Abstract
The focus of this paper is on the design of state constrained controllers which are robust to time invariant uncertain variables. Polynomial Chaos spectral expansion is used to parameterize the uncertain variables, which permits evaluation of the evolution of the uncertain states. The co-efficients of the truncated polynomial chaos expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A mapping into Bernstein polynomial space permits determination of bounds on the evolving states. Linear programming is used on the deterministic set of equation with constraints as the predetermined bounds to determine controllers which are robust to the epistemic uncertainties. Numerical examples are used to illustrate the benefit of the proposed technique for the design of rest-to-rest controllers subject to deformation constraints; which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass system.
| Original language | English (US) |
|---|---|
| Title of host publication | 2016 American Control Conference, ACC 2016 |
| Publisher | Institute of Electrical and Electronics Engineers Inc. |
| Pages | 2005-2010 |
| Number of pages | 6 |
| ISBN (Electronic) | 9781467386821 |
| DOIs | |
| State | Published - Jul 28 2016 |
| Event | 2016 American Control Conference, ACC 2016 - Boston, United States Duration: Jul 6 2016 → Jul 8 2016 |
Publication series
| Name | Proceedings of the American Control Conference |
|---|---|
| Volume | 2016-July |
| ISSN (Print) | 0743-1619 |
Other
| Other | 2016 American Control Conference, ACC 2016 |
|---|---|
| Country | United States |
| City | Boston |
| Period | 7/6/16 → 7/8/16 |
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All Science Journal Classification (ASJC) codes
- Electrical and Electronic Engineering
Cite this
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State constrained controller design for uncertain linear systems using polynomial Chaos. / Nandi, Souransu; Migeon, Victor; Singh, Tarunraj; Singla, Puneet.
2016 American Control Conference, ACC 2016. Institute of Electrical and Electronics Engineers Inc., 2016. p. 2005-2010 7525213 (Proceedings of the American Control Conference; Vol. 2016-July).Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
TY - GEN
T1 - State constrained controller design for uncertain linear systems using polynomial Chaos
AU - Nandi, Souransu
AU - Migeon, Victor
AU - Singh, Tarunraj
AU - Singla, Puneet
PY - 2016/7/28
Y1 - 2016/7/28
N2 - The focus of this paper is on the design of state constrained controllers which are robust to time invariant uncertain variables. Polynomial Chaos spectral expansion is used to parameterize the uncertain variables, which permits evaluation of the evolution of the uncertain states. The co-efficients of the truncated polynomial chaos expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A mapping into Bernstein polynomial space permits determination of bounds on the evolving states. Linear programming is used on the deterministic set of equation with constraints as the predetermined bounds to determine controllers which are robust to the epistemic uncertainties. Numerical examples are used to illustrate the benefit of the proposed technique for the design of rest-to-rest controllers subject to deformation constraints; which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass system.
AB - The focus of this paper is on the design of state constrained controllers which are robust to time invariant uncertain variables. Polynomial Chaos spectral expansion is used to parameterize the uncertain variables, which permits evaluation of the evolution of the uncertain states. The co-efficients of the truncated polynomial chaos expansion are determined using the Galerkin projection resulting in a set of deterministic equations. A mapping into Bernstein polynomial space permits determination of bounds on the evolving states. Linear programming is used on the deterministic set of equation with constraints as the predetermined bounds to determine controllers which are robust to the epistemic uncertainties. Numerical examples are used to illustrate the benefit of the proposed technique for the design of rest-to-rest controllers subject to deformation constraints; which are robust to uncertainties in the stiffness coefficient for the benchmark spring-mass system.
UR - http://www.scopus.com/inward/record.url?scp=84992051583&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84992051583&partnerID=8YFLogxK
U2 - 10.1109/ACC.2016.7525213
DO - 10.1109/ACC.2016.7525213
M3 - Conference contribution
AN - SCOPUS:84992051583
T3 - Proceedings of the American Control Conference
SP - 2005
EP - 2010
BT - 2016 American Control Conference, ACC 2016
PB - Institute of Electrical and Electronics Engineers Inc.
ER -