Work by Samira S. Farahani, Rupak Majumdar, Vinayak S. Prabhu, and Sadegh Soudjani, IEEE Transactions on Automatic Control August 2019
Keywords: Signal temporal logic, model predictive control, stochastic disturbances
Summary
The authors discuss a shrinking horizon model predictive control (SH-MPC) problem to generate control inputs for a discrete-time linear system under additive stochastic disturbance (either Gaussian or bounded support). The system specifications are through a signal temporal logic (STL) formula and encoded as a chance constraint into the SH-MPC problem. The SH-MPC problem is optimized for minimum input and maximum robustness.
The authors approximate the system robustness in the objective function using min-max and max-min canonical forms of min-max-plus-scaling (MMPS) functions. They under approximate the chance constraint by showing that any chance constraint on a formula can be transformed into chance constraints on atomic propositions, then they transform the latter into linear constraints.