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Published on: December 1, 2023
Nonlinear optimal control for the multi-variable tumor-growth dynamics
1Industrial Systems Institute, Unit of Industrial Automation, Rion Patras, Greece.
Abstract:
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.
Insights
This study introduces a novel nonlinear optimal control method for inhibiting tumor growth using chemotherapy. The new H-infinity control approach enhances treatment efficacy by optimizing drug delivery dynamics.
Area of Science:
- Oncology
- Control Theory
- Mathematical Biology
Background:
- Multivariable tumor-growth models are crucial for understanding chemotherapy's impact on cancer.
- Simultaneous infusion of multiple chemotherapeutic drugs requires sophisticated control strategies.
- Existing models often lack robust control mechanisms for dynamic tumor inhibition.
Purpose of the Study:
- To develop and validate a nonlinear optimal (H-infinity) control method for multivariable tumor-growth models.
- To improve the precision and effectiveness of chemotherapy drug delivery.
- To enhance the inhibition of tumor-cell proliferation through advanced control techniques.
Main Methods:
- Proving differential flatness properties for the tumor-growth model's state-space description.
- Employing approximate linearization via first-order Taylor expansion and Jacobian matrices.
- Designing a stabilizing H-infinity feedback controller using an algebraic Riccati equation.
- Utilizing Lyapunov analysis to demonstrate global stability of the control scheme.
Main Results:
- Successful design of a nonlinear optimal (H-infinity) controller for tumor-growth dynamics.
- Demonstration of differential flatness properties for the model.
- Validation of global stability through rigorous Lyapunov analysis.
- Comparative performance analysis against flatness-based control methods.
Conclusions:
- The developed nonlinear optimal (H-infinity) control method offers a promising approach for dynamic tumor growth inhibition.
- This control strategy provides enhanced precision in chemotherapy drug administration.
- The findings support the application of advanced control theory in cancer treatment optimization.
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