Multimodel Differential Games

  • Vladimir G. Boltyanski
  • Alexander S. Poznyak
Part of the Systems & Control: Foundations & Applications book series (SCFA)


In this chapter we focus on the construction of robust Nash strategies for a class of multimodel games described by a system of ordinary differential equations with parameters from a given finite set. Such strategies entail the “Robust equilibrium” being applied to all scenarios (or models) of the game simultaneously. The multimodel concept allows one to improve the robustness of the designed strategies in the presence of some parametric uncertainty. The game solution corresponds to a Nash-equilibrium point of this game. In LQ dynamic games the equilibrium strategies obtained are shown to be linear functions of the so-called weighting parameters from a given finite-dimensional vector simplex. This technique permits us to transform the initial game problem, formulated in a Banach space (the control functions are to be found) to a static game given in finite-dimensional space (simplex). The corresponding numerical procedure is discussed. The weights obtained appear in an extended coupled Riccati differential equation. The effectiveness of the designed controllers is illustrated by a two-dimensional missile guidance problem.


Differential Game Lateral Acceleration Algebraic Riccati Equation Isaacs Equation Evasion Game 
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Copyright information

© Springer Science+Business Media, LLC 2012

Authors and Affiliations

  • Vladimir G. Boltyanski
    • 1
  • Alexander S. Poznyak
    • 2
  1. 1.CIMATGuanajuatoMexico
  2. 2.Automatic Control DepartmentCINVESTAV-IPNMéxicoMexico

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