Data-Driven Controlled Invariant Sets for Gaussian Process State Space Models

We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We investigate the relationship between robust and probabilistic invariance, leveraging this rel...

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Bibliographic Details
Main Authors Griffioen, Paul, Zhong, Bingzhuo, Arcak, Murat, Zamani, Majid, Caccamo, Marco
Format Journal Article
LanguageEnglish
Published 15.07.2024
Subjects
Computer Science - Systems and Control
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DOI10.48550/arxiv.2407.11256

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Summary:We compute probabilistic controlled invariant sets for nonlinear systems using Gaussian process state space models, which are data-driven models that account for unmodeled and unknown nonlinear dynamics. We investigate the relationship between robust and probabilistic invariance, leveraging this relationship to design state-feedback controllers that maximize the probability of the system staying within the probabilistic controlled invariant set. We propose a semi-definite-programming-based optimization scheme for designing the state-feedback controllers subject to input constraints. The effectiveness of our results are demonstrated and validated on a quadrotor, both in simulation and on a physical platform.
DOI:10.48550/arxiv.2407.11256