Controllability Problem

Yuri Sachkov
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Yuri Sachkov: Program Systems Institute

Chapter Chapter 2 in Introduction to Geometric Control, 2022, pp 21-45 from Springer

Abstract: Abstract In this chapter we study the controllability problem. First we prove the classic Kalman controllability test for linear autonomous systems and a related sufficient local controllability condition for nonlinear systems via linearisation. Then we prove the fundamental Nagano–Sussmann Orbit theorem and its corollaries, including the Rashevskii–Chow and the Frobenius theorems. Finally, we prove an important Krener’s theorem on attainable sets of full-rank systems. Theoretical development is illustrated by the study of systems given in Sect. 1.1.1 .

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-031-02070-4_2

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DOI: 10.1007/978-3-031-02070-4_2

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