On the λ-equations for matching control laws

David Auckly, Lev Kapitanski

Research output: Contribution to journalArticle

55 Citations (Scopus)

Abstract

We discuss matching control laws for underactuated systems. We previously showed that this class of matching control laws is completely characterized by a linear system of first order partial differential equations for one set of variables (λ) followed by a linear system of first order partial differential equations for the second set of variables (ĝ, V̂). Here we derive a new first order system of partial differential equations that encodes all compatibility conditions for the λ-equations. We give four examples illustrating different features of matching control laws, The last example is a system with two unactuated degrees of freedom that admits only basic solutions to the matching equations. There are systems with many matching control laws where only basic solutions are potentially useful. We introduce a rank condition indicating when this is likely to be the case.

Original languageEnglish (US)
Pages (from-to)1372-1388
Number of pages17
JournalSIAM Journal on Control and Optimization
Volume41
Issue number5
DOIs
StatePublished - 2003
Externally publishedYes

Fingerprint

Partial differential equations
First order differential equation
Linear systems
Partial differential equation
Linear Systems
Underactuated System
Compatibility Conditions
First-order System
Systems of Partial Differential Equations
Degree of freedom
Likely
Class

Keywords

  • λ-equations
  • Matching control laws
  • Nonlinear control
  • Stabilization

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics
  • Control and Optimization

Cite this

On the λ-equations for matching control laws. / Auckly, David; Kapitanski, Lev.

In: SIAM Journal on Control and Optimization, Vol. 41, No. 5, 2003, p. 1372-1388.

Research output: Contribution to journalArticle

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