Armin Rund

Efficient high-resolution RF pulse design applied to simultaneous multi-slice excitation

RF pulse design via optimal control is typically based on gradient and quasi-Newton approaches and therefore suffers from slow convergence. We present a flexible and highly efficient method that uses exact second-order information within a globally convergent trust-region CG-Newton method to yield an improved convergence rate. The approach is applied to the design of RF pulses for single- and simultaneous multi-slice (SMS) excitation and validated using phantom and in vivo experiments on a 3T scanner using a modified gradient echo sequence.

On a State-Constrained PDE Optimal Control Problem arising from ODE-PDE Optimal Control

The subject of this paper is an optimal control problem with ODE as well as PDE constraints. As it was inspired, on the one hand, by a recently investigated flight path optimization problem of a hypersonic aircraft and, on the other hand, by the so called ”rocket car on a rail track“-problem from the pioneering days of ODE optimal control, we would like to call it ”hypersonic rocket car problem”. While it features essentially the same ODE-PDE coupling structure as the aircraft problem, the rocket car problem’s level of complexity is significantly reduced. Due to this fact it is possible to obtain more easily interpretable results such as an insight into the structure of the active set and the regularity of the adjoints. Therefore, the rocket car problem can be seen as a prototype of an ODE-PDE optimal control problem. The main objective of this paper is the derivation of first order necessary optimality conditions.

A convex penalty for switching control of partial differential equations

Abstract A convex penalty for promoting switching controls for partial differential equations is introduced; such controls consist of an arbitrary number of components of which at most one should be simultaneously active. Using a Moreau–Yosida approximation, a family of approximating problems is obtained that is amenable to solution by a semismooth Newton method. The efficiency of this approach and the structure of the obtained controls are demonstrated by numerical examples.

Parametric Sensitivity Analysis of Fast Load Changes of a Dynamic MCFC Model

Molten carbonate fuel cells are well suited for stationary power production and heat supply. In order to enhance service lifetime, hot spots, respectively, high temperature gradients inside the fuel cell have to be avoided. In conflict with that, there is the desire to achieve faster load changes while temperature gradients stay small. For the first time, optimal fast load changes have been computed numerically, including a parametric sensitivity analysis, based on a mathematical model of Heidebrecht. The mathematical model allows for the calculation of the dynamical behavior of molar fractions, molar flow densities, temperatures in gas phases, temperature in solid phase, cell voltage, and current density distribution. The dimensionless model is based on the description of physical phenomena. The numerical procedure is based on a method of line approach via spatial discretization and the solution of the resulting very large scale optimal control problem by a nonlinear programming approach.

Optimal control for a simplified 1D fuel cell model

Molten carbonate fuel cells are a promising technology for the operation of future stationary power plants. To enhance service life, a detailed knowledge of their dynamical behaviour is essential. The possibility of fast and save load changes is important for daily operation of these power plants. To predict the dynamical behaviour of fuel cells a hierachy of mathematical models has been developed in the past. Recently a systematic model reduction was applied to a 2D crossflow model. We present here the new 1D counterflow model and discuss a suitable discretization method. Accordingly we set up a method of optimal control following the first-discretize-then-optimize approach. Results are shown for simulation and optimal control in the case of load changes.

Simultaneous multislice refocusing via time optimal control

Joint design of minimum duration RF pulses and slice‐selective gradient shapes for MRI via time optimal control with strict physical constraints, and its application to simultaneous multislice imaging.

Nonconvex penalization of switching control of partial differential equations

Abstract This paper is concerned with optimal control problems for parabolic partial differential equations with pointwise in time switching constraints on the control. A standard approach to treat constraints in nonlinear optimization is penalization, in particular using L 1 -type norms. Applying this approach to the switching constraint leads to a nonsmooth and nonconvex infinite-dimensional minimization problem which is challenging both analytically and numerically. Adding H 1 regularization or restricting to a finite-dimensional control space allows showing existence of optimal controls. First-order necessary optimality conditions are then derived using tools of nonsmooth analysis. Their solution can be computed using a combination of Moreau–Yosida regularization and a semismooth Newton method. Numerical examples illustrate the properties of this approach.

Transfer of the bryson-denham-dreyfus approach for state-constrained ODE optimal control problems to elliptic optimal control problems

We transfer ideas known since the 1960ies from the theory of state-constrained optimal control problems for ordinary differential equations to optimal control problems for elliptic partial differential equations with distributed controls. Replacing the state constraint by equivalent terms leads to new kinds of topology-shape optimal control problems, which gives access to new necessary conditions for elliptic optimal control problems. These new necessary conditions reveal some striking advantages: Higher regularity of the multiplier associated with the state constraint and, in consequence, the ability to apply numerical solvers which do not need any regularization in order to deal with the multipliers. Moreover, the numerical solution can be splited between active and inactive set which improves the efficiency. Since the new necessary conditions can be regarded as a free boundary problem for the unknown interface in-between active and inactive sets, we use Shape-Calculus to formulate a Shape-Newton Scheme in function space in order to solve the optimality system. A finite element discretized version of this scheme shows encouraging results like a low number of iterations and high accuracy in detection of the active sets. Moreover, the numerical results indicate grid independency of this method and the method seems to be able to handle also changes of the topology of the active set.