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On the quadratic optimal control problem for Volterra integro- differential equations. (English) Zbl 0572.49011
The paper deals with the synthesis of the following optimal control problem: minimize \[ J(u)=\int^{T}_{0}\{| u(t)|^ 2+| x(t)|^ 2\}dt \] over all \((u,x)\in L^ 2(0,T)\times C(0,T)\) subject to the condition \[ \dot x(t)=\int^{t}_{0}K(t- s)x(s)ds+u(t),\quad x(0)=x_ 0. \] Using the abstract theory of ordinary differential equations, under appropriate hypothesis on the kernel K, a feedback law is given.
Reviewer: N.Luca
MSC:
49K99 Optimality conditions
45J05 Integro-ordinary differential equations
93C30 Control/observation systems governed by functional relations other than differential equations (such as hybrid and switching systems)
93B50 Synthesis problems
47D03 Groups and semigroups of linear operators
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References:
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