Optimal controllability of manpower system with linear quadratic performance index

Abstract

In classical manpower systems analysis, control of the system usually results in a set of admissible controls. This forms the basis for the use of the concepts of optimal control to distinguish this set of admissible controls for optimality. In this paper, the concepts of classical deterministic optimal control are extended to examine the optimal controllability of manpower system modeled by stochastic differential equations in terms of the differential flow matrices for both time varying and time invariant manpower systems. Necessary and sufficient conditions for controllability are given. The Hamilton–Jacobi–Bellman (HJB) equation is used to obtain an algebraic Riccati equation for an optimal tracking linear quadratic problem in a finite time horizon. A 2-norm optimality criterion which is equivalent to a minimum effort criterion is used to obtain a 2-norm optimal control for the system. An optimal time control is also obtained.