Global Stabilization of Nonlinear Systems with Inputs Subject to Magnitude and Rate Bounds: A Parametric Optimization Approach

A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of $\eta $-dimensional closed balls...

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Vydané v:SIAM journal on control and optimization Ročník 39; číslo 3; s. 682 - 706
Hlavní autori: Solís-Daun, Julio, Suárez, Rodolfo, Álvarez-Ramírez, José
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Philadelphia Society for Industrial and Applied Mathematics 2000
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ISSN:0363-0129, 1095-7138
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Abstract A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of $\eta $-dimensional closed balls $\mathcal{B}_{\mathbf{r}}^{\eta }(p)$, which are defined by means of a p-norm and a radius vector parameter $\mathbf{r}$. In order to derive the bounded control stabilizer, the resulting procedure implies that gains (as state-functions) are obtained from the solution to a set of c -parameterized nonlinear programming problems. In general, the resulting closed-loop system could be implicitly defined, i.e., consisting of a system of differential equations plus a set of nonlinear algebraic equations (required to compute the control). Special interest is focused on an important class of homogeneous systems that includes a class of globally asymptotically stabilizable systems by linear feedback and bilinear systems. For those systems, the problem of inputs subject to globally bounded rates is also addressed.
AbstractList A bounded feedback control design approach is proposed for the global asymptotic stabilization of a class of nonlinear systems with stable free dynamics. The control inputs and their derivatives are constrained to take values on sets defined by a Cartesian product of $\eta $-dimensional closed balls $\mathcal{B}_{\mathbf{r}}^{\eta }(p)$, which are defined by means of a p-norm and a radius vector parameter $\mathbf{r}$. In order to derive the bounded control stabilizer, the resulting procedure implies that gains (as state-functions) are obtained from the solution to a set of c -parameterized nonlinear programming problems. In general, the resulting closed-loop system could be implicitly defined, i.e., consisting of a system of differential equations plus a set of nonlinear algebraic equations (required to compute the control). Special interest is focused on an important class of homogeneous systems that includes a class of globally asymptotically stabilizable systems by linear feedback and bilinear systems. For those systems, the problem of inputs subject to globally bounded rates is also addressed.
Author Álvarez-Ramírez, José
Solís-Daun, Julio
Suárez, Rodolfo
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  givenname: José
  surname: Álvarez-Ramírez
  fullname: Álvarez-Ramírez, José
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CitedBy_id crossref_primary_10_1137_120886698
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crossref_primary_10_1137_120890156
crossref_primary_10_1137_16M1070141
crossref_primary_10_1002_rnc_693
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