Optimal LPV control with hard constraints
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- 作者：Andrew White ; Guoming Zhu ; Jongeun Choi
- 关键词：Hard constraints ; ℓ2 to ℓ∞ gain ; linear matrix inequality (LMI) ; linear parameter varying (LPV) systems ; LPV control
- 刊名：International Journal of Control, Automation and Systems
- 出版年：2016
- 出版时间：February 2016
- 年：2016
- 卷：14
- 期：1
- 页码：148-162
- 全文大小：1,105 KB
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Guoming Zhu (1) (2)
Jongeun Choi (1) (2)
1. Department of Mechanical Engineering, Michigan State University, East Lansing, MI, 48824, USA
2. Department of Electrical Engineering, Michigan State University, East Lansing, MI, 48824, USA - 刊物类别：Engineering
- 刊物主题：Control Engineering
- 出版者：The Institute of Control, Robotics and Systems Engineers and The Korean Institute of Electrical Engi
- ISSN：2005-4092
文摘
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 H 2=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. Keywords Hard constraints ℓ2 to ℓ∞ gain linear matrix inequality (LMI) linear parameter varying (LPV) systems LPV control