Abstract
We consider the stability of control prescribed by hybrid PDE–ODE systems modeling intermittent hormonal therapy of prostate cancer. Hybrid systems can be regarded as a generalization of optimal control. However, since the purpose of hybrid systems is not only minimization or maximization of a corresponding functional, it is not clear what is optimal in hybrid systems. In this paper, we shall give a concept of stability of the control prescribed by the hybrid PDE–ODE systems. Moreover, we show a sufficient condition on initial data for the existence of the stable control. Finally, we apply the main result to several mathematical models describing intermittent hormonal therapy of prostate cancer.
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