Risk-Awareness in Learning Neural Controllers for Temporal Logic Objectives
This work addresses the challenge of ensuring safety and performance in uncertain systems for applications like robotics, though it appears incremental by combining existing methods like control barrier functions and neural networks.
The paper tackles the problem of synthesizing neural network controllers for systems with uncertainty to satisfy hard safety constraints expressed in Signal Temporal Logic while optimizing performance, and demonstrates its approach on nonlinear control examples like a quad-rotor and unicycle with timing and safety objectives.
In this paper, we consider the problem of synthesizing a controller in the presence of uncertainty such that the resulting closed-loop system satisfies certain hard constraints while optimizing certain (soft) performance objectives. We assume that the hard constraints encoding safety or mission-critical task objectives are expressed using Signal Temporal Logic (STL), while performance is quantified using standard cost functions on system trajectories. In order to prioritize the satisfaction of the hard STL constraints, we utilize the framework of control barrier functions (CBFs) and algorithmically obtain CBFs for STL objectives. We assume that the controllers are modeled using neural networks (NNs) and provide an optimization algorithm to learn the optimal parameters for the NN controller that optimize the performance at a user-specified robustness margin for the safety specifications. We use the formalism of risk measures to evaluate the risk incurred by the trade-off between robustness margin of the system and its performance. We demonstrate the efficacy of our approach on well-known difficult examples for nonlinear control such as a quad-rotor and a unicycle, where the mission objectives for each system include hard timing constraints and safety objectives.