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Chun, H. M.; Turner, J. D.

A noniterative algebraic solution for Riccati equations satisfying two- point boundary-value problems. (English) Zbl 0579.93021

J. Optimization Theory Appl. 51, 355-362 (1986).
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.

MSC:

93B40 Computational methods in systems theory (MSC2010)
34B30 Special ordinary differential equations (Mathieu, Hill, Bessel, etc.)
65K10 Numerical optimization and variational techniques
15A24 Matrix equations and identities

Keywords:

noniterative algebraic method; differential Riccati equations; two-point boundary-value problems; quadratic optimization; piecewise periodic feedback gains; discrete-time algebraic Riccati equation

Software:

Algorithm 432
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Full Text: DOI

References:

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