Mixed Integer Linear Programming Approach for Control Synthesis with Weighted Signal Temporal Logic

What is it about?

This work introduces an optimization-based control synthesis approach for weighted Signal Temporal Logic (wSTL), an extension of Signal Temporal Logic (STL). wSTL allows users to express preferences, priorities, and satisfaction times using weights assigned to logical and temporal operators. We propose a Mixed Integer Linear Programming (MILP) approach for synthesizing systems based on wSTL specifications.

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Photo by Estée Janssens on Unsplash

Photo by Estée Janssens on Unsplash

Why is it important?

We extend the formal definition of wSTL to include until and release temporal operators and provide an efficient encoding for these operators in the MILP formulation. Unlike previous implementations, which used arithmetic-geometric mean robustness with gradient-based methods, the proposed encoding enables the use of a weighted version of traditional robustness and efficient global MILP solvers. The authors demonstrate the effectiveness of their approach through multiple case studies, highlighting the capabilities of wSTL's Boolean and temporal operators.

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