Jump conditions for sensitivity coefficients

Abstract

Publisher Summary This chapter focuses on jump conditions for sensitivity coefficients. The presence of discontinuous functions in a system of differential equations does not permit a straightforward application of the ordinary variational equations for the calculation of sensitivity coefficients. At the discontinuity points the variational equations are not defined. These difficulties especially occur when sensitivity techniques are used for the solutions of two-point boundary problems in optimal control syntheses, because of the usual bang-bang characteristics of optimal trajectories. Statement of the fundamental problem contains a sufficiently general definition of such discontinuous relations. It is found that at the discontinuity points, the sensitivity coefficients have to satisfy jump conditions, which are derived in the chapter. The chapter discusses the well-known definition of sensitivity coefficients for those systems of differential equations that do not lead to jump conditions. The chapter also discusses initial condition sensitivity coefficient, parameter sensitivity coefficients, and the jump condition.