In the first technical chapter of the book, we introduce fundamental notions of stability for dynamical systems, and review ways in which stability can be enforced through feedback control. Central to our treatment is the notion of a control Lyapunov function, which maps stability requirements to control constraints. The most important statement that we make in this chapter is that stability can be enforced as a constraint in an optimization problem, which paves the way to seamless integration with safety, which is treated later in the book. This chapter is organized as follows. In Sect. 2.1, we define stability and Lyapunov functions, and review the main stability verification results based on Lyapunov theory. We introduce control Lyapunov functions in Sect. 2.2, where we also discuss enforcing stability as a constraint in an optimization problem. We present two widely used methods for designing control Lyapunov functions in Sect. 2.3. We conclude with references, discussions, and suggestions for further reading in Sect. 2.4.


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    Title :

    Stabilizing Control Design


    Additional title:

    synth. Lectures on Computer sci.


    Contributors:
    Cohen, Max (author) / Belta, Calin (author)


    Publication date :

    2023-05-16


    Size :

    24 pages





    Type of media :

    Article/Chapter (Book)


    Type of material :

    Electronic Resource


    Language :

    English




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