ISSN:
1573-2878
Keywords:
Optimal control
;
distributed-parameter systems
;
control of partial differential equations
;
sufficiency conditions
;
Green's formula
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract First-order necessary and sufficient conditions are obtained for the following quasilinear distributed-parameter optimal control problem: $$max\left\{ {J(u) = \int_\Omega {F(x,u,t) d\omega + } \int_{\partial \Omega } {G(x,t) \cdot d\sigma } } \right\},$$ subject to the partial differential equation $$A(t)x = f(x,u,t),$$ wheret,u,G are vectors andx,F are scalars. Use is made of then-dimensional Green's theorem and the adjoint problem of the equation. The second integral in the objective function is a generalized surface integral. Use of then-dimensional Green's theorem allows simple generalization of single-parameter methods. Sufficiency is proved under a concavity assumption for the maximized Hamiltonian $$H^\circ (x,\lambda ,t) = \max \{ H(x,u,\lambda ,t):u\varepsilon K\} $$ .
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934748
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