Control Of Dynamical Processes And Geometrical Structures

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

Modern control theory basically deals with dynamical systems on smooth manifolds. However, many practical systems such as multiple agents do not have such structures. The axiomatic control theories should adequately reflect in terms of their internal language of notions and control problems. In terms of these theories, the control structures can make up various hierarchies. According to Kalman, for example, the most general structure is represented by a controllability–reachability structure over which the optimal control structure is built. This approach regarding the structure of optimal control and Yang–Mills fields was discussed in Yatsenko (1985) and Butkovskiy and Samoilenko (1990).

In this chapter, the geometrical description problem of multiple agents is studied. We discuss mathematical aspects of the “unified game theory (UGT)” and “theory of control structure (TCS)”. We consider a game as a hierarchical structure. It is assumed that each agent can be described by a fiber...


Vector Field Fiber Bundle Multiagent System Affine System Mill Field 
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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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