线性稳态大系统优化与控制的二次等价性原理与点凸化技术(PCT)

本文研究了线性稳态大系统优化与控制问题中的二次等价性原理,证明了非退化的线性规划问题可以等价为正定二次规划问题,线性稳态控制问题可以等价为具有线性约束二次凸目标的稳态控制问题.基于等价性原理,本文提出了点凸化技术(PCT),用于凸化不能应用关联平衡法(IBM)的线性问题,最后给出应用例子,说明PCT在求解线性稳态大系统优化与控制问题中的应用.

Quadratic Equivalence Principle and Point Convexifying Technique in Optimization and Control of Linear Steady State Systems

The formulation and proof of a quadratic equivalence principle are presented in thispaper. The principle states that a non-degenerate linear programming problem is equivalentto a separable quadratic one obtained by adding a special penalty terms to the original problemBased on this principle, a point convexifying technique is introduced, which can be used toconvexify linear programming or linear steady state control problems so that the interactionbalance method can be applied. A simple example is given to illustrate the application ofthe technique.