Two-level Decomposition Research Articles

Global steady state simulation of complex technological systems - an unified approach

In general, mathematical models of steady state simulation schemas of complex technological processes are formed by sets of algebraic equations. The formal description of global approach to the solution of such sets is presented. The utilization of preliminary solution of linear equations of the set for its reduction and for the expression of dependency of the so-called eliminated variables on the remaining ones, as arguments of the reduced set, (i.e. the first decomposition level) is considered. The determination of disjoint subsystems of the reduced set (i.e. the subsets of nonlinear equations which may be solved serially and independently of each other in a sequence) and the determination of the hierarchy of their solution, when there are several such subsystems, is meant as the second decomposition level. The possibility of including of special models with particular computational algorithms in the equation-like model of complex system and the way of solution of such a problem with the mentioned two-level decomposition is also discussed. The including of both types of decomposition and the solution of the reduced set of equations in common computational block is dealt with.

The evaluation of the spectrum of multi-level logic networks

The relationship between the spectral coefficients of the functions in a two-level decomposition and the overall function spectrum are considered, and an algebraic relationship established to give the latter from the former. These algebraic relationships hold for binary or higher-valued logic systems. The extension to three- or more-level realisations is mathematically straightforward.

New Results on the Two-Level Decomposition and Coordination of the Linear Regulator Problem

The problem of the optimal regulator for linear large scale plants is studied. The procedure is based on the concept of hierarchically structured multilevel systems. For this purpose the originally stated problem is decomposed into a sum of infimal subproblems which are to coordinate in an appropriate manner. This paper presents some results from a more detailed investigation in which some known decomposition and coordination methods are examined with respect to their applicability for process computer controlled systems. Some appropiate methods have been developed and their usability is demonstrated by numerical examples.

Über dekompositionsmethoden der optimierung komplexer chemisch-technologischer systeme

Two two-level decomposition methods for complex chemical engineering system optimization have been developed. In the first one input and output block variables are fixed. Two variations of this method are proposed: the variation with complete and that with incomplete decomposition. In the second method the block variable interrelations are transfered into the objective function.

Decomposition technique for minimum time trajectories

A decomposition technique is presented for minimum-time trajectories which are characterized by intermediate constraints and discontinuities. The optimization of such multiple are trajectories is usually a formidable task. One optimization method, trajectory decomposition, breaks the original trajectory at points of discontinuity into separate arcs and then optimizes each are subject to prescribed boundary conditions. This constitutes a first level of control. Each first-level solution is evaluated by a second-level controller, which iteratively specifies new are boundary conditions in order to achieve an optimum solution. Unfortunately, this two-level method cannot be applied directly to minimum-time trajectories. The two-level trajectory decomposition method is extended here to a three-level technique for treating the minimum-time trajectory. The first level again optimizes each are for specified intervention parameters. The new second level, the time interface controller, exploits certain homogeneity properties to satisfy time transversality conditions at all boundaries and to couple the first-level solution arcs in time. The third level, the state interface controller, satisfies state transversality conditions at the arc junctions iteratively while driving the trajectory to its optimum. The new three-level procedure represents a feasible decomposition because each solution trajectory in the iterative sequence is physically realizable. The technique also offers a decentralization of control effort and reduction of initial-value sensitivities. An example problem is formulated.

Control model simplification using a two-level decomposition technique

Control model simplification using a two-level decomposition technique