时间最优控制的一种算法

本文提出了对于控制作用和状态均受约束的多入多出线性系统的求解时间最优控制问题的算法。在离散数学模型的基础上,首先应用求解线性规划问题的有界变量单纯形方法求出满足控制约束的控制序列,然后再利用割平面方法处理状态约束,以求得满足约束条件的最优控制。除时间最优外,本算法还允许提出线性形式的附加目标函数。在具有附加目标函数时为能有效地处理状态约束,推导出了有界变量对偶单纯形方法。本算法通过扩展状态或部分扩展状态,可应用于一类有状态滞后的系统。为提高计算效率和减少存储容量,采取改进了的跳步算法和压缩存储技术等措施。

AN ALGORITHM FOR TIME OPTIMAL CONTROL

An algorithm is presented for solving the problem of time optimal control of multivariable linear systems with bounds both in control and state variables, and with delay in state. Based on the discrete state equation of the system, the bounded variable simplex method of linear programming (LP) is first applied to find the control sequences which meet the control constrains, then the cutting plane method is used to deal with state constraints. An additional objective function can be presented besides time optimal. In order to efficiently solve the s tate constrained problem with additional objective function, the dual simplex method for bounded variables of LP is developed. The algorithm, can be applied to the system with delay in state by augmenting states or part of the states. Some techniques such as improved skip-step algorithm and condensed memory method are used to improve the efficiency of the algorithm.