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...
Saved in:
| Published in: | SIAM journal on control and optimization Vol. 39; no. 3; pp. 682 - 706 |
|---|---|
| Main Authors: | , , |
| Format: | Journal Article |
| Language: | English |
| Published: |
Philadelphia
Society for Industrial and Applied Mathematics
2000
|
| Subjects: | |
| ISSN: | 0363-0129, 1095-7138 |
| Online Access: | Get full text |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Summary: | 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. |
|---|---|
| Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 content type line 14 |
| ISSN: | 0363-0129 1095-7138 |
| DOI: | 10.1137/S0363012997330233 |