Rolf Klötzler

Multiobjective dynamic programming

In this paper the method of dynamic programming is carried to recurrence computations of sets of optimal values for discrete dynamic systems and vector-valued objective functions.

Pontryagin’s Maximum Principle for Multidimensional Control Problems

A weak maximum principle is shown for general problems

Distributional Controls in Processes with Hammerstein Type Integral Equations

{\text{minimize}}\,f\left( {x,{\text{ }}w} \right)\,\,{\text{on }}{X_0} \times {X_{\text{1}}}\,{\text{with respect to}}\,linear\,{\text{state constraints}}\,{A_0}x = {A_{\text{1}}}w

On a distributional version of Pontryagin's maximum

in Banach spaces X 0 and local convex topological vector spaces X 1, where f(x, •) is a convex functional on X 1 and X j are linear and continuous operators from X j to a Hilbert space X (j = 0,1). The proved theorem is applied to Dieudonne-Rashevsky-type and relaxed control problems.

Dualität bei diskreten steuerungsproblemen

The present paper deals with an application of a new general duality principle to parametric variational problems for simple integrals on state restrictions. It is developed a both-sided estimate of the optimal value and its numerical realization by means of graph theory methods.

Minimal surfaces as webs of optimal transportation flows

The paper deals with problems of optimal control in which the control in general appears nonlinear and in distributional sense, that means as limits of regular distributional sequences. For this a generalization of necessary conditions of optimality is provided (whibh is also sufficient in the linear case).

A priori Schranken für Eigenwerte von Sturm-Liouvilleschen Eigenwertproblemen

In this paper a modified form of Pontryagins maximum principle is developed, which also holds for problems of optimal control with respect to functions of several independent variables.

A-priori-abschätzungen von optimalwerten zu steuerungsproblemen. teil ii

The paper deals with problems of optimal control under state and control restrictions in which the control appears linear and in distributional sense. For this a generalization of Pontryagins maximum principle is provided.