By H. E. Rauch

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Extra info for Applications of Nonlinear Programming to Optimization and Control. Proceedings of the 4th IFAC Workshop, San Francisco, USA, 20–21 June 1983

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L5(Z3)}. +ς| = Ρ ( ζ ) 2 η 23 = {(ξΐ,ξ2,1)|ξΐ+ξ2 S ρ(1) 2 } . (14) ΙΙΦΙΙ = { / ^ [ φ 2 + | ν φ | 2 ] α χ } 1 / 2 + { / ~ J A(y) . - [ x 2 ^ + g | ) + g f ] - O i n S . (15) rn s (16) where P = (aeRVk4)1/3. (17) The solution y only depends on X, ßq. , ßq Once ßq. and ßq have been fixed, the optimal design problem consists in finding the parameter X and the shape function p which minimizes the volume J(X,p) = nX/JpK)2d£ (18) 1/3 y ' (19) VARIATIONAL FORMULATION OF THE NON-LINEAR BOUNDARY VALUE PROBLEM Consider the functional 5 D Lemma 3 .

C. (1959, revised 1966). Vari­ able metric method for minimization. Argonne National Laboratory Report ANL-5990. D. Powell (1963). A rapidly convergent descent method for minimization, Br. Computer J. , b_, 163-168. E. Nelson, Jr. (1977). Flying qualities design of the Northrop YF-17 fighter prototypes. Soc. Automotive Engineers, Business Aircraft Meeting, paper 770469. M. (1972). Applied Nonlinear Programming. McGraw-Hill, New York. , B. Golubev, and T. Kopelman (1980). Flight control design based on nonlinear model with uncertain parame­ ters.

To overcome t h i s d i f f i c u l t y , we develop a technique f o r re­ placing the o r i g i n a l performance-specifying inequalities by more t r a c t a b l e majorizations. 1. Decomposition of Open Loop Gain and Phase The structure of the plant model allows two kinds of s i m p l i f i c a t i o n : Theorem 4 . 1 . ψ(χ) = max{ Π Suppose that in ( 1 7 ) , (18b) xΩ i ψ (x,oü)+b(o))} (19a) ω^Ω i=l where ψ Ί (χ,ω) = max φ Ί (χ,α Ί ω). , nv-l and Ω are compact intervals. Then, n -1 Suppose in (11), (13a), (14) and (15) we make the simplifying assumption that £(s) Ξ 1 and consider the computations our algorithms (Gonzaga, Polak and Trahan, 1980; Mayne and Polak, 1980; Polak and Mayne, 1976) will need to perform to solve these inequalities.

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