Eckhard Arnold

Applying New Numerical Algorithms to the Solution of Discrete-Time Optimal Control Problems

In this paper optimal control problems are transformed into structured large-scale nonlinear programming problems. The method of sequential quadratic programming is used for their numerical solution. After an overview about the method, single modules are discussed with respect to the treatment of the problem dimension. Derivatives of nonlinear equations are calculated by automatic differentiation. The sparse Hessian of the problem is partitioned into separate blocks that are updated numerically. Convex linear-quadratic subproblems are treated with a polynomial-time algorithm. The resulting large sparse systems of linear equations are solved with direct factorization. The implementation of the algorithm in the HQP tool is compared with alternative solvers, using a typical optimal control problem as example and increasing its dimension.

Operational Control of Integrated Quality and Quantity in Water Systems

Abstract The paper considers an operational control of water supply and distribution systems. An integrated formulation of the operational control problem is presented which allows to achieve truly optimal operation of a water network with respect to the water quantity and quality. Two approaches, implicit and explicit, to solve the problem are presented and discussed. A mixed-integer implicit solver and a genetic explicit solver are derived and tested on Neuhaus Water Supply System.

An SQP-type solution method for constrained discrete-time optimal control problems

The considered nonlinear, constrained discrete-time optimal control problem is stated as follows:

MODEL BASED PREDICTIVE CONTROL OF RIVER RESERVOIRS

J = F({x^N}) + \sum\limits_{k = 0}^{N -1} {f_0^k} ({x^k},{u^k}) \to Min

Modell-prädiktive Trajektoriengenerierung für flachheitsbasierte Folgeregelungen am Beispiel eines Hafenmobilkrans (Model-predictive Trajectory Generation for Flatness-based Nonlinear Tracking Control with Application to Boom Cranes)

subject to the state equation:

Anwendung genetischer Algorithmen zur optimalen Steuerung von Pumpen in Trinkwasserversorgungssystemen

{x^{k + 1}} = {f^k}({x^k},{u^k}),k = 0, \ldots ,N -1,