双线性系统多目标控制问题研究

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---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.

Multi-objective Control Problem of Bilinear Systems

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.