Abstract
This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ℓ2 to ℓ∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H∞ performance criterion is also considered as well. Controllers with a guaranteed ℓ2 to ℓ∞ gain and a guaranteed H∞ performance (ℓ2 to ℓ2 gain) are a special family of mixed H2=H∞ controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed ℓ2 to ℓ∞ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ℓ2 to ℓ∞ gain and >H∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.
| Original language | English |
|---|---|
| Pages (from-to) | 148-162 |
| Number of pages | 15 |
| Journal | International Journal of Control, Automation and Systems |
| Volume | 14 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2016 Feb 1 |
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All Science Journal Classification (ASJC) codes
- Control and Systems Engineering
- Computer Science Applications
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Optimal LPV control with hard constraints. / White, Andrew; Zhu, Guoming; Choi, Jongeun.
In: International Journal of Control, Automation and Systems, Vol. 14, No. 1, 01.02.2016, p. 148-162.Research output: Contribution to journal › Article
TY - JOUR
T1 - Optimal LPV control with hard constraints
AU - White, Andrew
AU - Zhu, Guoming
AU - Choi, Jongeun
PY - 2016/2/1
Y1 - 2016/2/1
N2 - This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ℓ2 to ℓ∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H∞ performance criterion is also considered as well. Controllers with a guaranteed ℓ2 to ℓ∞ gain and a guaranteed H∞ performance (ℓ2 to ℓ2 gain) are a special family of mixed H2=H∞ controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed ℓ2 to ℓ∞ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ℓ2 to ℓ∞ gain and >H∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.
AB - This paper considers the optimal control of polytopic, discrete-time linear parameter varying (LPV) systems with a guaranteed ℓ2 to ℓ∞ gain. Additionally, to guarantee robust stability of the closed-loop system under parameter variations, H∞ performance criterion is also considered as well. Controllers with a guaranteed ℓ2 to ℓ∞ gain and a guaranteed H∞ performance (ℓ2 to ℓ2 gain) are a special family of mixed H2=H∞ controllers. Normally, H2 controllers are obtained by considering a quadratic cost function that balances the output performance with the control input needed to achieve that performance. However, to obtain an optimal controller with a guaranteed ℓ2 to ℓ∞ gain (closely related to the physical performance constraint), the cost function used in the H2 control synthesis minimizes the control input subject to maximal singular-value performance constraints on the output. This problem can be efficiently solved by a convex optimization with linear matrix inequality (LMI) constraints. The main contribution of this paper is the characterization of the control synthesis LMIs used to obtain an LPV controller with a guaranteed ℓ2 to ℓ∞ gain and >H∞ performance. A numerical example is presented to demonstrate the effectiveness of the convex optimization.
UR - http://www.scopus.com/inward/record.url?scp=84957951173&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84957951173&partnerID=8YFLogxK
U2 - 10.1007/s12555-014-0248-4
DO - 10.1007/s12555-014-0248-4
M3 - Article
AN - SCOPUS:84957951173
VL - 14
SP - 148
EP - 162
JO - International Journal of Control, Automation and Systems
JF - International Journal of Control, Automation and Systems
SN - 1598-6446
IS - 1
ER -