The robust minimal controllability problem for switched linear continuous-time systems

• Type: Article in International Conference Proceedings Book
• Date: 2018

Authors

Ramos, G (Author) Other; Pequito, S (Author) Other; Caleiro, C (Author) Other

Conference proceedings International

Title: Proceedings of the American Control Conference

Pages: 210-215

2018 Annual American Control Conference, ACC 2018

27 June 2018 through 29 June 2018

Indexing

Scopus - 3 Citations

Other information

Authenticus ID: P-00P-HT9

DOI: 10.23919/acc.2018.8431919

Abstract (EN): In this paper, we address the robust minimal controllability problem for switched linear continuous-time systems. The problem is to determine the minimal subset of state variables to actuate such that the switching linear system is controllable, under the scenario where a set of actuators may fail along the time. Two variations of this problem are considered, depending on whether we want to design an input matrix for each mode (i.e., a different set of actuators that may fail in each mode), or if we want to design a common input matrix common across all the modes, and a set of actuators may fail. In both cases, we want to ensure that, given an initial condition, we can drive the system towards any desired state. For both problems, we characterize the sparsest input matrices which ensure that the system is controllable, whenever the autonomous dynamics' matrix of each mode is simple, and for which a left-eigenbasis is available. We reduce these problems to set multi-covering problems, showing that using a sufficient condition for controllability, the first is NP-complete. These allow us to deploy known, close-to-optimal, polynomial algorithms approximating the solutions of the problems we study. © 2018 AACC.

Language: English

Type (Professor's evaluation): Scientific