Adaptive Tracking Control for Uncertain Cancer-Tumor-Immune Systems

Nonlinear optimal control for the multi-variable tumor-growth dynamics

The multivariable tumor-growth dynamic model has been widely used to describe the inhibition of tumor-cells proliferation under the simultaneous infusion of multiple chemotherapeutic drugs. In this article, a nonlinear optimal (H-infinity) control method is developed for the multi-variable tumor-growth model. First, differential flatness properties are proven for the associated state-space description. Next, the state-space description undergoes approximate linearization with the use of first-order Taylor series expansion and through the computation of the associated Jacobian matrices. The linearization process takes place at each sampling instant around a time-varying operating point which is defined by the present value of the system's state vector and by the last sampled value of the control inputs vector. For the approximately linearized model of the system a stabilizing H-infinity feedback controller is designed. To compute the controller's gains an algebraic Riccati equation has to be repetitively solved at each time-step of the control algorithm. The global stability properties of the control scheme are proven through Lyapunov analysis. Finally, the performance of the nonlinear optimal control method is compared against a flatness-based control approach.

Simultaneous Multi-Treatment Strategy for Brain Tumor Reduction via Nonlinear Control

Background: Recently proposed brain-tumor treatment strategies prioritize fast reduction of tumor cell population while often neglecting the radiation or chemotherapeutic drug dosage requirements to achieve it. Moreover, these techniques provide chemotherapy based treatment strategies, while ignoring the toxic side effects of the drugs employed by it. Methods: This study updates the recently proposed brain-tumor system dynamics by incorporating radiotherapy along with chemotherapy to simultaneously initiate both therapies for a more comprehensive and effective response against tumor proliferation. Afterwards, based on the upgraded system dynamics, this study proposes a novel multi-input sigmoid-based smooth synergetic nonlinear controller with the aim to reduce the dosage requirements of both therapies while keeping the overall system response robust and efficient. The novelty of this study lies in the combination of radiotherapy and chemotherapy inputs in a way that prioritizes patients health and well-being, while integrating advanced synergetic control technique with a sigmoid function based smoothing agent. Results: The proposed method reduced baseline radiation and chemo drug dosages by 57% and 33% respectively while effectively suppressing tumor growth and proliferation. Similarly, the proposed controller reduced the time required for complete tumor mitigation by 60% while reducing the radiation and chemotherapeutic drug intensity by 93.8% and 21.3% respectively. Conclusions: This study offers significant improvement in tumor treatment methodologies by providing a safer, less riskier brain-tumor treatment strategy that has promising potential to improve survival rates against this menacing health condition so that the affected patients may lead a healthier and better quality of life.