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Nonlinear state feedback for \(\ell^ 1\) optimal control. (English) Zbl 0798.93030

Summary: This paper considers \(\ell^ 1\) optimal control problems with full state feedback. In contrast to \({\mathcal H}^ \infty\) optimal control, previous work has shown that linear \(\ell^ 1\) optimal controllers can be dynamic and of arbitrarily high order. However, this paper shows that continuous memoryless nonlinear state feedback performs as well as dynamic linear state feedback. The derivation, which is nonconstructive, relies on concepts from viability theory.

MSC:

93C10 Nonlinear systems in control theory
93B52 Feedback control
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References:

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