Boundary-value technique to solve linear state regulator problems

TLDR: In this paper, a method is proposed to solve free endpoint optimal control problems with linear state and quadratic cost by translating the problem into a two-point boundary value problem.

Abstract: In this paper, a method is proposed to solve free endpoint optimal control problems with linear state and quadratic cost. After translating the problem into a two-point boundary-value problem (TPBVP) that arises from the optimization of the Hamiltonian, two pointst 1 andt 2,t 1<t 2, belonging to the given interval of integration [t 0,t f], are chosen and conditions are derived at these points appropriately. Then, letting τ=(t−t 0)/∈, σ=(t f−t)/∈, the τ-scaled, the original, and the σ-scaled TPBVP's are solved on the intervals [t 0,t 1], [t 1,t 2], and [t 2,t f] respectively as boundary-value problems.