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Optimal control for large-scale systems: A recursive approach. (English) Zbl 0820.93003

A recursive fixed-point-type method is presented for the study of the optimal control problem of large-scale systems. The numerical calculation of the exact optimal control is impracticable owing to the complexity of large-scale systems. To reduce the computations and investigate the properties of large-scale systems, intuition and experience may indicate how to split a large-scale design problem into a set of simpler subsystem problems. Recently, the problem of decomposition of a large-scale system based on the perturbation method has received the attention of many researchers. The control is obtained by decomposition of the system to ‘epsilon coupled’ subsystems so that only low-order systems are involved in algebraic computations. It is shown that the developed reduced-order parallel algorithms converge to the desired solution. Owing to its recursive nature, the presented method is conceptually simple and very suitable for parallel programming. An illustrative numerical example is given to verify the proposed approach.

MSC:

93A15 Large-scale systems
93B11 System structure simplification
93B40 Computational methods in systems theory (MSC2010)
49N10 Linear-quadratic optimal control problems
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References:

[1] DOI: 10.1080/00207177808922407 · Zbl 0373.93003 · doi:10.1080/00207177808922407
[2] DOI: 10.1007/BFb0005209 · doi:10.1007/BFb0005209
[3] HILL D., Experiments in Computational Matrix Algebra (1988) · Zbl 0668.65023
[4] JAMSHIDI M., Large-Scale Systems Modeling and Control (1983) · Zbl 0646.93003
[5] DOI: 10.1049/piee.1969.0166 · doi:10.1049/piee.1969.0166
[6] KWAKHRNAAK H., Linear Optimal Control System (1972)
[7] DOI: 10.1109/TPAS.1985.319158 · doi:10.1109/TPAS.1985.319158
[8] DOI: 10.1109/TAC.1978.1101704 · Zbl 0385.93001 · doi:10.1109/TAC.1978.1101704
[9] DOI: 10.1016/0005-1098(90)90010-F · Zbl 0701.93104 · doi:10.1016/0005-1098(90)90010-F
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