Control of nonlinear underactuated systems

David Auckly, Lev Kapitanski, Warren White

Research output: Contribution to journalArticlepeer-review

108 Scopus citations


In this paper we introduce a new method to design control laws for nonlinear, underactuated systems. Our method produces an infinite-dimensional family of control laws, whereas most control techniques only produce a finite-dimensional family. These control laws each come with a natural Lyapunov function. The inverted pendulum cart is used as an example. In addition, we construct an abstract system that is open-loop unstable and cannot be stabilized using any linear control law and demonstrate that our method produces a stabilizing control law.

Original languageEnglish (US)
Pages (from-to)354-369
Number of pages16
JournalCommunications on Pure and Applied Mathematics
Issue number3
StatePublished - Mar 2000
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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