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Extremals in the problem of minimum time obstacle avoidance for a 2D double integrator system

Osmolovskii N. P., Figura A., Koska M., Wojtowicz M.

Control and Cybernetics

2015

Vol. 44, no. 2

185--209

This paper provides an analysis of time optimal control problem of motion of a material point in the plane outside the given circle, without friction. The point is controlled by a force whose absolute value is limited by one. The closure of exterior of the circle plays the role of the state constraint. The analysis of the problem is based on the minimum principle.

Optimality conditions for a class of optimal boundary control problems with quasilinear elliptic equations

Casas E., Dhamo V.

Control and Cybernetics

2011

Vol. 40, no 2

457-490

First- and second-order optimality conditions are established for the boundary optimal control of quasilinear elliptic equations with pointwise constraints on the control. The theory is developed for Neumann controls in polygonal domains of dimension two. For the derivation of second-order sufficient optimality conditions, which is the main goal of this paper, the regularity of the solutions to the state equation and its linearization is studied in detail. Moreover, a Pontryagin principle is proved. The main difficulty in the analysis of these problems is the nonmonotone character of the state equation.