ISSN:
1573-2878
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Sufficient conditions for bang-bang and singular optimal control are established in the case of linear operator equations with cost functionals which are the sum of linear and quadratic terms, that is,Ax=u,J(u)=(r,x)+β(x,x), β〉0. For example, ifA is a bounded operator with a bounded inverse from a Hilbert spaceH into itself and the control setU is the unit ball inH, then an optimal control is bang-bang (has norm l) if 0⩽β〈1/2;∥A −1*r∥·∥A −1∥−2, but is singular (an interior point ofU) if β〉1/2∥A −1*r∥·∥A∥2.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00928120
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