Distributed Robust Set-Invariance of Interconnected Linear Systems
We introduce a class of distributed control policies for networks of discrete-time linear systems with polytopic additive disturbances. The objective is to restrict the network-level state and controls to user-specified polyhedral sets for all times. This problem arises in many safety-critical applications. We consider two problems. First, given a communication graph characterizing the structure of the information flow in the network, we find the optimal distributed control policy by solving a single linear program. Second, we find the sparsest communication graph required for the existence of a distributed invariance-inducing control policy. Illustrative examples, including one on platooning, are presented.
Sadra Sadraddini, Calin Belta, "Distributed Robust Set-Invariance of Interconnected Linear Systems" American Control Conference (ACC), 2018, Milwaukee, WI, (submitted)
Files:
- ana_invariance.py: classes and functions
- Example 1: Coupled Double Integrators
- Example 2: Platooning
- Problem 1: Optimal Policy Design
- Problem 2: Optimal Graph Design
- .m files: plotting
- .txt files: where the trajectories and outputs are saved