The general discrete-time Single-Input Single-Output (SISO) mixed H2/l1 control problem is considered in this paper. It is found that the existing results of duality theory cannot be directly applied to this infinite dimension optimisation problem. By means of two finite dimension approximate problems, to which duality theory can be applied, the dual of the mixed H2/l1 control problem is verified to be the limit of the duals of these two approximate problems.
Optimal control mixed H2/l1 control duality theory
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G. Zames. Feedback and optimal sensitivity: model reference transformations, multiplicative seminorms and approximate inverses. IEEE Transactions on Automatic Control, vol. 26, no. 2, pp. 301–320, 1981.CrossRefMathSciNetGoogle Scholar
D. C. Youla, H. A. Jabr, J. J. Bongiorno. Modern Wiener-Hopf design of optimal controllers-part II: the multivariable case. IEEE Transactions on Automatic Control, vol. AC-21, no. 3, pp. 319–338, 1976.CrossRefMathSciNetGoogle Scholar
M. Vidyasagar, Optimal rejection of persistent bounded disturbances. IEEE Transactions on Automatic Control, vol. 31, no. 6, pp. 527–534, 1986.CrossRefMathSciNetGoogle Scholar
I. Kaminer, P. P. Khargonekar, M. A. Rotea. Mixed H2/H∞ control for discrete time systems via convex optimization. Automatica, vol. 29, no. 1, pp. 57–70, 1993.CrossRefMathSciNetGoogle Scholar
M. Sznaier, J. Bu. On the properties of the solutions to mixed l1/H∞ control problems, In Preprints 13th IFAC Congress, San Francisco, USA, vol. G, pp. 249–254, 1996.Google Scholar
M. V. Salapaka, M. Dahleh, P. Voulgaris. Mixed objective control synthesis: optimal l1/H2 control. SIAM Journal of Control and Optimization, vol. 35, no. 5, pp. 1672–1689, 1997.CrossRefMathSciNetGoogle Scholar
P. Voulgaris. Optimal H2/l1 control: the SISO case. In Proceedings of IEEE International Conference on Decision and Control, vol. 4, pp. 3181–3186, 1994.Google Scholar
J. Wu, J. Chu. Mixed H2/l1 control for discrete time systems. In Preprints 13th IFAC Congress, San Francisco, USA, vol. G, pp. 453–457, 1996.Google Scholar
J. Wu, J. Chu. Approximation methods of scalar mixed H2/l1 problems for discrete-time systems. IEEE Transactions on Automatic Control, vol. 44, no. 10, pp. 1869–1874, 1999.CrossRefMathSciNetGoogle Scholar
M. V. Salapaka, M. Khammash, M. Dahleh. Solution of MIMO H2/l1 problem without zero interpolation. SIAM Journal of Control and Optimization, vol. 37, no. 6, 1865–1873, 1999.CrossRefMathSciNetGoogle Scholar
N. Elia, M. A. Dahleh. Control design with multiple objectives. IEEE Transactions on Automatic Control, vol. 42, no. 5, pp. 596–613, 1997.CrossRefMathSciNetGoogle Scholar
M. V. Salapaka, M. Dahleh, P. G. Voulgaris. MIMO optimal control design: the interplay between the H2 and the l1 norms. IEEE Transactions on Automatic Control, vol. 43, no. 10, pp. 1374–1388, 1998.CrossRefMathSciNetGoogle Scholar
J. Brinkhuis. Introduction to duality in optimization theory. Journal of Optimization Theory and Applications, vol. 91, pp. 523–542, 1996.CrossRefMathSciNetGoogle Scholar