Acta mathematica scientia,Series A ›› 2014, Vol. 34 ›› Issue (6): 1440-1449.

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Double Iterative Algorithm for Different Constrained Solution of Discrete Coupled Algebraic Riccati Equation

 SONG Wei-Hong, ZHANG Kai-Yuan, NIE Yu-Feng   

  1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi'an 710072
  • Received:2013-04-25 Revised:2014-03-20 Online:2014-12-25 Published:2014-12-25
  • Supported by:

    国家自然科学基金(11071196)资助

Abstract:

By using Neumann series of inverse matrix,discrete coupled algebraic Riccati equation with unknown matrix inverse in discrete-time jump linear quadratic control problems can be transformed into the high degree polynomial matrix equations.Then Newton's method is applied to find different constrained solution of polynomial matrix equations, and the modified conjugate gradient method is used to solve different constrained solution or different constrained least square solution of linear matrix equations derived from each iterative step of Newton's method.In this way, a double iterative method is established to solve for different constrained solution of discrete coupled algebraic Riccati equation.Different constrained solution of discrete coupled algebraic Riccati equation is only required by double iterative algorithm.But it may not be unique.Besides there are not additional limits to its coefficient matrix of discrete coupled algebraic Riccati equation.The effectiveness of the double iterative method is demonstrated by numerical examples.

Key words: Discrete coupled algebraic Riccati equation, Different constrained solution, Newton´s method, Modified conjugate gradient method, Double iterative method

CLC Number: 

  • 49M15
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