This paper proposes a new distributed model predictive control (DMPC) for positive Markov jump systems subject to uncertainties and constraints. The uncertainties refer to interval and polytopic types, and the constraints are described in the form of 1-norm inequalities. A linear DMPC framework containing a linear performance index, linear robust stability conditions, a stochastic linear co-positive Lyapunov function, a cone invariant set, and a linear programming based DMPC algorithm is introduced. A global positive Markov jump system is decomposed into several subsystems. These subsystems can exchange information with each other and each subsystem has its own controller. Using a matrix decomposition technique, the DMPC controller gain matrix is divided into nonnegative and non-positive components and thus the corresponding stochastic stability conditions are transformed into linear programming. By virtue of a stochastic linear co-positive Lyapunov function, the positivity and stochastic stability of the systems are achieved under the DMPC controller. A lower computation burden DMPC algorithm is presented for solving the min-max optimization problem of performance index. The proposed DMPC design approach is extended for general systems. Finally, an example is given to verify the effectiveness of the DMPC design.

本文针对不确定性和约束条件，提出了一种新的正Markov跳变系统的分布式模型预测控制（DMPC）。不确定性涉及区间和多位题类型，并且约束以1-范数不等式的形式描述。引入了线性DMPC框架，该框架包含线性性能指标，线性鲁棒稳定性条件，随机线性共正Lyapunov函数，锥不变集和基于线性规划的DMPC算法。全局正马尔可夫跳跃系统被分解为几个子系统。这些子系统可以彼此交换信息，并且每个子系统都有自己的控制器。使用矩阵分解技术，DMPC控制器增益矩阵分为非负分量和非正分量，因此将相应的随机稳定性条件转换为线性规划。通过随机线性共正Lyapunov函数，可以在DMPC控制器下实现系统的正性和随机稳定性。为了解决性能指标的最小-最大优化问题，提出了一种计算负担较小的DMPC算法。提议的DMPC设计方法已扩展到通用系统。最后，给出一个例子来验证DMPC设计的有效性。为了解决性能指标的最小-最大优化问题，提出了一种计算负担较小的DMPC算法。提议的DMPC设计方法已扩展到通用系统。最后，给出一个例子来验证DMPC设计的有效性。为了解决性能指标的最小-最大优化问题，提出了一种计算负担较小的DMPC算法。提议的DMPC设计方法已扩展到通用系统。最后，给出一个例子来验证DMPC设计的有效性。