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**11 - 13**of**13**### The Finite Criss-Cross Method for Hyperbolic Programming

- Informatica, Technische Universiteit Delft, The Netherlands
, 1996

"... In this paper the finite criss-cross method is generalized to solve hyperbolic programming problems. Just as in the case of linear or quadratic programming the criss-cross method can be initialized with any, not necessarily feasible basic solution. Finiteness of the procedure is proved under the ..."

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In this paper the finite criss-cross method is generalized to solve hyperbolic programming problems. Just as in the case of linear or quadratic programming the criss-cross method can be initialized with any, not necessarily feasible basic solution. Finiteness of the procedure is proved under the usual mild assumptions. Some small numerical examples illustrate the main features of the algorithm. Key words: hyperbolic programming, pivoting, criss-cross method iii 1 Introduction The hyperbolic (fractional linear) programming problem is a natural generalization of the linear programming problem. The linear constraints are kept, but the linear objective function is replaced by a quotient of two linear functions. Such fractional linear objective functions arise in economical models when the goal is to optimize profit/allocation type functions (see for instance [12]). The objective function of the hyperbolic programming problem is neither linear nor convex, however there are several ...

### Efficient and Robust Power Management of Reduced Cost Distributed Power Electronics for

"... Batteries in a fuel-cell power system are essential to providing the additional power during the sharp load-transients. This necessitates a power-electronics subsystem (PES), which controls the energy flow between the fuel-cell stack, the battery, and the application load during the transient and in ..."

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Batteries in a fuel-cell power system are essential to providing the additional power during the sharp load-transients. This necessitates a power-electronics subsystem (PES), which controls the energy flow between the fuel-cell stack, the battery, and the application load during the transient and in the steady states. In this paper, a distributed PES (comprising a multimodule dc-dc boost converter) is proposed for a fuel-cell and battery based hybrid power system, which provides higher cost effectiveness, efficiency, and footprint savings. This is realized by interfacing both the fuel-cell stack and the battery to the distributed PES using transfer switches, which are so controlled such that during a load transient, power from both the battery power and the fuel-cell stack is fed to the load via the PES while the stack energy input is adjusted for the new load demand. During the steady-state, the control implements a dynamic-power-management strategy such that only an optimal number of power converter modules of the distributed PES are activated yielding improved optimal energy-conversion efficiency and performance. Furthermore, using a composite Lyapunov-method-based methodology, the effect of dynamic change in the number of active power converter modules with varying load conditions on the stability of the PES is also outlined. Finally, the PES concept is experimentally validated by interfacing a multimodule bidirectional dc-dc boost converter with Nexa ® proton exchange membrane (PEM) fuel-cell stacks from Ballard Power Systems. �DOI: 10.1115/1.3119059