By Ivan Bratko (auth.), Andrej Dobnikar, Uroš Lotrič, Branko à ter (eds.)
The two-volume set LNCS 6593 and 6594 constitutes the refereed court cases of the tenth overseas convention on Adaptive and ordinary Computing Algorithms, ICANNGA 2010, held in Ljubljana, Slovenia, in April 2010. The eighty three revised complete papers awarded have been rigorously reviewed and chosen from a complete of a hundred and forty four submissions. the 1st quantity contains forty two papers and a plenary lecture and is geared up in topical sections on neural networks and evolutionary computation.
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Additional resources for Adaptive and Natural Computing Algorithms: 10th International Conference, ICANNGA 2011, Ljubljana, Slovenia, April 14-16, 2011, Proceedings, Part I
B(q −1 ) = ⎣ ⎦ . . n ,1 n ,1 n ,nu −1 b1 y q −1 + . . + bnyB q −nB . . b1 y q n ,nu −nB + . . + bnyB q The backward shift operator is denoted by q −1 , integers nA , nB , τ deﬁne the order of dynamics, τ ≤ nB . Outputs of the dynamic part are ⎡ nu nB ⎤ nA ⎤ ⎢ ⎢ x1 (k) ⎢ ⎢ .. ⎥ ⎢ x(k) = ⎣ . ⎦ = ⎢ ⎢ ⎢ xny (k) ⎣ ⎡ b1,r l ur (k − l) − a1l x1 (k − l) ⎥ ⎥ r=1 l=1 l=1 ⎥ ⎥ .. ⎥ . ⎥ nu nB nA ⎥ ny ,r ny bl ur (k − l) − al xny (k − l) ⎦ r=1 l=1 (4) l=1 The nonlinear steady-state part of the model is described by the equation y(k) = g(x(k)) where the function g : Rny → Rny is represented by ny MultiLayer Perceptron (MLP) feedforward neural networks with one hidden layer .
S N (k) S N −1 (k) . . e. using the prediction equation (11), the MPC optimisation problem (2) becomes an easy to solve quadratic programming task min u(k) y ref (k) − G(k) u(k) − y 0 (k) 2 + u(k) 2 Λ subject to umin ≤ J u(k) + u(k − 1) ≤ umax (14) − umax ≤ u(k) ≤ umax y min ≤ G(k) u(k) + y 0 (k) ≤ y max Deﬁnitions of all vectors and matrices are given in . The discussed MPC algorithm is named MPC with Nonlinear Prediction and Approximate Linearisation (MPC-NPAL) in contrast to the MPC-NPL algorithm with an inverse steady-state model and exact linearisation .
Vm ) ∈ Rm , then (i) there exists an argminimum f + of Ez over HK (X), which satisfies f+ = m ci Kui , where c = (c1 , . . , cm ) = K[u]+ v, i=1 and for all f ∈ argmin(HK (X), Ez ), f + K ≤ f o K ; (ii) for all α > 0, there exists a unique argminimum f α of Ez,α,K over HK (X), which satisfies o m fα = cα i Kui , where α −1 cα = (cα v; 1 , . . , cm ) = (Km [u] + α Im ) i=1 (iii) limα→0 f α − f + K = 0. Note that both argminima, f + and f α , are elements of the set spanm GK (X) and thus they belong to sets of functions computable by one hidden-layer networks with units from the dictionary GK (X).