| Summary: | <p>Convex optimisation is concerned with reformulating nonlinear optimisation problems into convex programs which are computationally tractable and whose solution is globally optimal. When leveraged in single-shot optimisation or multi-stage optimisation problems such as model predictive control, convex programs can accelerate computation tremendously, paving the way to online implementations of algorithms that were long thought to be intractable. This is particularly attractive in the context of safety-critical aerospace applications where a reliable solution is often required in real time.</p>
<p>This thesis investigates the use of convex optimisation and model predictive control in emerging applications from green aviation and urban air mobility. This work is motivated by the need to decarbonise the air transport industry in order to meet the requirements of net zero transport.</p>
<p>At first we consider the problem of energy management for a hybrid-electric aircraft. Through a convex formulation of mathematical models of the propulsion system, a computationally tractable optimisation problem is constructed whose globally optimal solution is used to arbitrate in real time the power demand of the aircraft between the gas turbine and electric motor, allowing significant fuel savings. Computation times are also reduced by an order of magnitude thanks to a custom implementation of a first order solver, enabling fast real-time implementations for new generations of electric and hybrid aircraft.</p>
<p>We then explore the use of difference of convex functions (DC) decomposition to compute optimal trajectories for the transition of a tiltwing vertical take-off and landing (VTOL) aircraft in the presence of uncertainty. A DC decomposition of the dynamics is computed and convexity is exploited to bound uncertain system trajectories tightly, allowing to define a robust optimisation for air transport of people in urban areas.</p>
<p>Finally, building on the theory of DC functions decomposition, a systematic data-driven approach to obtain computationally tractable robust model predictive control (MPC) algorithms for nonlinear systems has been developed and applied to VTOL aircraft in urban air mobility scenarios. The resulting control scheme offers robustness guarantees to model uncertainty and exogenous disturbances, laying the foundation for future widespread adoption in safety-critical applications related to decarbonisation of the transport sector, green aviation and urban air mobility.</p>
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