A trend of increasing the number of forward gears of step-gear automatic transmissions (ATs) has emerged recently due to the legislative and market pressure for CO2 reduction and improved fuel economy. For the increased number of AT gears (up to ten, nowadays), the number of shift types and shift events grows significantly. For instance, in new generation ATs, multi-step gear shifts may be executed frequently in order to improve the driving performance. They include double-transition shifts, which require close coordination between multiple (typically four) clutch control inputs. The increasing shift complexity makes the development of AT control system more demanding, which calls for the development of new shift control optimisation tools and requires more exhaustive control system simulation and optimisation studies. Those studies are based on AT dynamics models, which can be of full order (covering the full spectrum of simulation and optimisation tasks) or reduced order (related to specific gears or shifts, and accounting for locked clutches). The reduced-order models are simpler and computationally more efficient, but their number exponentially grows with the number of AT gears, thus, burdening the modelling effort. Therefore, the development of methods that allow for automated generation of computationally efficient mathematical models is of particular interest. The thesis firstly presents modelling of vehicle powertrain system, where the emphasis is on automated AT modelling and automated AT model-order reduction. Next, numerical optimisation of AT control trajectory is conducted for the purpose of gaining insights into the optimal behaviour of AT for various single-transition and double-transition shifts. Finally, different viable definitions of control variable profiles (i.e. different open-loop control strategies) are proposed and multi-objective optimization of parameters of these profiles is carried out. The obtained optimisation results are employed for assessing the proposed control strategies, as well as for designing a more realistic control system that interacts with driver commands and accounts for various driving conditions. The main aim of the thesis is to propose procedures for automated modelling and automated model-order reduction of an advanced AT with a large number of gears, and based on these models, to propose the design of an optimal shift control system that ensures high shift quality and including robustness in the presence of variations of transmission actuation parameters. The thesis is organised in nine chapters, whose content is summarised in what follows. Chapter 1: Introduction. Outlines the motivation for conducted research, presents a literature overview, and gives the main hypothesis and an overview of the thesis. Chapter 2: Modelling of powertrain dynamics. Outlines a control-oriented powertrain model to be used in the simulation and optimisation studies in the next chapters. The powertrain model is divided into several submodels representing its main components (engine, torque converter, driveline and vehicle), including the key submodel that describes dynamics of a 10-speed AT. An analytical full-order state-space model of a 10-speed AT is derived by using a full-order bond graph model of the considered AT. Powertrain simulation models created in MATLAB/Simulink and 20-sim software environments are also presented. Chapter 3: Automated modelling and automated model-order reduction for automatic transmission. First, a method for automated generation of a full-order numerical AT model from an AT bond graph model is proposed. The proposed numerical method is implemented within the 20-sim and MATLAB software environments, where 20-sim is used to draw the bond graph and export it to (or simulate it by) a MATLAB script. Next, an automated model-order reduction method is proposed for an arbitrary, user-specified clutch state. The method is based on determining the locked-clutch torque variables and their substitution into the full-order statespace model input vector, as well as finding a linear relation between the reduced-order and full-order model state variables. The obtained reduced-order AT models are simpler and computationally more efficient, and are therefore widely used in the remaining part of the thesis for the purpose of computer simulations and optimisations, as well as for analyses of shift dynamics and control system design. Chapter 4: Method for optimisation of AT shift control trajectories. Proposes a method for optimisation of AT shift control trajectories, which aims at gaining insights into the optimal shift control performance and shift control trajectory shaping. After formulating the AT shift control optimisation problem, a pseudospectral collocation method is introduced to optimise AT clutch and engine control trajectories for comfortable and energy-efficient shifts. Since the optimisation method requires a smooth formulation of plant model, the emphasized clutch model non-linearity around the zero slip speed has been found to be a major difficulty to be resolved through proper modelling of the optimisation problem. Therefore, different approaches of describing the friction behaviour have been considered and assessed in a wider framework of this work, starting from simple explicit static