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Control of Bilinear Systems

  • Panos M. Pardalos
  • Vitaliy Yatsenko
Chapter
Part of the Springer Optimization and Its Applications book series (SOIA, volume 11)

Bilinear systems are an important subclass of nonlinear systems with numerous applications in engineering, biology, and economics (Mohler, 1973; Espana and Landau, 1978; Brockett, 1979; Baillieul, 1978, 1998). Most papers consider time-invariant continuous bilinear systems with linear feedback. In almost all references stability problems are studied using a sufficient condition for the existence of a feedback control. These studies usually do not deal with stability problems with a large class of inputs as considered here. The linear-quadratic optimal control problem is apparently one of the simplest and most thoroughly studied. It is not surprising, therefore, that the nonlinear analogues of this problem have long since attracted the attention of control scientists (Andreev, 1982; Aganovic, 1995; Bloch and Crouch, 1996; Bloch, 1998; Jurdjevic, 1998; Agrachev and Sachkov, 2004). The symplectic structure of the linear-quadratic problem was also studied in Faibusovich (1988a, 1991), and...

Keywords

Optimal Control Problem Hopf Bifurcation Adaptive Control Control Dynamic Error Indicator 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Copyright information

© Springer Science+Business Media, LLC 2008

Authors and Affiliations

  • Panos M. Pardalos
    • 1
  • Vitaliy Yatsenko
    • 2
  1. 1.Department of Industrial and SystemsUniversity of FloridaGainesvilleU.S.A.
  2. 2.Institute of Space ResearchNASUKyivUkraine

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