Abstract: This paper presents a stabilizing incremental model predictive control (MPC) algorithm for discrete-time multivariable linear systems with measurable disturbances. Taking the incremental state-space model as the predictive model, the finite horizon optimal control problem of MPC is formulated and the corresponding MPC controller is determined, which has a structure combining measurable disturbance feedforward with time-delay state feedback. Using the Lyapunov-Krasovskii stability theory of time-delay systems, we establish some sufficient conditions guaranteeing the stability of the closed-loop system with no constraints. Finally, the simulation example of a constrained biaxial contouring control system is employed to illustrate the validity of the algorithm proposed here.

Key words: Model predictive control, multivariable control, stability, time-delay, contour control

摘要： 考虑一类扰动可测的离散时间多变量线性系统，提出一种稳定化增量模型预测控制(MPC)算法。以控制增量状态空间模型作为预测模型，定义MPC的有限时域最优控制问题，得到具有可测扰动前馈-时滞状态反馈结构的MPC控制器。进一步，利用时滞系统(Lyapunov-Krasovskii，L-K)稳定性理论，建立无约束闭环预测控制系统的稳定性充分条件。最后通过对约束平面轮廓控制系统进行仿真控制研究，仿真结果验证了所提出算法的正确性和有效性。

关键词: 模型预测控制, 多变量控制, 稳定性, 时滞, 轮廓控制