Impulsive Control of Tumor Growth via Nonlinear Model Predictive Control Using Direct Multiple Shooting

Abstract

Nonlinear Model Predictive Control (NMPC) is utilized to compute optimal administration protocols for chemotherapeutic treatment. By using model-based methods, the side effects of the drug can be mitigated in conjunction with a decrease in treatment expenses. The designed controller was able to provide the protocol in the form of impulses that can model administration by injection, using a smooth approximation of the Dirac delta distribution. For the implementation of the NMPC algorithm, Direct Multiple Shooting (DMS) was chosen so that the computational time of the problem remains reasonable. Numerical effects on the stability of the computation were discussed, with a solution for each issue present. The controller was also tested on virtual patients, with data from mice experiments, which concluded in applicable treatment protocols.

Experimental Closed‐Loop Control of Breast Cancer in Mice

“…, 􏽢 x ⊺ , 0.1) with 0.1 as initial administration for each optimized control. For the prediction horizon, we used N � 3 in previous works [13]; however, in order to improve the stability of the scheme, we choose N � 6 in this article. e prediction intervals Δt � t i+1 − t i � 3 were set according to the time between each injection during the experiment.…”

“…In separate work, the NMPC was designed using direct multiple shooting and impulsive input action in the prediction model [13]. e impulsive action was realized using a continuous approximation of Dirac impulses leading to continuously differentiable trajectories of the system.…”