M. Soledad Aronna

QUADRATIC ORDER CONDITIONS FOR BANG-SINGULAR EXTREMALS

This paper deals with optimal control problems for systems affine in the control variable. We consider 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 derive a second order sufficient condition for the scalar control case.

A Shooting Algorithm for Optimal Control Problems with Singular Arcs

In this article, we propose a shooting algorithm for a class of optimal control problems for which all control variables appear linearly. The shooting system has, in the general case, more equations than unknowns and the Gauss–Newton method is used to compute a zero of the shooting function. This shooting algorithm is locally quadratically convergent, if the derivative of the shooting function is one-to-one at the solution. The main result of this paper is to show that the latter holds whenever a sufficient condition for weak optimality is satisfied. We note that this condition is very close to a second order necessary condition. For the case when the shooting system can be reduced to one having the same number of unknowns and equations (square system), we prove that the mentioned sufficient condition guarantees the stability of the optimal solution under small perturbations and the invertibility of the Jacobian matrix of the shooting function associated with the perturbed problem. We present numerical tests that validate our method.

A note on systems with ordinary and impulsive controls

We investigate an everywhere defined notion of solution for control systems whose dynamics depend nonlinearly on the control

L1 limit solutions for control systems

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On optimal control problems with impulsive commutative dynamics

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Ensuring successful introduction of Wolbachia in natural populations of Aedes aegypti by means of feedback control

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Global stabilizing feedback law for a problem of biological control of mosquito-borne diseases

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Second order necessary and sufficient optimality conditions for singular solutions of partially-affine control problems

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Correction to: Optimal control of infinite dimensional bilinear systems: application to the heat and wave equations

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Infimum Gaps for Limit Solutions

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