Parametric Optimization by Primal Method in Multilevel Systems

This paper deals with optimal control in multilevel systems. The decomposition of a system into N subsystems is presented as a problem of formulating the performance index P(m) as a function of N components P(P1, P2,..., PN) and of transforming the system constraint m?R into a set of constraints m1?IR1(v), m2?R2(v),..., v?Rv, where v is the coordination variable. Ways of achieving this goal as applicable to typical systems are presented. Some aspects of choosing the coordination variable and the tradeoffs involved are discussed. Lagrangian methods as used previously by Lasdon and Pearson are shown to be a particular case of parametric optimization, and the range of their applicability is specified. Simple examples of static optimization serve to illustrate the approach.