AI 中文总结
提出混合QPSO-SQP方法，将Michaelis-Menten饱和纳入化学-免疫治疗调度，通过三区域最小化法则实现连续剂量调节，并验证PMP最优性。
AI 中文摘要
联合化学-免疫治疗的最优调度通常被表述为一个控制仿射最优控制问题，除非出现奇异弧，否则该问题通常产生边界选择（bang-bang型）协议。这种结构虽然方便，但忽略了高剂量率下的饱和药效动力学。我们将Michaelis-Menten饱和直接纳入治疗通道，使得动力学变为非控制仿射，且哈密顿量在每个控制中变为非线性。在严格正的暴露惩罚下，哈密顿量允许一个显式的三区域逐点最小化法则：每个输入在下界、上界或唯一内部最小化点处被选择。在内部区间上，严格Legendre条件成立，因此连续调节剂量作为正则内部极值出现，而非奇异弧或平滑伪影。由此产生的转录是非凸的；因此我们使用混合量子粒子群优化（QPSO）-序列二次规划（SQP）流水线，其中QPSO提供约束感知的暖启动，SQP在配点网格上强制执行可行性和Karush-Kuhn-Tucker（KKT）最优性。代价状态重构证实了Pontryagin最小原理（PMP）结构和预测的边界/内部区域转换。
英文摘要
Optimal scheduling of combined chemo-immunotherapy is often formulated as a control-affine optimal control problem, which generically yields boundary-selected (bang-bang-type) protocols unless singular arcs occur. This structure, while convenient, neglects saturating pharmacodynamics at high dose rates. We incorporate Michaelis-Menten saturation directly into the therapy channels, making the dynamics non-control-affine and the Hamiltonian nonlinear in each control. With strictly positive exposure penalties, the Hamiltonian admits an explicit three-regime pointwise minimization law: each input is chosen at the lower bound, the upper bound, or as a unique interior minimizer. On interior intervals the strict Legendre condition holds, so continuously modulated dosing arises as a regular interior extremal rather than a singular-arc or smoothing artifact. The resulting transcription is nonconvex; we therefore use a hybrid Quantum Particle Swarm Optimization (QPSO)-Sequential Quadratic Programming (SQP) pipeline, where QPSO provides a constraint-aware warm start and SQP enforces feasibility and Karush-Kuhn-Tucker (KKT) optimality on a collocation grid. Costate reconstruction corroborates the Pontryagin Minimum Principle (PMP) structure and the predicted boundary/interior regime transitions.
Comments23 pages, 6 figures, 3 tables. Published in Discrete and Continuous Dynamical Systems - Series B
Journal refDiscrete and Continuous Dynamical Systems - Series B, 38 (2026), 280-302
