Journal of Applied Mathematics

  • J. Appl. Math.
  • Volume 2013, Special Issue (2013), Article ID 805829, 9 pages.

Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint

Guiling Li and Weihai Zhang

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Abstract

This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraint for the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.

Article information

Source
J. Appl. Math., Volume 2013, Special Issue (2013), Article ID 805829, 9 pages.

Dates
First available in Project Euclid: 7 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.jam/1399493683

Digital Object Identifier
doi:10.1155/2013/805829

Mathematical Reviews number (MathSciNet)
MR3147880

Zentralblatt MATH identifier
06950884

Citation

Li, Guiling; Zhang, Weihai. Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint. J. Appl. Math. 2013, Special Issue (2013), Article ID 805829, 9 pages. doi:10.1155/2013/805829. https://projecteuclid.org/euclid.jam/1399493683


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