TY - JOUR
T1 - Optimal LPV control with hard constraints
AU - White, Andrew
AU - Zhu, Guoming
AU - Choi, Jongeun
N1 - Publisher Copyright:
© 2016, Institute of Control, Robotics and Systems and The Korean Institute of Electrical Engineers and Springer-Verlag Berlin Heidelberg.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.
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.
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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 -