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.


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    Title :

    Controllability Problem


    Additional title:

    Springer Optimization


    Contributors:


    Publication date :

    2022-04-12


    Size :

    25 pages





    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English






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