Robust Control for Signal Temporal Logic Specifications using Average   Space Robustness
  Control systems that satisfy temporal logic specifications have become increasingly popular due to their applicability to robotic systems. Existing control methods, however, are computationally demanding, especially when the problem size becomes too large. In this paper, a robust and computationally efficient model predictive control framework for signal temporal logic specifications is proposed. We introduce discrete average space robustness, a novel quantitative semantic for signal temporal logic, that is directly incorporated into the cost function of the model predictive controller. The optimization problem entailed in this framework can be written as a convex quadratic program when no disjunctions are considered and results in a robust satisfaction of the specification. Furthermore, we define the predicate robustness degree as a new robustness notion. Simulations of a multi-agent system subject to complex specifications demonstrate the efficacy of the proposed method. 
Lars Lindemann and Dimos V. Dimarogonas
cs.SY