Two point Boundary Value Problems about "bvp4c"

is "bvp4c" is a "direct" method of solving an optimal control problem, I see it uses collacation and mesh refinement which are said as direct methods in references .

I have a optimal control problem formulated with states and costates with boundary conditions . What i dont understand is , is "bvp4c" called a direct method method? does it transcribe into "Nonlinear Programming problem?"

Answer 1

[Raunak Gupta]

Hi,

Direct method used for optimal control problem discretize the control problem into a nonlinear constrained optimization problem. bvp4c also divide the range of integration in case of multipoint Boundary value problem. The collocation technique uses a mesh for dividing the interval of integral to subintervals. Thus, solver solves the algebraic equations arising from the boundary condition and this process is repeated until error in numerical solution doesn’t exceed the tolerance criteria.

Thus, the boundary condition and the algorithm used in bvp4c makes it a direct method as final equation to solve on the subinterval are algebraic (can be linear or non-linear depending upon the integration problem).

You may refer to the following examples and reference for exploring more:

• Tutorials on solving BVPs with bvp4c
• Solving BVP with Multiple Boundary Conditions

[Karthi Ramachandran]

Thank you for the answer Raunak, so I can understand that it is indeed a direct method and I need not separately transcribe my optimal control two point boundary value problem into a Nonlinear Programming problem which wants me to use fmincon