Minimax Adaptive Control for a Finite Set of Linear Systems

Fuente: arXiv
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Main Author: Rantzer, Anders
Format: Preprint
Published: 2020
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author Rantzer, Anders
author_facet Rantzer, Anders
contents An adaptive controller with bounded l2-gain from disturbances to errors is derived for linear time-invariant systems with uncertain parameters restricted to a finite set. The gain bound refers to the closed loop system, including the non-linear learning procedure. As a result, robustness to unmodelled dynamics (possibly nonlinear and infinite-dimensional) follows from the small gain theorem. The approach is based on a new zero-sum dynamic game formulation, which optimizes the trade-off between exploration and exploitation. An explicit upper bound on the optimal value function is stated in terms of semi-definite programming and a corresponding simple formula for an adaptive controller achieving the upper bound is given. Once the uncertain parameters have been sufficiently estimated, the controller behaves like standard H-infinity optimal control.
format Preprint
id arxiv_https___arxiv_org_abs_2011_10814
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle Minimax Adaptive Control for a Finite Set of Linear Systems
Rantzer, Anders
Optimization and Control
An adaptive controller with bounded l2-gain from disturbances to errors is derived for linear time-invariant systems with uncertain parameters restricted to a finite set. The gain bound refers to the closed loop system, including the non-linear learning procedure. As a result, robustness to unmodelled dynamics (possibly nonlinear and infinite-dimensional) follows from the small gain theorem. The approach is based on a new zero-sum dynamic game formulation, which optimizes the trade-off between exploration and exploitation. An explicit upper bound on the optimal value function is stated in terms of semi-definite programming and a corresponding simple formula for an adaptive controller achieving the upper bound is given. Once the uncertain parameters have been sufficiently estimated, the controller behaves like standard H-infinity optimal control.
title Minimax Adaptive Control for a Finite Set of Linear Systems
topic Optimization and Control
url https://arxiv.org/abs/2011.10814