This thesis presents an efficient and extensible numerical software framework for real-time model-based control. We are motivated by complex and challenging mechatronic applications spanning from flight control of fixed-wing aircraft and thrust vector control drones to autonomous driving. In the first part, we present PolyMPC, a novel C++ software framework for real-time embedded nonlinear optimal control and optimisation. A key feature of the package is a highly optimised implementation of the pseudospectral collocation method that exploits instruction set parallelism available on many modern computer architectures. Polynomial representation of the state and control trajectories allows the tool to be used as a standalone controller and as an efficient solver for low-level tracking controllers in hierarchical schemes. Algorithmically, the choice is made towards computational speed. For nonlinear problems, we combine a sequential quadratic programming (SQP) strategy with the alternating direction method of multipliers (ADMM) for quadratic programs (QP), which is especially favourable for embedded applications thanks to the low computational cost per iteration. In the second part, the developed numerical methods and software are used to experimentally study optimisation-based control of airborne wind energy (AWE) systems. For this purpose, we designed and built a small-scale prototype of a single-line rigid-wing AWE kite which comprises an aircraft fitted with necessary sensors and computers and a fully autonomous ground station for tether control. The prototype serves as a research platform for studying flight navigation and control systems thanks to very flexible custom mission management and control software. We further develop a dynamic optimisation based methodology for parameter identification and provide a validated flight simulator that matches well the real behaviour of the system. Finally, a model-predictive path following flight controller is designed and tested in real-world experiments. The third part of the thesis is concerned with the application of real-time nonlinear model predictive control (NMPC) to autonomous driving at the limits of handling, which requires high sampling rates and robustness of the motion control system. We propose a dynamic optimization-based hierarchical framework for the local refinement of the racing lines that takes into account the nonlinear vehicle and actuator dynamics, adaptive tyre constraints, and the safety corridor around the initial path. The top layer receives a discrete obstacle-free local path computed by a coarse planner and transforms it into auto-differentiable look-up tables (LUT) for efficient continuous sampling. Separately, we investigated the problem of safe trajectory planning under parametric model uncertainties motivated by automotive applications. We use generalised polynomial chaos expansions for efficient nonlinear uncertainty propagation and distributionally robust inequalities for chance constraint approximation. Inspired by tube-based model predictive control, an ancillary feedback controller is used to control the deviations of stochastic modes from the nominal solution, and therefore, decrease the variance. Our approach reduces conservatism related to nonlinear uncertainty propagation while guaranteeing constraint satisfaction with a high probability.