Indirect numerical solution of constrained optimal control problems with parameters

The first-order necessary conditions for the extremum of typical optimal control problems lead to boundary-value problems in differential-algebraic equations (BVP-DAE). This paper presents a procedure for the numerical solution of these BVP-DAE. Here, the algebraic equations are nonlinear and not easily eliminated from the boundary-value problem. The solution method presented is based on the multiple shooting technique. In this approach the time domain is divided into subintervals. By requiring that the differential-algebraic equations be continuous from one interval to the next, and satisfy the boundary conditions leads to a set of shooting equations. Efficient techniques for integrating the differential-algebraic equations, and solving the shooting equations are discussed