Dissertation > Excellent graduate degree dissertation topics show

Stochastic Linear-Quadratic Control Problem with Dual Interior Point Algorithms

Author: MaHuan
Tutor: ChengMingSong
School: Dalian University of Technology
Course: Computational Mathematics
Keywords: Interior Point Algorithm Dual Logarithmic Barrier Methods Stochastic Algebraic Riccati Equation Semidefinite Programming Linear Equations
CLC: O232
Type: Master's thesis
Year: 2010
Downloads: 30
Quote: 0
Read: Download Dissertation

Abstract


The stochastic linear-quadratic (LQ) control problem is considered in this paper.Under the condition that the stochastic LQ control problem is mean-square stabilizable, it gives rise to a stochastic algebraic Riccati equation (SARE) which can be transformed into a semidefinite programming (SDP). In this paper, by exploiting the inherent structure of the SDP problem, an effective solving method is proposed for it.Firstly, the background and development of the stochastic LQ control problem are introduced. Then the semidefinite programming problem is described and dual logarithmic barrier methods for solving it are introduced.Then, the dual interior point algorithm for stochastic linear-quadratic control problem is stated in detail. Firstly, the SDP is transformed into the standard form, and it is proved that this problem can be solved by the interior point algorithm. However, large-scale and dense linear equations need to be solved during each step of iteration. For small sized problem, it can be solved directly. However, for the much larger dimension, it is difficult to solve it efficiently, because it requires much more storage for the data and computation. Here, the symmetric positive definiteness of the coefficient matrix is proved, so it can be solved by the conjugate gradient methods. By taking advantage of particular sparsity of matrices in the SDP, an effective method without using too much storage is given.Finally, some numerical examples which are mean-square stabilizable are constructed and the feasibility of the proposed methods is proved by doing the numerical tests.

Related Dissertations

  1. Contributions to Transmissibility of Diagonally Dominant Matrices and Estimates for Bounds for Spectral Radius of Block Iterative Matrices of Iterative Method,O241.6
  2. The Research of Practical Method Used for Power System Dynamic Reactive Power Optimization,TM761.1
  3. Primary autologous epidermal cell transplantation for the treatment of burns experimental study,R644
  4. Based on the evolution of the FPGA hardware solving linear equations of high -dimensional,O241.6
  5. Infinite self-similar structure equivalent elastic modulus prediction,TB301
  6. Two semidefinite programming numerical solution,O221
  7. Computing Two Classes of Quadratic Constraint Quadratic Optimization Problems by SDP Relaxation,O224
  8. On the Interior Point Algorithm for Optimization Problem with Free Variables,O224
  9. The Study on Several Algorithms for Semidefinite Programming,O221.2
  10. The Study on Search Directions of Interior-point Methods for Semidefinite Programming,O221.2
  11. Two Kinds of Prediction Approaches for the Fuzzy Random Times Series,O159
  12. Large cycle block tridiagonal linear equations parallel algorithms,O241.6
  13. Researches on the Combined Homotopy Interior Point Method,O241
  14. Distribution grid intelligent reactive compensation technology research and application,TM714.3
  15. New Algorithm for Transportation Problem,O221.1
  16. Study of the Primal-Dual Interior-Point Algorithm for Optimization Problem and Application in the Area of Venture Investment,TP301.6
  17. Research of Reactive Power Pricing in Power System Based on Optimal Power Flow,F407.61
  18. Modern Interior Point Optimization Theory for Resarch of Optimal Power Flow Problems in Power System,TM711
  19. Quantum State Discrimination and Quantum State Transformation Based on Semidefinite Programming,O413.1
  20. Traveling salesman problem and Ant Colony Algorithm for Nonlinear Equations,TP301.6

CLC: > Mathematical sciences and chemical > Mathematics > Control theory, information theory ( mathematical theory ) > Optimal control
© 2012 www.DissertationTopic.Net  Mobile