Risk-Averse Control for Continuous-Time Stochastic System Under Signal Temporal Logic Constraints

Signal Temporal Logic (STL) has become a powerful formalism for specifying complex temporal-spatial behaviors in autonomous systems. Handling STL constraints within stochastic setting has received increasing research interest but still poses challenges. This paper proposes a general framework to efficiently solve continuous-time nonlinear stochastic optimal control problems under chance STL constraints. The STL formulae are implemented through extended dynamics, yielding a more classical chance constraint on the terminal state uniquely that we reliably relax via Conditional Value-at-Risk. The resulting new optimal control problem is then solved using established algorithms from risk-averse control. The efficiency and feasibility of the proposed approach are demonstrated through numerical simulations.