Necessary conditions for problems with higher derivative bounded state variables

Abstract

This paper combines the separate works of two authors. Tan proves a set of necessary conditions for a control problem with second-order state inequality constraints (see Ref. 1). Russak proves necessary conditions for an extended version of that problem. Specifically, the extended version augments the original problem by including state equality constraints, differential and isopermetric equality and inequality constraints, and endpoint constraints. In addition, Russak (i) relaxes the solvability assumption on the state constraints, (ii) extends the maximum principle to a larger set, (iii) obtains modified forms of the relationH =H _t and of the transversality relation usually obtained in problems of this type, and (iv) proves a condition concerning μ_α(t ¹), the derivative of the multiplier functions at the final time.