APPLICATION OF PONTRYAGIN'S MAXIMUM PRINCIPLE TO STATISTICAL PROCESS CONTROL OPTIMIZATION

摘要

The optimization of a statistical process control with a variable sampling interval is studied. A control performance index is the expected loss, caused by delay in detecting process change. It is to be minimized by a proper choice of a sampling interval. The mathematical model of this problem is a nonstandard variational calculus problem with two types of constraints, an isoperimetric constraint and two geometric constraints. The integrands in the cost functional and the isoperimetric constraint are independent of the derivative of the minimizing function. Therefore, the classical Euler-Lagrange equation approach is not applicable when analyzing this extremal problem. The optimization problem depends on the signal-to-noise ratio parameter. The original problem is transformed to an equivalent optimal control problem. Based on the value of the parameter, the latter is decomposed into two simpler problems, solved by application of Pontryagin's Maximum Principle. The theoretical results are evaluated by numerical simulations.