ISSN:
1573-2878
Keywords:
Existence theorems
;
linear equations
;
Volterra equations
;
bang-bang control
;
convexity
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We consider a Mayer problem of optimal control monitored by an integral equation of Volterra type: $$x(t) = x(t_1 ) + \int_{t_1 }^t { [h(t,s)x(s) + g(t, s)f(s, u(s))] ds,} $$ where the measurable control functionu satisfies a constraint of the formu(t) ∈U(t) ⊂E m,t 1≤t≤t 2, andg is a continuous kernel. Using the resolvent kernel associated with the kernelh, we prove the existence of an optimal usual solution for orientor fields without convexity assumptions. Further, ifU is a fixed compact set, we show the existence of an optimal bang-bang control.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00934052
Permalink