Abstract
In this work, a nominal-plus-neighboring-optimal control approach is suggested for the treatment of cancer using the adoptive cellular immunotherapy. The main goal of this therapy is to minimize both tumor concentration and treatment costs while restoring natural defense mechanisms and activating immune response. In the presence of an additional initial concentration of cancer cells, the biological effects of the introduction of a neighboring-optimal treatment in addition to the existing nominally therapy are explored and investigated. The optimal control problem is presented by defining appropriate objective functions. The Pontryagin’s maximum principle and the Pontryagin procedure are both used to obtain optimal solutions for subsequently providing nominal and neighboring-optimal control configurations. The optimal systems are derived and solved numerically using an adapted iterative method with a Runge–Kutta fourth order scheme.
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