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Control synthesis for Čaplygin polynomial systems. (English) Zbl 0962.93021

Powerful analytic tools have been developed in order to investigate controllability of nonlinear systems. But, on the other hand, there are no effective synthesis procedures. In other words, we can (more or less) easily determine whether an arbitrary nonlinear system can be steered from any given point into certain prescribed state – but are unable (except in the case of a few special type systems) to design controls that will solve the controllability problem. The control synthesis is important both for theoretical and practical applications of control theory. For example, the feedback design problem can be solved by constructing several piecewise constant controls.
Here, the author discusses a control synthesis procedure for a certain type of polynomial systems known as Čaplygin polynomial systems. Several examples illustrate the method developed here.

MSC:

93B29 Differential-geometric methods in systems theory (MSC2000)
93B50 Synthesis problems
93B05 Controllability
93C10 Nonlinear systems in control theory
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