LQ-Stochastic Multimodel Control

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


The main goal of this chapter is to illustrate the possibilities of the MP approach for a class of Min-Max Control Problems for uncertain systems described by a system of linear stochastic differential equations with a controlled drift and diffusion terms and unknown parameters within a given finite set. The problem belongs to the class of Min-Max Optimization Problems on a fixed finite horizon (where the cost function contains both an integral and a terminal term) and on an infinite one (the loss function is a time-averaged functional). The solution is based on the results on the Robust Stochastic Maximum Principle (RSMP) derived in the previous chapter. The construction of the Min-Max LQ optimal controller is shown to be reduced to a finite-dimensional optimization problem related to the solution of the Riccati equation parametrized by the weights to be found.


Riccati Equation Adjoint Equation Previous Chapter Algebraic Riccati Equation Linear Quadratic Problem 
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  1. Poznyak, A.S. (2008), Advanced Mathematical Tools for Automatic Control Engineers, Vol. 1: Deterministic Technique, Elsevier, Amsterdam. Google Scholar
  2. Willems, J.C. (1971), ‘Least squares optimal control and algebraic Riccati equations’, IEEE Trans. Autom. Control 16(3), 621–634. MathSciNetCrossRefGoogle Scholar

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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