双线性系统多目标控制问题研究

Multi-objective Control Problem of Bilinear Systems

研究了双线性系统的多目标控制问题.首先把多目标控制问题,通过效用函数技术转化为一个单目标最优控制问题,其中,效用函数是多个二次型性能指标的非线性函数,因此,在动态规划的意义下是不可分的.然后,为了克服不可分对求解带来的困难,提出了一种两级最优控制算法.下级用动态规划求解一个参数化的具有双线性一二次型结构的辅助Lagrangian问题;上级迭代调整辅助Lagrangian问题中的参数向量.不断重复这个过程,直至最优性条件被满足.

The control problem of bilinear systems with multiple objectives is studied. First, the multi-objective control problem is converted into a single objective optimal control problem using the utility function technology. The utility function is a nonlinear function of multiple quadratic performance indices, and therefore it is non-separable in the sense of dynamic programming. Then, to overcome this difficulty, a two-level optimal control algorithm is proposed. At the lower level, the formulated auxiliary Lagrangian problem is of a parametric bilinear-quadratic structure and it is solved by dynamic programming. Finally, the weighting vector in the auxiliary Lagrangian problem is adjusted by the upper level iteratively. This two-level process repeats until an optimal condition is satisfied.