret, så behöver den föreslagna metoden inte på förhand ta hänsyn till det önskade mönstret. Vi kallar denna typ av formationsstyrning för intrinsisk formationsstyrning. Mönster så som regelbundna polygoner, antipodala formeringar och Platonska kroppar kan uppnås som Nashjämvikter i spelet, samtidigt som kollisioner mellan agenter undviks på ett naturligt sätt. Artikel C behandlar kreditutvärderingsproblemet genom att lägga till dynamisk nätverksinformation. Fördelarna med en sådan integrering undersöks i två scenarier. Då kreditvärdigheten enbart är individberoende utformas ett optimalt Bayesiskt filter för riskvärdering, där observationer från nätverket används för att tillhandahålla en referens för banken på framtida finansiella beslut. Vidare föreslås en rekursiv Bayesisk estimator (stickprovsvariabel) för att förbättra noggrannheten på den skattade kreditvärdigheten genom att integrera även den dynamiska nätverkstopologin. Inom den föreslagna ramverket för tidsutveckling kan vi visa att, för kunder inom ett visst intervall av värderingar, har den utformade estimatorn högre precision än alla effektiva estimatorer och medelkvadrafelet är strikt mindre än den nedre gränsen från Cramér-Raos olikhet. / <p>QC 20190603</p>

<p>This thesis presents a method for the design of a predictive controller with variable step sizes.Predictive methods such as receding horizon control (or model predictive control) use aa fixed sampling frequency when updating the inputs. In the proposed method, the switchingtimes are incorporated into an optimization problem, thus resulting in anadaptive step-size control process. The controller with variable timesteps is shown to require less tuning and to reduce the number of expensive model evaluations.An alternate solution approach had to be developed to accommodate the new problem formulation.The controller's stability is proven in a context that does not require terminal cost or constraints.The thesis presents examples that compare the performance of the variable switching time controllerwith the receding horizon method with a fixed step size. This research opens many roads for futureextension of the theoretical work and practical applications of the controller.</p> / Doctor of Science (PhD)

Transit operators are increasingly interested in improving efficiency, reliability, and performance of commuter trains while reducing their operating costs. In this context, the application of optimal control theory to the problem of train control can help towards achieving some of these objectives. However, the traction and braking systems of commuter trains often exhibit significant time delays, making the control of commuter trains highly challenging. Previous literature on optimal train control ignores delays in actuation due to the inherent difficulty present in the optimal control, and in general, the control, of input-delay systems. In this thesis, optimal control of a commuter train is presented under two cases: (i) equal, and (ii) unequal time delays in the train traction and braking commands. The solution approach uses the economic model predictive control framework, which involves formulating and solving numerical optimization problems to achieve minimum mixed energy-time optimal control in discretized spatial and time domains. The optimization problems are re-solved repeatedly along the track for the remainder of the trip, using the latest sensor measurements. This would essentially establish a feedback mechanism in the control to improve robustness to modelling errors. A key feature of the proposed methods is that they are model-based controllers, they explicitly incorporate model information, including time delays, in controller synthesis hence avoiding performance degradation and potential instability. To address the issue of input-delays, the well-established predictor approach is used to compensate for input-delays. The case of equal traction-braking delays is treated in discretized spatial domain, which uses an already developed convex approximation to the optimization problem. The use of the convex approximation allows for robust and rapid computation of the optimal control solution. The non-equal traction-braking delays scenario is formulated in time domain, leading to a nonconvex optimization problem. An alternative formulation for minimum-time optimal control problems is presented for delay-free systems that simplifies the solution of minimum-time optimal control problems compared to conventional minimum-time optimal control formulations. This formulation along with the predictor approach is used to help solve the train optimal control problem in the case of non-equal traction-braking delays. The non-equal traction-braking delay controller is compared with the equal traction-braking delay controller by insertion of an artificial delay to make the shorter delays equal to the longer delay. Results of numerical simulations demonstrate the validity and effectiveness of the proposed controllers. / Thesis / Master of Applied Science (MASc)

This thesis presents the design, modeling, and control of a fully-actuated multi-rotor unmanned aerial vehicle (UAV). Unlike conventional multi-rotors, which suffer from two degrees of underactuation in their propeller plane, the choice of an unconventional propeller configuration in the new drone leads to an even distribution of actuation across the entire force-torque space. This allows the vehicle to produce any arbitrary combination of forces and torques within a bounded magnitude and hence execute motion trajectories unattainable with conventional multi-rotor designs. This system, referred to as the \omninospace, decouples the position and attitude controllers, simplifying the motion control problem. Position control is achieved using a PID feedback loop with gravity compensation, while attitude control uses a cascade architecture where the inner loop follows an angular rate command set by the outer attitude control loop. A novel model is developed to capture the disturbance effects among interacting actuator airflows of the \omninospace. Given a desired actuator thrust, the model computes the required motor command using the current battery voltage and thrusts of disturbing actuators. A system identification is performed to justify the use of a linear approximation for parameters in the model to reduce its computational footprint in real-time implementation. The \omni benefits from two degrees of actuation redundancy resulting in a control allocation problem where feasible force-torques may be produced through an infinite number of actuator thrust combinations. A novel control allocation approach is formulated as a convex optimization to minimize the \omnis energy consumption subject to the propeller thrust limits. In addition to energy savings, this optimization provides fault tolerance in the scenario of a failed actuator. A functioning prototype of the \omni is built and instrumented. Experiments carried out with this prototype demonstrate the capabilities of the new drone and its control system in following various translational and rotational trajectories, some of which would not be possible with conventional multi-rotors. The proposed optimization-based control allocation helps reduce power consumption by as much as 6\%, while being able to operate the drone in the event of a propeller failure. / Thesis / Master of Applied Science (MASc)