Hoc OPTIMIZATION : A CAUSAL POWER SERIES APPROACH *

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 HOC> theory. In contrast. to previolls work on this topic (lIndiana J. Math., 36 (1987), pp. 693-7091. rOper. 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 t.o reduce a causal optimal design problem (for nonlinear systems) to a cla.ssical 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, Birkhiiuser , Boston, 19901 .