A new approach on designing l 1 optimal regulator with minimum order for SISO linear systems

  • Xiang Liu
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Abstract

For a SISO linear discrete-time system with a specified input signal, a novel method to realize optimal l 1 regulation control is presented. Utilizing the technique of converting a polynomial equation to its corresponding matrix equation, a linear programming problem to get an optimal l 1 norm of the system output error map is developed which includes the first term and the last term of the map sequence in the objective function and the right vector of its constraint matrix equation, respectively. The adjustability for the width of the constraint matrix makes the trade-off between the order of the optimal regulator and the value of the minimum objective norm become possible, especially for achieving the optimal regulator with minimum order. By norm scaling rules for the constraint matrix equation, the optimal solution can be scaled directly or be obtained by solving a linear programming problem with l 1 norm objective.

Keywords

Linear discrete-time systems l1 norm Optimal control Matrix equation Linear programming 
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References

  1. [1]
    M. A. Dahleh, J. B. Pearson. Minimization of a regulated response to a fixed input[J]. IEEE Trans. on Automatic Control, 1988, 33(5): 722–731.CrossRefMathSciNetGoogle Scholar
  2. [2]
    G. Deodhare, M. Vidyasagar. Controlsystems design via infinite linear programming[J]. Int. J. Control, 1992, 55(6): 1351–1380.MathSciNetGoogle Scholar
  3. [3]
    A. Casavola, E. Mosca. Minimization of a closed-loop response to a fixed input for SISO systems[J]. IEEE Trans. on Automatic Control, 1997, 42(10): 1581–1587.CrossRefMathSciNetGoogle Scholar
  4. [4]
    M. Khammash. Solution of the l 1 optimal control problem without zero interpolation[C]// Proc. 1996 Conf. Decision Control. Kobe, Japan, 1996: 4040–4045.Google Scholar
  5. [5]
    M. Khammash. A new approach to the solution of the l 1 control problem: The scaled-Q method[J]. IEEE Trans. on Automatic Control, 2000, 45(2): 180–187.CrossRefMathSciNetGoogle Scholar
  6. [6]
    A. A. Stoorvogel. Nonlinear L1 optimal controllers for linear systems[J]. IEEE Trans. on Automatic Control, 1995, 40(4): 694–696.CrossRefMathSciNetGoogle Scholar

Copyright information

© Editorial Board of Control Theory & Applications 2006

Authors and Affiliations

  • Xiang Liu
    • 1
  1. 1.National Laboratory of Industrial Control TechnologyZhejiang UniversityHangzhouChina

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