Nonlinear H∞ Optimization: A Causal Power Series Approach
Tannenbaum, Allen R.
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In this paper, using a power series methodology a design procedure applicable to analytic nonlinear plants is described. The technique used is a generalization of the linear H∞ theory. In contrast to previous work on this topic ([Indiana J. Math., 36 (1987), pp. 693–709], [Oper. Theory Adv. Appl., 41 (1989), pp. 255–277], [SIAM J. Control Optim., 27 (1989), pp. 842–860] ), the authors are now able to incorporate explicitly a causality constraint into the theory. In fact, it is shown that it is possible to reduce a causal optimal design problem (for nonlinear systems) to a classical interpolation problem solvable by the commutant lifting theorem [Harmonic Analysis of Operators on Hilbert Space, North-Holland, Amsterdam, 1970], [The Commutant Lifitng Approach to Interpolation Problems, Birkhäuser, Boston, 1990].