Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics

A pseudospectral method for budget-constrained infinite horizon optimal control problems

“…We have presented the extension of the indirect pseudospectral method for infinite horizon optimal control problems which arises in a natural way from the method developed in [17] through incorporating an additional isoperimetric, or also called budget-constraint, into the discretization scheme applied to the system of necessary optimality conditions in form of a Pontryagin Type maximum Principle, established in [13]. The quality and the convergence rate of the method presented here is comparable with those of the method in [17] and this fact gives us a reason to presume similar quality of convergence for the whole class of budget-constrained control problems, although we do not present any rigorous convergence proof here.…”

“…We refer some additional assumptions, stated in [13]: Assumption 4. Let ρ > 0 be chosen in such a way that for any T ≥ τ the solution ζ of the initial value problemζ…”

“…Further, the following necessary optimality conditions in form of a Pontryagin Type Maximum Principle hold true, cf. [13].…”

“…Theoretical results concerning the existence of optimal solutions and necessary optimality conditions in form of a Pontryagin Type Maximum Principle for this class of problems were considered in [11], [13].…”