Title: Formal Synthesis of Control Strategies for Positive Monotone Systems,
Abstract: We design controllers from formal specifications for positive discrete-time
monotone systems that are subject to bounded disturbances. Such systems are
widely used to model the dynamics of transportation and biological networks.
The specifications are described using signal temporal logic (STL), which can
express a broad range of temporal properties. We formulate the problem as a
mixed-integer linear program (MILP) and show that under the assumptions made in
this paper, which are not restrictive for traffic applications, the existence
of open-loop control policies is sufficient and almost necessary to ensure the
satisfaction of STL formulas. We establish a relation between satisfaction of
STL formulas in infinite time and set-invariance theories and provide an
efficient method to compute robust control invariant sets in high dimensions.
We also develop a robust model predictive framework to plan controls optimally
while ensuring the satisfaction of the specification. Illustrative examples and
a traffic management case study are included.