Journal of Optimization Theory and Applications

, Volume 51, Issue 2, pp 355–362 | Cite as

A noniterative algebraic solution for Riccati equations satisfying two-point boundary-value problems

  • H. M. Chun
  • J. D. Turner
Technical Note


A noniterative algebraic method is presented for solving differential Riccati equations which satisfy two-point boundary-value problems. This class of numerical problems arises in quadratic optimization problems where the cost functionals are composed of both continuous and discrete state penalties, leading to piecewise periodic feedback gains. The necessary condition defining the solution for the two-point boundary value problem is cast in the form of a discrete-time algebraic Riccati equation, by using a formal representation for the solution of the differential Riccati equation. A numerical example is presented which demonstrates the validity of the approach.

Key Words

Optimal control piecewise periodic feedback gains two-point boundary-value problems continuous-time Riccati equation discrete-time Riccati equation continuous-time Lyapunov equation 


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Copyright information

© Plenum Publishing Corporation 1986

Authors and Affiliations

  • H. M. Chun
    • 1
  • J. D. Turner
    • 1
  1. 1.Control Theory/Dynamics GroupCambridge Research Division of Photon Research AssociatesCambridge

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