Abstract
The problem of the admissible feedback synthesis for nonlinear systems with discontinuous right-hand side is considered. Sufficient conditions for solvability of this problem are proved. The neighborhood of the origin is broken in a finite number of domains G 1,G 2,…,G k . In each G j a control system \(\dot{x}=f_{j}(x,u)\) is given. The problem of the admissible feedback synthesis is completely studied for control systems of the form \(\dot{x}=a_{j}(x)+\gamma_{j}(x,u) b_{j}(x)\), where \(u\in \Omega_{j} \subset \Bbb{R}\) for x∈G j . The controllability function method is used to construct the feedback control.
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Communicated by B.T. Polyak
The work was partially supported by Polish Ministry of Science and High Education grant N N514 238438.
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Korobov, V.I., Korotyayeva, Y.V. Feedback Control Design for Systems with x-Discontinuous Right-Hand Side. J Optim Theory Appl 149, 494–512 (2011). https://doi.org/10.1007/s10957-011-9800-z
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DOI: https://doi.org/10.1007/s10957-011-9800-z