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)
Quadratic Equivalence Principle and Point Convexifying Technique in Optimization and Control of Linear Steady State Systems
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摘要: 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.Abstract: The formulation and proof of a quadratic equivalence principle are presented in this paper. The principle states that a non-degenerate linear programming problem is equivalent to a separable quadratic one obtained by adding a special penalty terms to the original problem Based on this principle, a point convexifying technique is introduced, which can be used to convexify linear programming or linear steady state control problems so that the interaction balance method can be applied. A simple example is given to illustrate the application of the technique.
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