Interval signal temporal logic for robust optimal control
L. Baird, S. Coogan
IEEE Conference on Decision and Control, 2024
Abstract
We propose a robust optimal control strategy for linear systems subject to bounded disturbances constrained to satisfy a Signal Temporal Logic (STL) formula with uncertain predicates. We encode such constraints using Interval STL (I-STL), an extension of STL to interval signals and predicates that accommodates efficient numerical implementations for verification and synthesis using interval arithmetic methods. Given an I-STL constraint, a quadratic cost function, and a bounded hyper-rectangular disturbance set, we construct a second robust optimal control problem using an embedding system with double the state dimension and the same cost function such that a solution to this second problem is feasible for the original problem. Moreover, owing to the numerical efficiencies of I-STL and the embedding, the computational complexity of this problem is, at worst, approximately equivalent to solving a non-robust optimal STL synthesis problem with double the state dimension, and we solve this problem as a mixed-integer quadratic program. We present a case study of a miniature blimp modeled as a 12-dimensional linear system subject to disturbances and tasked with a mission specified in I-STL with multiple nested temporal operators.