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Implementation of two-level algorithms using fixed-point arithmetic. (English) Zbl 0594.93025

Summary: The effect of using fixed-point arithmetic in the digital implementation of two-level control algorithms is examined. Analytical expressions are developed to predict the change in the expected minimum cost and associated matrices. It is shown that there is a favourable match between the analytical predictions and averaged simulation experiments. The use of finite-precision machines increases the expected theoretical minimum cost and makes the two-level algorithm become slow and thus require excessive iterations to converge.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93C05 Linear systems in control theory
93C55 Discrete-time control/observation systems
49M99 Numerical methods in optimal control
65G30 Interval and finite arithmetic
65K10 Numerical optimization and variational techniques
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References:

[1] FRANKLIN G. F., Digital Control of Dynamic Systems (1980)
[2] DOI: 10.1109/TSMC.1977.4309677 · Zbl 0353.93006
[3] MAHMOUD M. S., Discrete Systems Analysis, Conirol and Optimization (1984) · Zbl 0548.93053
[4] SAGE A. P., Optimum Systems Control (1977) · Zbl 0388.49002
[5] SINGH M. G., Systems Decomposition, Optimization and Control (1978)
[6] DOI: 10.1109/TAES.1981.309093
[7] DOI: 10.1109/TASSP.1977.1162977 · Zbl 0378.93055
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