Continuous-time probabilistic ultimate bounds and invariant sets: Computation and assignment. (September 2016)

• Record Type: Journal Article
• Authors: Kofman, Ernesto; De Doná, José A.; Seron, Maria M.; Pizzi, Noelia
• Is Part Of: Automatica. Volume 71(2016)
• Page Start: 98
• Page End: 105
• Publication Date: 2016-09
• Subjects: Invariant sets -- Ultimate bounds -- Stochastic differential equations -- Linear systems -- Probabilistic methods; Automatic control -- Periodicals; Automation -- Periodicals; 629.805
• DOI: 10.1016/j.automatica.2016.04.041
• Languages: English
• ISSNs: 0005-1098

Abstract

Abstract: The concepts of ultimate bounds and invariant sets play a key role in several control theory problems, as they replace the notion of asymptotic stability in the presence of unknown disturbances. However, when the disturbances are unbounded, as in the case of Gaussian white noise, no ultimate bounds nor invariant sets can in general be found. To overcome this limitation we introduced, in previous work, the notions of probabilistic ultimate bound (PUB) and probabilistic invariant set (PIS) for discrete-time systems. This article extends the notions of PUB and PIS to continuous-time systems, studying their main properties and providing tools for their calculation. In addition, the use of these concepts in robust control design by covariance assignment is presented.