models, through explicit dynamics models, toward torque-source-based implicit approaches subject to the clutch passivity constraint. The proposed optimisation method is verified and the clutch models assessed based on the example of 10-speed AT for different single-transition shift control scenarios. The characteristic AT dynamics effects are analysed by using a systematic and illustrative graphical approach based on the bond graph methodology and an equivalent dual-clutch model. Chapter 5: Optimisation of AT control trajectories for double-transition shifts. The AT control trajectory optimisation method presented in the previous chapter is utilized in this chapter for the purpose of double-transition shift control optimisation including engine torque control. With the aim to gain insights into optimal control action and coordination, six different DTS control strategies are proposed and assessed. These strategies are incorporated into the optimisation problem formulation through additional, shift phase-related constraints that the optimisation algorithm needs to satisfy. The proposed optimal strategies are assessed for an example of characteristic double-transition downshifts. Based on the summarized optimisation results obtained for different levels of clutch energy loss penalisation, it is found that the strategy characterized with quick release of the off-going clutches can provide an optimal compromise between shift comfort performance and energy loss reduction. The main features of optimised double-transition power-on downshift dynamics are analysed by using the reduced-order bond graph model. Chapter 6: Parameter optimisation of control profiles for single-transition shifts. This chapter proposes a method for multi-objective parameter optimisation and assessment of piecewiselinear time profiles of AT control trajectories, which are easy to interpret, implement and calibrate. The optimisation is aimed to find parameters defining the piecewise linear shift control profiles, which provide a good trade-off between the shift comfort and performance. The optimisation problem is solved by using the multi-objective genetic algorithm MOGA-II. As an extension of the parameter optimisation approach, a method for robust parameter optimisation is proposed, which aims at ensuring high shift quality and robustness in the presence of transmission actuation parameter variations. The objective is to find shift control profile parameters that simultaneously minimize mean values of vehicle jerk and shift duration indices as well as their standard deviations for improved robustness against change of transmission parameters. The overall optimisation approach is demonstrated on an example of a single-transition power-on upshift, and the obtained optimisation results are analysed and compared with control trajectory optimisation results. Chapter 7: Parameter optimisation of control profiles for double-transition shifts. The method for multi-objective parameter optimisation of piecewise linear control profiles is applied in this chapter to the case of more demanding double-transition power-on downshift. First, different definitions of piecewise linear control profiles (i.e. control strategies) are proposed for performing such downshifts. Next, control profile parameter optimisations are run for different shift scenarios, i.e. for various double-transition downshifts and different shift control strategies. Finally, the control strategies are assessed based on several performance indices extracted from parameter optimisation results. The assessment results, including qualitative and quantitative comparisons with the control trajectory optimisation results, show that the control strategy for which the off-going clutches are quickly released gives the best overall performance. Chapter 8: Scalable optimal shift control law. In this chapter, a systematic approach for proper scaling of shift control profiles obtained in chapters 6 and 7 is proposed, which aims at providing good shift quality in a wide range of shift conditions (e.g. for different transmission input torque and speed values at which the shift is initiated). In addition to such an adjustment of open-loop control profiles to driver commands, the shift control system is extended with closed-loop control actions for ensuring high shift quality and robustness in the presence of realistic powertrain uncertainties. The overall shift control system is thoroughly examined through computer simulations. Chapter 9: Conclusion. Outlines the main findings and the following major contributions of the doctoral thesis: (i) a method for automated modelling of an advanced automatic transmission with a large number of gears and an automated model order reduction method for an arbitrary, user-specified clutch state; (ii) optimisation of double-transition shift control trajectories related to clutch torque capacities and engine torque, and analysis of the obtained results with the aim of defining optimal gear shift characteristics; and (iii) profiling piecewise linear control trajectories for double-transition shifts, formulation of scalable control law in coordination with driver commands, and optimisation of piecewise-linear profiles including achieving robustness with respect to variation of transmission actuation parameters.