Abstract
A class of optimal control problems for infinite dimensional impulsive antiperiodic boundary value problem is considered. Using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of the semigroup governed by original principle operator, we present the existence of optimal controls. At last, an example is given for demonstration.
Highlights
Antiperiodic and periodic motions arise naturally in the mathematical modeling of a variety of physical process
The suitable impulsive evolution operator corresponding to homogenous impulsive periodic system was introduced and its properties boundedness, periodicity, compactness, and exponential stability were given
In this paper, using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of semigroup generated by original principle operator A, we present the existence of antiperiodic optimal controls for problem P1
Summary
Antiperiodic and periodic motions arise naturally in the mathematical modeling of a variety of physical process. In this paper, using exponential stabilizability and discussing the impulsive evolution operators, without compactness and exponential stability of semigroup generated by original principle operator A, we present the existence of antiperiodic optimal controls for problem P1. In order to study impulsive antiperiodic system on infinite dimensional spaces, we constructed the impulsive evolution operator {S ·, · } associated with A and {Ck; τk}∞k 1 which is very important in sequel It can be seen from the discussion on linear impulsive antiperiodic system that the invertibility of I S T0, 0 is the key of the existence of antiperiodic P C-mild solution of system 1.2. I SF T0, 0 is inverse and I SF T0, 0 −1 ∈ £b H
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