Self-triggered impulsive control of nonlinear time delay systems: Application to chemotherapeutic dose-regimen design

This paper proposes a self-triggered impulsive control for nonlinear time-delay systems, where the time instant of the next impulsive input is calculated based on the last measurement and the values of the systems’ parameters. Contrary to event-triggered scheme where the actuation is discrete but a continuous monitoring of the system’s states is necessary, in the self-triggered approach, both sampling and actuation are performed at distinct moments of time. Utilizing Lyapunov–Razumikhin method and by upper-bounding the system’s trajectory, the global asymptotic stability of the system’s equilibrium is verified when the rate of change in the Lyapunov function is exponential. In the general case, the global ultimate boundedness of the system’s trajectory is shown where the ultimate bound can be set arbitrarily small. As an application, for the first time, the problem of dose regimen design is formulated in the sampled data framework. Then, based on the obtained theoretical results, the appropriate regimen is suggested. In particular, time-triggered and self-triggered therapy protocols for docetaxel, a phase specific chemotherapeutic drug which is administered intravenously, are proposed. Clinical constraints such as maximum tolerated dose, discontinuous drug administration, and intermittent measurements are met in the proposed therapy protocols. According to in-silico results, both proposed self-triggered and time-triggered dose regimens outperform the traditional weekly fixed dose administration. Finally, the robustness of the proposed schemes to parameter uncertainties is evaluated through an extensive set of simulations.