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Robust-Adaptive Control of Linear Systems: beyond Quadratic Costs

Edouard Leurent 1, 2, 3 Denis Efimov 2 Odalric-Ambrym Maillard 1, 4
1 SEQUEL - Sequential Learning
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
2 VALSE - Finite-time control and estimation for distributed systems
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
4 Scool - Scool
Inria Lille - Nord Europe, CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille (CRIStAL) - UMR 9189
Abstract : 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 different communities. However, the existing theory deals only with the case of quadratic costs (the LQ problem), which limits applications to stabilisation and tracking tasks only. In order to handle more general (non-convex) costs that naturally arise in many practical problems, we carefully select and bring together several tools from different communities, namely non-asymptotic linear regression, 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 combines with a data-driven robust model selection strategy, which enables to relax the modelling assumptions. Last, we strive to preserve tractability at any stage of the method, that we illustrate on two challenging simulated environments.
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https://hal.inria.fr/hal-03004060
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Submitted on : Friday, November 13, 2020 - 2:53:42 PM
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  • HAL Id : hal-03004060, version 1
  • ARXIV : 2002.10816

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Edouard Leurent, Denis Efimov, Odalric-Ambrym Maillard. Robust-Adaptive Control of Linear Systems: beyond Quadratic Costs. NeurIPS 2020 - 34th Conference on Neural Information Processing Systems, Dec 2020, Vancouver / Virtual, Canada. ⟨hal-03004060⟩

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