Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
권호 표지

INDEFINITE STOCHASTIC LQ CONTROL WITH CROSS TERM VIA SEMIDEFINITE PROGRAMMING

  • Luo, Chengxin (Department of Apllied Mathematics, Dalian University of Technology, Department of Mathematics, Shenyang Normal University) ;
  • Feng, Enmin (Department of Apllied Mathematics, Dalian University of Technology)
  • 발행 : 2003.09.01

⟨ 이전 논문 다음 논문 ⟩

초록

An indefinite stochastic linear-quadratic(LQ) optimal control problem with cross term over an infinite time horizon is studied, allowing the weighting matrices to be indefinite. A systematic approach to the problem based on semidefinite programming (SDP) and .elated duality analysis is developed. Several implication relations among the SDP complementary duality, the existence of the solution to the generalized Riccati equation and the optimality of LQ problem are discussed. Based on these relations, a numerical procedure that provides a thorough treatment of the LQ problem via primal-dual SDP is given: it identifies a stabilizing optimal feedback control or determines the problem has no optimal solution. An example is provided to illustrate the results obtained.

키워드

참고문헌

  1. SIAM J. Contr. v.6 On a Riccati equation of stochasitic control W.M.Wonham
  2. IEEE Trans. Auto. Contr. v.AC16 Special issues on linear-quadratic-Guassian problem M.Athens
  3. Lecture Notes in Math. v.972 Lecture on stochastic control, part Ⅰ Bensonssan
  4. IEEE Trans. Aut. Contr. v.45 Linear matrix inequalities, Riccati equations and indefinite stochastic LQ controls M.Ait Rami;X.Y.Zhou
  5. Stochastic controls: Hamiltonian systems and HJB equations J.Yong;X.Y.Zhou
  6. SIAM J. Control Optim. v.36 Stochastic LQR with indefinite control weight costs S.Chen;X.Li;X.Y.Zhou
  7. SIAM Rev. v.38 Semidefinite Programming L.Vandenberghe;S.Boyd
  8. SIAM J. Optim. v.5 no.1 Interior point methods in semidefinite programming with applications to combinatorial optiization Farid Aliadeh
  9. Math. Progr. v.69 A primal-dual potential reduction method for problems involving matrix inequalities L.Vandenberghe;S.Boyd
  10. SIAM J. Appl. Math. v.17 Conditions for positive and nonnegative definiteness in terms of pseudoinverses A.Albert
  11. SIAM J. Control Optim. v.40 Stochastic LQ control via semidefinite programming D.D.Yao;S.Zhang;X.Y.Zhou
  12. Optimal Control-Linear Quadratic Methods B.D.O.Anderson;J.B.Moore
  13. Report 9719/A Duality results for conic convex programming Z.Q.Luo;J.F.Sturm;S.Zhang