Primal (quantity), dual (price) linear optimal control problems and the weak duality theorem

Abstract

In the continuation primal and dual optimal control problems are formulated. The disticntion between state and control variables, state equations and control variable constraints are discarded. A general treatment is achieved by the introduction of a matrix F. The derivation of the dual from the primal follows approximately the approach by J.B. Rosen. The corresponding weak duality theorem is deduced. It is then indicated how typical optimal control formulations may be obtained by the specialisation of the matrices and vectors and their substitution.