Input–to–state stability of dissipative PI control for a class of semilinear heat equations. Issue 19 (2021)

• Record Type: Journal Article
• Authors: Schaum, A.; Feketa, P.; Meurer, T.
• Is Part Of: IFAC-PapersOnLine. Volume 54:Issue 19(2021)
• Page Start: 281
• Page End: 286
• Publication Date: 2021
• Subjects: Semilinear heat equations -- PI control -- dissipativity -- disturbances -- input–to–state stability; Automatic control -- Periodicals; 629.805
• DOI: 10.1016/j.ifacol.2021.11.091
• Languages: English
• ISSNs: 2405-8963

Abstract

Abstract: The input–to–state stability (ISS) of dissipative PI control for a class of semilinear heat equations is addressed. Based on recent results on sufficient conditions for closed–loop exponential stability of dissipative PI control for the considered system class with actuator offsets (Schaum et al., 2020) the behavior in presence of unmatched distributed disturbances and measurement uncertainties is explicitly delimited. For this purpose the obtained dissipativity inequalities are connected with Lyapunov characterizations of ISS. An optimization procedure for the choice of sensor and actuator locations as well as the control gains is proposed. The results are illustrated using numerical simulations.