On Second-Order Necessary Conditions for Broken Extremals

On Second-Order Necessary Conditions for Broken Extremals

We consider optimal control problems with initial–final state equality and inequality constraints and running mixed state-control equality constraints given by smooth functions. The mixed constraints satisfy the regularity assumption of linear independence of gradients with respect to the control. We present simple proofs of second-order necessary conditions for (extended) weak minimum for extr...

Quadratic order conditions for bang-singular extremals

This paper deals with optimal control problems for systems affine in the control variable. We have nonnegativity constraints on the control, and finitely many equality and inequality constraints on the final state. First, we obtain second order necessary optimality conditions. Secondly, we get a second order sufficient condition for the scalar control case. The results use in an essential way t...

Optimality of Broken Extremals

In this paper we analyse the optimality of broken Pontryagin extremal for an n -dimensional affine control system with a control parameter, taking values in a k dimensional closed ball. We prove the optimality of broken normal extremals when n = 3 and the controllable vector fields form a contact distribution, and when the Lie algebra of the controllable fields is locally orthogonal to the sing...

Marginal values and second-order necessary conditions for optimality

Second-order Necessary Conditions for Optimal Impulsive Control

Second-order conditions of optimality for an impulsive control problem are presented and derived from those for an appropriate abstract optimization problem with equality, inequality and set inclusion constraints. An important feature of these conditions is that they do not degenerate for abnormal control processes in spite of the absence of a priori normality assumptions on the data of the pro...