English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper, a nonlinear 2D Optimal Control Problem (2DOCP) is considered.The quadratic performance index of a nonlinear cost function is endowed withthe state and control functions. In this problem, the dynamic constraint of thesystem is given by a classical diffusion equation. This article is concernedwith a generalization of Lagrangian functions. Besides, a GeneralizedLagrangian Jacobi-Gauss-Radau (GLJGR)-collocation method is introduced andapplied to solve the aforementioned 2DOCP. Based on initial and boundaryconditions, the time and space variables t and x are consideredJacobi-Gauss-Radau points clustered on first or end of interval respectively.Then, to solve the 2DOCP, Lagrange Multipliers are used and the optimal controlproblem is reduced to a parameter optimization problem. Numerical resultsdemonstrate its accuracy, efficiency, and versatility of the presented method.

Generalized Lagrangian Jacobi-Gauss-Radau collocation method for solving  a nonlinear 2-D optimal control problem with the classical diffusion equation