Jump Discontinuous Two Point Boundary Value Problems In Optimal Control

Abstract

Multiple shooting algorithms are developed for linear two-point boundary value problems (TPBVP's) in which the state vector is subjected to jump discontinuities at discrete points. These jump-discontinuous TPBVP's arise in optimal control and optimal estimation. Examples of such problems are given both to motivate the problem and to demonstrate the algorithms. The algorithms convert the TPBVP into a set of linear algebraic equations which may be solved using any linear equation solver. The existence and uniqueness of the solution is proven.