H∞ control of nonlinear systems with positive input with application to antiangiogenic therapy

There are many systems in practice that can have only positive (nonnegative) input, typical examples for such systems are physiological systems. Moreover, the parameters of these systems are usually not known exactly or may vary over time, thus application of robust controllers represents a reasonable possibility. Most model-based controller design methods are developed for systems that can (or must) have negative and positive inputs as well, thus a dynamical extension is given here to the original system that ensures that the input of the original system is positive but the extended system can have negative input as well. The current paper investigates a robust control design method with positive input for an automatic therapy possibility in the case of antiangiogenic targeted molecular therapy using a recently published tumor growth model based on mice experiments. The extended system is transformed into an integrator series that is further modified using state-feedback to prepare the system for H∞ norm-based controller synthesis. The simulations demonstrate the robustness of the controller and the positivity of the input.