Abstract
In this paper a generalization of the indirect pseudo-spectral method, presented in [17], for the numerical solution of budget-constrained infinite horizon optimal control problems is presented. Consideration of the problem statement in the framework of weighted functional spaces allows to arrive at a good approximation for the initial value of the adjoint variable, which is inevitable for obtaining good numerical solutions. The presented method is illustrated by applying it to the budget-constrained linear-quadratic regulator model. The quality of approximate solutions is demonstrated by an example.
Highlights
In the last decades, developing numerical solution methods for infinite horizon optimal control problems has emerged a lot of attention and a plenty of new results were obtained, cf. [5], [7], [9], [17]
We intend to describe an indirect numerical solution method, i.e. it acts according to the scheme ”first optimize, discretize”, and represents an extended version of the indirect pseudospectral method presented in [17], for a class of budget-constrained infinite horizon optimal control problems
We do not provide a rigorous convergence result of the suggested pseudospectral method here, the results observed above as well as solutions for other optimal control problems provided by pseudo-spectral method such as inverse pendulum problem or Lotka-Volterra optimal control problem, cf. [1], allow us to assume that the chosen strategy would lead to comparable convergence results for other budgetconstrained optimal control problems
Summary
In the last decades, developing numerical solution methods for infinite horizon optimal control problems has emerged a lot of attention and a plenty of new results were obtained, cf. [5], [7], [9], [17]. Among them, both direct and indirect solution methods were established. We extend the indirect pseudospectral method, introduced in [17], onto the class of budget-constrained infinite horizon optimal control problems.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
