Abstract
Existence of viable (controlled invariant) solutions of a control system is investigated by using the concept of viability kernel of a set (largest closed controlled invariant subset.) Results are exploited to prove convergence of a modified version of the zero dynamics algorithm to a closed viability domain. This is needed to obtain dynamical feedbacks, i.e., differential equations governing the evolution of viable controls. Among such differential equations, the one leading to heavy solutions (in the sense of heavy trends), governing evolution of controls with minimal velocity is singled out.
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Aubin, JP., Frankowska, H. (1991). Viability Kernel of Control Systems. In: Byrnes, C.I., Kurzhansky, A.B. (eds) Nonlinear Synthesis. Progress in Systems and Control Theory, vol 9. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4757-2135-5_2
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DOI: https://doi.org/10.1007/978-1-4757-2135-5_2
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