Upper and lower sparse abstractions of monotone control systems form a complete pair: the upper one admits controller refinement and the lower one certifies controller absence, in both model-based and data-driven settings.
Efficient finite abstraction of mixed monotone systems,
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Complete Abstractions of Monotone Control Systems: From Model-based to Data-Driven Systems
Upper and lower sparse abstractions of monotone control systems form a complete pair: the upper one admits controller refinement and the lower one certifies controller absence, in both model-based and data-driven settings.