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.
HYBRID SYSTEMS MODELING FOR GAS TRANSMISSION NETWORK
