Adaptive Stochastic MPC under Unknown Noise Distribution
- URL: http://arxiv.org/abs/2204.01107v1
- Date: Sun, 3 Apr 2022 16:35:18 GMT
- Title: Adaptive Stochastic MPC under Unknown Noise Distribution
- Authors: Charis Stamouli, Anastasios Tsiamis, Manfred Morari, George J. Pappas
- Abstract summary: We address the MPC problem for linear systems, subject to chance state constraints and hard input constraints, under unknown noise distribution.
We design a distributionally robust and robustly stable benchmark SMPC algorithm for the ideal setting of known noise statistics.
We employ this benchmark controller to derive a novel adaptive SMPC scheme that learns the necessary noise statistics online.
- Score: 19.03553854357296
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In this paper, we address the stochastic MPC (SMPC) problem for linear
systems, subject to chance state constraints and hard input constraints, under
unknown noise distribution. First, we reformulate the chance state constraints
as deterministic constraints depending only on explicit noise statistics. Based
on these reformulated constraints, we design a distributionally robust and
robustly stable benchmark SMPC algorithm for the ideal setting of known noise
statistics. Then, we employ this benchmark controller to derive a novel
robustly stable adaptive SMPC scheme that learns the necessary noise statistics
online, while guaranteeing time-uniform satisfaction of the unknown
reformulated state constraints with high probability. The latter is achieved
through the use of confidence intervals which rely on the empirical noise
statistics and are valid uniformly over time. Moreover, control performance is
improved over time as more noise samples are gathered and better estimates of
the noise statistics are obtained, given the online adaptation of the estimated
reformulated constraints. Additionally, in tracking problems with multiple
successive targets our approach leads to an online-enlarged domain of
attraction compared to robust tube-based MPC. A numerical simulation of a DC-DC
converter is used to demonstrate the effectiveness of the developed
methodology.
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