Formal Synthesis of Control Strategies for Positive Monotone Systems
For control engineers working with transportation and biological networks, this work offers a formal method to synthesize controllers from temporal logic specifications, though it is incremental as it combines existing techniques (MILP, STL, invariant sets) for a specific system class.
This paper develops a formal synthesis framework for designing controllers for positive monotone systems subject to bounded disturbances, using signal temporal logic (STL) specifications. The approach formulates the problem as a mixed-integer linear program (MILP) and provides an efficient method for computing robust control invariant sets, demonstrated on a traffic management case study.
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.