Abstract nonlinear control systems

Shantanu Singh, George Weiss, Marius Tucsnak

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


We investigate abstract nonlinear infinite dimensional systems of the form: dot x(t) in Ax(t)-{mathcal{M}}(x(t)) + Bu(t). These are obtained by subtracting a nonlinear maximal monotone (possibly multi-valued) operator {mathcal{M}} from the semigroup generator A of a linear system. While the linear system may have un-bounded linear damping (for instance, boundary damping), the operator {mathcal{M}} is "bounded"in the sense that it is defined on the whole state space. We show that under some assumptions, such nonlinear infinite dimensional systems have unique classical and generalized solutions. Moreover, these solutions are Lipschitz continuous on any finite time interval and right differentiable. Our approach uses the theory of maximal monotone operators and the Crandall-Pazy theorem about nonlinear contraction semigroups, which we apply to a Lax-Phillips type nonlinear semigroup that represents the entire system, with states and input signals. We illustrate the theory with Maxwell's equations in a bounded domain with a nonlinear conductor.

Original languageEnglish
Title of host publication60th IEEE Conference on Decision and Control, CDC 2021
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages7
ISBN (Electronic)9781665436595
StatePublished - 2021
Event60th IEEE Conference on Decision and Control, CDC 2021 - Austin, United States
Duration: 13 Dec 202117 Dec 2021

Publication series

NameProceedings of the IEEE Conference on Decision and Control


Conference60th IEEE Conference on Decision and Control, CDC 2021
Country/TerritoryUnited States

All Science Journal Classification (ASJC) codes

  • Control and Systems Engineering
  • Modelling and Simulation
  • Control and Optimization


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