Control Design for Risk-Based Signal Temporal Logic Specifications

Sleiman Safaoui*, Lars Lindemann, Dimos V. Dimarogonas, Iman Shames, Tyler H. Summers

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

11 Citations (Scopus)


We present a general framework for risk semantics on Signal Temporal Logic (STL) specifications for stochastic dynamical systems using axiomatic risk theory. We show that under our recursive risk semantics, risk constraints on STL formulas can be expressed in terms of risk constraints on atomic predicates. We then show how this allows a (stochastic) STL risk constraint to be transformed into a risk-tightened deterministic STL constraint on a related deterministic nominal system, enabling the application of existing STL methods. For affine predicate functions and a (coherent) Distributionally Robust Value at Risk measure, we show how risk constraints on atomic predicates can be reformulated as tightened deterministic affine constraints. We demonstrate the framework using a Model Predictive Control (MPC) design with an STL risk constraint.

Original languageEnglish
Article number9103559
Pages (from-to)1000-1005
Number of pages6
JournalIEEE Control Systems Letters
Issue number4
Publication statusPublished - Oct 2020
Externally publishedYes


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