2017/06/22 by Andrii Mironchenko, Mironchenko, Andrii, Iasson Karafyllis +3
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Dynamical Systems (math.DS) #FOS: Mathematics #Numerical methods for differential equations #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1706.07224
openalex publication_date 2017/06/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/08/01
We introduce a monotonicity-based method for studying input-to-state\nstability (ISS) of nonlinear parabolic equations with boundary inputs. We first\nshow that a monotone control system is ISS if and only if it is ISS w.r.t.\nconstant inputs. Then we show by means of classical maximum principles that\nnonlinear parabolic equations with boundary disturbances are monotone control\nsystems.\n With these two facts, we establish that ISS of the original nonlinear\nparabolic PDE with constant \boundary disturbances is equivalent to ISS\nof a closely related nonlinear parabolic PDE with constant \distributed\ndisturbances and zero boundary condition. The last problem is conceptually\nmuch simpler and can be handled by means of various recently developed\ntechniques. As an application of our results, we show that the PDE backstepping\ncontroller which stabilizes linear reaction-diffusion equations from the\nboundary is robust with respect to additive actuator disturbances.\n