joint work with Christof Büskens
In many industrial applications solutions of optimal control problems are used, where the need for low computational times outweighs the need for absolute optimality. For solutions of fully discretized optimal control problems we propose two methods to approximate the solutions of problems with modified parameter values in real-time by using sensitivity derivatives. Using the NLP solver WORHP, the quality and applicability of both methods are illustrated by the application of an oscillation free movement of a container crane in a high rack warehouse.
joint work with Boris Mordukhovich
The talk concerns the study a new class of optimal control problems of (Moreau) sweeping process. A major motivation for our study of such challenging optimal control problems comes from the application to the crowd motion model in a practically adequate planar setting with nonconvex but prox-regular sweeping sets. Based on a constructive discrete approximation approach and advanced tools of variational analysis and generalized differentiation, we derive necessary optimality conditions for discrete-time and continuous-time sweeping control systems expressed entirely via the problem data.
In this talk we study certain classes of fixed end-point optimal control problems of Lagrange with nonlinear dynamics, inequality and equality isoperimetric restraints and pointwise mixed time-state-control inequality and equality constraints. The diminishing of the gap between the classical necessary and sufficient conditions for optimality becomes the main novelty of the talk. In fact, we illustrate the properties of the new theory by exhibiting some singular and purely essentially bounded optimal controls satisfying all conditions of the corresponding sufficiency theorems.