Abstract
We use the topological tool of Nielsen fixed-point theory to study the controllability of perturbed linear control processes whose control space can be reduced to a finite-dimensional one. These methods produce a lower bound on the number of controls that achieve a given target. We concentrate particularly on the case where the perturbation has sublinear growth, and we exhibit examples of multiple controls of various types that are detected by the Nielsen theory method.
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Communicated by R. Conti
This research was partly supported by the Research Grant “Teoria del Controllo dei Sistemi Dinamici,” Ministero della Pubblica Istruzione, Roma, Italy.
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Brown, R.F., Zezza, P. Multiple local solutions to nonlinear control processes. J Optim Theory Appl 67, 463–485 (1990). https://doi.org/10.1007/BF00939645
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DOI: https://doi.org/10.1007/BF00939645