Boundary-value technique to solve linear state regulator problems

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 pointst₁ andt₂,t₁<t₂, belonging to the given interval of integration [t₀,t_f], are chosen and conditions are derived at these points appropriately. Then, letting =(t–t₀)/, =(t_f–t)/, the -scaled, the original, and the -scaled TPBVP's are solved on the intervals [t₀,t₁], [t₁,t₂], and [t₂,t_f] respectively as boundary-value problems.The authors are deeply indebted to Dr. S. M. Roberts for his valuable comments and suggestions, which improved the clarity of the paper.