The aim of this paper is to prove the local existence, uniqueness and the exact controllability of the mild solutions of semilinear initial value control problems in suitable Banach spaces using semigroup theory "compact semigroup" and Schauder fixed point theorem.
this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical
The dynamical system is the concept used to describe the behavior of several phenomena in our daily life. It comes in two types; linear and nonlinear. Two essential properties characterize the latter, stability and chaos, which in turn are classified into two categories, continuous and discrete, for the models that exhibiting chaotic behavior, which sometimes needs to be stabilized and synchronized. There are various approaches for such a purpose. In this work, the chaotic behavior of the 2D-logistic map is stabilized without adding any control parameters. This approach is considered efficient for models whose analytic solutions are challenging to find. Moreover, the modulus for the Jacobian matrix eigenvalues is greater than unity. Finally, the feasibility and effectiveness of this stabilizing method are demonstrated through some Numerical analysis.
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