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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

Example text

Optimum solutions have been obtained for systems with varying plant d y n a m i c s subject to c l a s s i c a l d e s i g n o b j e c ­ t i v e s , r e q u i r e m e n t s and c o n s t r a i n t s . The p r o b l e m s w h i c h h a v e b e e n i n v e s t i g a t e d con­ sider a s i g n i f i c a n t l y l a r g e n u m b e r of active c o n t r o l v a r i a b l e s , far beyond t h e scope of c o n v e n t i o n a l d e s i g n p r o c e d u r e s in w h i c h only the r e s u l t s of a fixed set of p a r a m e t e r v a l u e s c a n b e analyzed in a s i n g l e computer run.

1 (38) h. -r.. i+l,3 13 13 Associate with each pair (i,j) the point P.. ). By labeling each triangle ij J 13 with its^three vertices the "triangularization of Ω. is h τ, = {(P. ,P. ,P. g + l5 · 1 < i < N-1, 1 5 j < M-l}. IS The finite element approximation is vv = { w c 0 ( V' (40) φ, is linear on each triangle in τ μ } . The dimension of W. (Ω. ) i s K=MxN and an e l e ­ ft n ment φ, of W, (S, ) i s completely s p e c i f i e d by the K-vector φ = {φ Jl 5 I < K}, φ , . 1 W . = φ, ψ Ύ κ(r. / £ .

Relative stability can be measured with respect to the systemTs openloop frequency response (OLFR), and perfor­ mance with respect to the system's closed-loop frequency response (CLFR). , gain and phase margins having units of db and deg, respec­ tively; (4) a simple objective function which is a smooth function (continuous first partial derivatives) of the compensator parameters, and which has minimum modality; and (5) a function which has quadratic or quadratic-like properties, so that quadratic or near-quadratic convergence of the algor­ ithm can be expected.

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