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针对状态矩阵基于参数不确定集的约束线性变参数系统(Linear Parameter Varying system),以减小在线计算量为目的,给出一种保性能的有限时域闭环预测控制算法。当LPV系统满足当前时刻参数值及参数边界值已知等条件时,将有限时域预测控制的目标优化问题看作是一个多级决策过程,根据动态规划的无后效性原理,从k=N时刻的优化目标值J*k开始,由k=N→0求解优化问题,从而获得显式描述的反馈控制律;随后通过证明分析了系统的闭环稳定性。数值仿真表明,基于动态规划的闭环预测控制算法不但能够获得理想的控制效果,而且与基于LMI的鲁棒预测控制算法相比,能够明显降低在线计算量。
In order to reduce the amount of online computation, a finite time-domain closed-loop predictive control algorithm with guaranteed performance is proposed for the Linear Parameter Varying system with state matrix based on parameter uncertainty set. When the LPV system satisfies the conditions such as the parameter value and the parameter boundary value known at present, the target optimization problem of finite time-domain predictive control is regarded as a multi-level decision-making process. According to the principle of no post-efficiency of dynamic programming, Starting from the optimal target value J * k at time N and solving the optimization problem from k = N → 0, the explicit feedback control law is obtained. Then the closed-loop stability of the system is analyzed. The numerical simulation shows that the closed-loop predictive control algorithm based on dynamic programming can not only achieve the desired control effect, but also reduce the online computational cost significantly compared with the robust predictive control algorithm based on LMI.