切换系统的离散时间MPC及其在生物医学问题中的应用
Discrete-time MPC for switched systems with applications to biomedical problems
摘要：
切换系统中的操纵控制动作是时变切换信号描述了许多工程问题，主要涉及到生物医学应用。在这样的背景下，控制系统意味着在每个时间步从给定的有限族中选择一个自治系统。即使当这种选择可以通过解决动态规划（DP）问题来完成时，这种解决方案通常也难以应用，并且不能明确地考虑状态/控制约束。在这项工作中，提出了一种新的基于集合的模型预测控制（MPC）策略，以处理切换系统的易处理的形式。MPC公式的核心最优化问题是一个易于求解的混合整数最优化问题，其解以滚动时域的方式应用。模拟两个生物医学应用以测试控制器：（i）减弱病毒突变和药物抗性对病毒载量的影响的药物时间表，以及（ii）用于三阴性乳腺癌治疗的药物时间表。数值结果表明，所提出的策略优于可用的治疗方案。
英文摘要：
Switched systems in which the manipulated control action is the time-depending switching signal describe many engineering problems, mainly related to biomedical applications. In such a context, to control the system means to select an autonomous system - at each time step - among a given finite family. Even when this selection can be done by solving a Dynamic Programming (DP) problem, such a solution is often difficult to apply, and state/control constraints cannot be explicitly considered. In this work a new set-based Model Predictive Control (MPC) strategy is proposed to handle switched systems in a tractable form. The optimization problem at the core of the MPC formulation consists in an easy-to-solve mixed-integer optimization problem, whose solution is applied in a receding horizon way. Two biomedical applications are simulated to test the controller: (i) the drug schedule to attenuate the effect of viral mutation and drugs resistance on the viral load, and (ii) the drug schedule for Triple Negative breast cancer treatment. The numerical results suggest that the proposed strategy outperform the schedule for available treatments.
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