We designed three new controllers: a sigmoid-based controller, a polynomial dynamic inversion-based controller, and a proportional–integral–derivative (PID) impulsive controller for cancer differentiation therapy. We compared these three controllers to existing control strategies to show the improvement in performance and compare their robustness. The sigmoid-based controller adds a sigmoid term associated with the error of the controlled state and a selected observed state. The sigmoid term is multiplied by a control gain, thereby decreasing the control effort for state transition. The polynomial dynamic inversion-based controller adds a cubic error term in the error dynamic aiming to achieve a shorter convergence time to the desired value of the controlled state. The PID impulsive controller considers the accumulated controlled state error and the rate of change of the controlled state error, thereby forcing the controlled state to converge to the desired value and alleviating the damping effect in the steady state. For the considered cancer network, the 3 new cancer control strategies exhibit superior and robust performance. The PID impulsive controller has a significant improvement in robustness compared to the impulsive controller and has greater potential for cancer differentiation therapy.

我们设计了三种新的控制器：基于 sigmoid 的控制器、基于多项式动态反演的控制器和用于癌症分化治疗的比例积分微分 (PID) 脉冲控制器。我们将这三种控制器与现有的控制策略进行了比较，以显示性能的改进并比较它们的鲁棒性。基于 sigmoid 的控制器添加了与受控状态和所选观测状态的误差相关的 sigmoid 项。S 形项乘以控制增益，从而减少状态转换的控制工作。基于多项式动态反演的控制器在误差动态中添加了三次误差项，旨在以更短的时间收敛到受控状态的期望值。PID脉冲控制器考虑累积的受控状态误差和受控状态误差的变化率，从而迫使受控状态收敛到期望值，并减轻稳态时的阻尼效应。对于所考虑的癌症网络，3 种新的癌症控制策略表现出卓越而稳健的性能。PID脉冲控制器相比脉冲控制器在鲁棒性方面有显着提高，在癌症分化治疗方面具有更大的潜力。