超差特征量指标约束下的离散系统待机控制

Opportunity-awaiting control for linear discrete-time systems with constraints on exceeding tolerance characteristic indices

由目标跟踪过程中出现的实际情形提出一类新的离散系统待机控制问题.将系统跟踪中断(控制失败)概率这一关键性指标转化为一组由滞留时间、超差时间以及随机穿越周期等构成的超差特征量指标集的约束;推导出带状目的域下超差特征量指标的解析表达式,研究了其与区域极点指标之间的相容性条件;当上述指标相容时,利用线性矩阵不等式(LMI),采用差分进化算法(DE)对待机控制策略进行满意优化求解;最后通过一个算例验证了所提方法的有效性.

Based on the practical situation in target tracking process, an opportunity-awaiting control scheme for a class of linear discrete-time systems with constraints on exceeding tolerance characteristic （ETC） indices is put forward. First, the tracking interruption （control failure） probability is transformed to a set of ETC indices including the residence time, exceeding tolerance time and the random passage period time. Secondly, formulas of the ETC indices on the zonal target area are derived, and the consistency of the circular pole index and ETC indices is analyzed. When the above indices are consistent, a differential evolution （DE） algorithm is employed together with linear matrix inequality（LMI） method to find a satisfactory control strategy. Finally, a numerical example is presented to illustrate the proposed method.