Probabilistic Control of Uncertain Linear Systems Using Stochastic Reachability. Issue 14 (2015)

• Record Type: Journal Article
• Authors: Asselborn, Leonhard; Stursberg, Olaf
• Is Part Of: IFAC-PapersOnLine. Volume 48:Issue 14(2015)
• Page Start: 167
• Page End: 173
• Publication Date: 2015
• Subjects: Ellipsoidal calculus -- discrete time systems -- uncertain dynamics -- stochastic reachability -- linear matrix inequalities -- semi-definite programming -- stochastic stability; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2015.09.452
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: This paper proposes an approach to algorithmically synthesize control strategies for set-to-set transitions of discrete-time uncertain systems based on reachable set computations in a stochastic setting. For given Gaussian distributions of the initial states and disturbances, state sets wich are reachable to a chosen confidence level under the effect of time-variant control laws are computed by using principles of the ellipsoidal calculus. The proposed algorithm iterates over LMI-constrained semi-definite programming problems to compute probabilistically stabilizing controllers, while ellipsoidal input constraints are considered. An example for illustration is included.