Guaranteed Continuity and Computational Improvement in SDRE Controllers for Cancer Treatment Analysis

Abstract

This study provides a novel analysis and design of the state-dependent Riccati equation (SDRE) control in cancer treatment application. The key assumption to ensure continuous SDRE controllers—in terms of the solvability of pointwise Riccati equations—is replaced by a simplified equivalent condition, which largely alleviates the computational burden. At the discontinuities, an alternative solution is novelly suggested, because the conventional/empirical α−parameterization technique to seek a continuous SDRE implementation without breakdowns is analyzed to be ineffective, which is the first counterexample in literature. Representatively, among discontinuities, an objective conflict against tumor eradication is discovered. Another value of the proposed analysis is supported by the generality demonstrations, in various fields beyond biomedical systems. Finally, the robustness of SDRE scheme to parameter variations is established via simulations, which more promotes the alternative solution as applied throughout the treatment course.