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/

Global: Zendy Plus annual

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

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

A new method is developed for solving optimal control problems whosesolutions are nonsmooth. The method developed in this paper employs a modifiedform of the Legendre-Gauss-Radau orthogonal direct collocation method. Thismodified Legendre-Gauss-Radau method adds two variables and two constraints atthe end of a mesh interval when compared with a previously developed standardLegendre-Gauss-Radau collocation method. The two additional variables are thetime at the interface between two mesh intervals and the control at the end ofeach mesh interval. The two additional constraints are a collocation conditionfor those differential equations that depend upon the control and an inequalityconstraint on the control at the endpoint of each mesh interval. The additionalconstraints modify the search space of the nonlinear programming problem suchthat an accurate approximation to the location of the nonsmoothness isobtained. The transformed adjoint system of the modified Legendre-Gauss-Radaumethod is then developed. Using this transformed adjoint system, a method isdeveloped to transform the Lagrange multipliers of the nonlinear programmingproblem to the costate of the optimal control problem. Furthermore, it is shownthat the costate estimate satisfies one of the Weierstrass-Erdmann optimalityconditions. Finally, the method developed in this paper is demonstrated on anexample whose solution is nonsmooth.

Modified Legendre-Gauss-Radau Collocation Method for Solving Optimal Control Problems with Nonsmooth Solutions