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Journal of Zhejiang University SCIENCE A 2000 Vol.1 No.1 P.66-70

http://doi.org/10.1631/jzus.2000.0066


MIXED I2/I1 CONTROL FOR DISCRETE-TIME SYSTEMS VIA LAGRANGE MULTIPLIER THEORY


Author(s):  WU Jun, CHU Jian

Affiliation(s):  Institute of Industrial Process Control, Yuquan Campus of Zhejiang University,Hangzhou, 310027, China

Corresponding email(s): 

Key Words:  mixed l2/l1 control, approximate analysis, lagrange multiplier theory


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WU Jun, CHU Jian. MIXED I2/I1 CONTROL FOR DISCRETE-TIME SYSTEMS VIA LAGRANGE MULTIPLIER THEORY[J]. Journal of Zhejiang University Science A, 2000, 1(1): 66-70.

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Abstract: 
The dual formulation of the discrete-time mixed l2/l1 control design problem was achieved by using the duality theory of Lagrange multipliers. For some special dual mixed l2/l1 problems, an approximation method for the optimal value is introduced. A suboptimal value of the infinite-dimensional dual problem can be obtained by solving a sequence of truncated problems. The convergence property of the solution scheme is investigated. This paper gives a low approximation method for the primal problem.

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Reference

[1]Dahleh, M.A. and Khammash, M., 1993. Controller design for plants with structured uncertainty. Automatica, 29(1): 37-56.

[2]Dullerud, G.E. and Francis, B.A., 1992. L1 analysis and design of sampled-data systems. IEEE Trans. Automat. Contr., 37(4): 436-446.

[3]Francis, B.A., 1987. A Course in H Control Theory. Springer-Verlag, Berlin, p.57-66.

[4]Luenberger, D.G., 1969. Optimization by Vector Space Methods. John Wiley, New York, p.149-159.

[5]McDonald, J.S. and Pearson, J.B., 1991. l1 optimal control of multivariable systems with output norm constraints. Automatica, 27(2): 317-329.

[6]Staffans, O.J., 1993. The four-block model matching problem in l1 and infinite-dimensional linear programming. SIAM J. Contr. Optim., 31(3): 747-779.

[7]Wu, Jun and Chu, Jian, 1996. Mixed H2/l1 control for discrete-time systems. Proc. 13th IFAC Congress, San Francisco, vol.G; p.453-457.

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