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Keywords:
reachability analysis; chance constraint; first-step constraint; predictive control; recursive feasibility
reachability analysis; chance constraint; first-step constraint; predictive control; recursive feasibility
Summary:
This study presents a novel data-driven predictive control approach for unknown nonlinear systems under bounded process and measurement noises. A chance-constrained reachability analysis control framework is proposed to provide probabilistic safety and robustness guarantees by characterizing the likely evolution of system behavior under risk-aware control. A zonotopic deep Koopman reachability analysis is used to design a data-driven controller without acquiring prior knowledge of the statistical properties of the noise. Unlike previous set-based approaches that enforce hard constraints under worst-case scenarios, the proposed method balances robustness and performance more effectively, reducing conservatism while still ensuring safety with bounded risk. It also guarantees recursive feasibility using a first-step constraint technique. A simulation study is conducted on a stirred-tank reactor system and a cart-damper-spring system to demonstrate the effectiveness of the proposed approach, with numerical results supporting the theoretical claims and highlighting its practical applicability.
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