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Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint

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  • Guiling Li
  • Weihai Zhang

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.

Suggested Citation

  • Guiling Li & Weihai Zhang, 2013. "Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-9, December.
    • Handle: RePEc:hin:jnljam:805829
    DOI: 10.1155/2013/805829
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