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

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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.

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Authors and Affiliations

  1. National Laboratory of Industrial Control Technology, Zhejiang University, Hangzhou, Zhejiang, 310027, China

    Xiang Liu

Authors
  1. Xiang Liu
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Additional information

This work was supported by the National Science Foundation of China(No.60274036).

Xiang LIU was born in 1964, and is the associate professor of Department of Control Science & Engineering of Zhejiang University. Research interests include digital programming control, robust control, intelligent production scheduling.

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Liu, X. A new approach on designing l 1 optimal regulator with minimum order for SISO linear systems. J. Control Theory Appl. 4, 155–158 (2006). https://doi.org/10.1007/s11768-006-5026-2

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  • DOI: https://doi.org/10.1007/s11768-006-5026-2

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