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The form of the n-th iteration of the operator q=fd/dx

100%

Szymkat M.

Mathematica Applicanda

1983

tom 11

nr 22

Artykuł nie zawiera streszczenia

Motivated by applications in linear dynamical systems, the author studies q^n(f), where q is the operator f●(d/dx) and qn is its n-th iteration. q^n(f) is a polynomial F(f(0),f(1),...,f(n)) in the derivatives f(0)=f,...,f(n) of f with integer coefficients. Special attention is paid to determining the coefficients of F. The author presents algorithms for computing the coefficients and also shows that the sum of all coefficients of F equals n!. The paper ends with some remarks on the number of coefficients of F, which is related to the number-theoretic unrestricted partition function.

Evolution of structure for direct control optimization

63%

Szymkat M., Korytowski A.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2007

tom 27

nr 1

165-193

The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and flat generations are described in detail and illustrated with computational examples.

Ograniczanie wyników

1 Discussiones Mathematicae, Differential Inclusions, Control and Optimization

1 Mathematica Applicanda

2 Szymkat M.

1 Korytowski A.

1 2007

1 1983

Wyniki wyszukiwania

The form of the n-th iteration of the operator q=fd/dx

Evolution of structure for direct control optimization