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We consider the problem of robust and adaptive model predictive control (MPC)of a linear system, with unknown parameters that are learned along the way(adaptive), in a critical setting where failures must be prevented (robust).This problem has been studied from different perspectives by differentcommunities. However, the existing theory deals only with the case of quadraticcosts (the LQ problem), which limits applications to stabilisation and trackingtasks only. In order to handle more general (non-convex) costs that naturallyarise in many practical problems, we carefully select and bring togetherseveral tools from different communities, namely non-asymptotic linearregression, recent results in interval prediction, and tree-based planning.Combining and adapting the theoretical guarantees at each layer is non trivial,and we provide the first end-to-end suboptimality analysis for this setting.Interestingly, our analysis naturally adapts to handle many models and combineswith a data-driven robust model selection strategy, which enables to relax themodelling assumptions. Last, we strive to preserve tractability at any stage ofthe method, that we illustrate on two challenging simulated environments.

Robust-Adaptive Control of Linear Systems: beyond Quadratic Costs