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$H_{∞}$control for non-linear stochastic systems: the output-feedback case
| Content Provider | Scilit |
|---|---|
| Author | Berman, N. Shaked, U. |
| Copyright Year | 2008 |
| Description | The H$ _{∞}$ output-feedback control problem for non-linear stochastic systems is considered. A solution for a large class of non-linear stochastic systems is introduced (including non-linear diffusion systems as a subclass). This solution is based on a bounded real lemma for non-linear stochastic systems that was previously established via a stochastic dissipativity concept. The theory yields sufficient conditions for the closed-loop system to possess a prescribed L$ _{2}$-gain bound in terms of two Hamilton Jacobi inequalities: one that is associated with the state feedback part of the problem is n-dimensional (where n is the underlying system's state dimension) and the other inequality that stems from the estimation part is 2n-dimensional. Both stationary and non–stationary systems are considered. Stability of the closed-loop system is established, both in the mean-square and the in-probability senses. As the solution to the Hamilton Jacobi inequalities may, in general, lead to a non–realisable state estimator, a modification of the associated 2n-dimensional Hamilton Jacobi inequality is made in order to circumvent this realisation problem, while preserving the system's L$ _{2}$-gain bound. For time-invariant systems, the problem of robust output-feedback is considered in the case of norm-bounded uncertainties. A solution is then derived in terms of linear state-dependent matrix inequalities. |
| Related Links | http://www.nt.ntnu.no/users/skoge/prost/proceedings/ifac2005/Fullpapers/02535.pdf |
| Ending Page | 1746 |
| Page Count | 14 |
| Starting Page | 1733 |
| ISSN | 00207179 |
| e-ISSN | 13665820 |
| DOI | 10.1080/00207170701840136 |
| Journal | International Journal of Control |
| Issue Number | 11 |
| Volume Number | 81 |
| Language | English |
| Publisher | Informa UK Limited |
| Publisher Date | 2008-09-18 |
| Access Restriction | Open |
| Subject Keyword | Journal: International Journal of Control Automotive Engineering Stochastic Systems Nonlinear Systems Disturbance Attenuation Linear State-dependent Noise Matrix Inequalities Stochastic Stability |
| Content Type | Text |
| Resource Type | Article |
| Subject | Control and Systems Engineering Computer Science Applications |
