Reachability of Nonlinear Systems With Unknown Dynamics

Shafa, Taha; Ornik, Melkior

doi:10.1109/tac.2022.3170855

Cited by 4 publications

(1 citation statement)

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“…Backward reachability analysis has also been extensively studied as a useful tool to solve constrained control problems. Existing techniques include set-based methods [1], [10]- [12], discrete-abstractions [13], [14], Hamilton-Jacobi (HJ) reachability [15], [16], and more recent work for unknown dynamics [17]. However, most of the existing methods cannot be extended to general nonlinear systems, especially when the state space dimension is large [15].…”

Section: A Related Workmentioning

confidence: 99%

Koopman-Inspired Implicit Backward Reachable Sets for Unknown Nonlinear Systems

Balim,

Aspeel,

Liu

et al. 2023

IEEE Control Syst. Lett.

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Koopman liftings have been successfully used to learn high dimensional linear approximations for autonomous systems for prediction purposes, or for control systems for leveraging linear control techniques to control nonlinear dynamics. In this paper, we show how learned Koopman approximations can be used for state-feedback correct-by-construction control. To this end, we introduce the Koopman over-approximation, a (possibly hybrid) lifted representation that has a simulation-like relation with the underlying dynamics. Then, we prove how successive application of controlled predecessor operation in the lifted space leads to an implicit backward reachable set for the actual dynamics. Finally, we demonstrate the approach on two nonlinear control examples with unknown dynamics.

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