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Author: Henrion, René × End date: 2019 × Start date: 2010 × Type: Text × Subject: Optimal control × WGL Institute: WIAS ×

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    Optimal control of the sweeping process over polyhedral controlled sets
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2015) Colombo, Giovanni; Henrion, René; Hoang, Nguyen D.; Mordukhovich, Boris S.
    The paper addresses a new class of optimal control problems governed by the dissipative and discontinuous differential inclusion of the sweeping/Moreau process while using controls to determine the best shape of moving convex polyhedra in order to optimize the given Bolza-type functional, which depends on control and state variables as well as their velocities. Besides the highly non-Lipschitzian nature of the unbounded differential inclusion of the controlled sweeping process, the optimal control problems under consideration contain intrinsic state constraints of the inequality and equality types. All of this creates serious challenges for deriving necessary optimality conditions. We develop here the method of discrete approximations and combine it with advanced tools of first-order and second-order variational analysis and generalized differentiation. This approach allows us to establish constructive necessary optimality conditions for local minimizers of the controlled sweeping process expressed entirely in terms of the problem data under fairly unrestrictive assumptions. As a by-product of the developed approach, we prove the strong W1;2-convergence of optimal solutions of discrete approximations to a given local minimizer of the continuous-time system and derive necessary optimality conditions for the discrete counterparts. The established necessary optimality conditions for the sweeping process are illustrated by several examples.
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    Path planning and collision avoidance for robots : dedicated to Prof. Dr. Helmut Maurer on the occasion of his 65th birthday
    (Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2011) Gerdts, Matthias; Henrion, René; Hömberg, Dietmar; Landry, Chantal; Maurer, Helmut
    An optimal control problem to find the fastest collision-free trajectory of a robot surrounded by obstacles is presented. The collision avoidance is based on linear programming arguments and expressed as state constraints. The optimal control problem is solved with a sequential programming method. In order to decrease the number of unknowns and constraints a backface culling active set strategy is added to the resolution technique.