Optimal LPV control with hard constraints
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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.
KeywordsHard constraints ℓ2 to ℓ∞ gain linear matrix inequality (LMI) linear parameter varying (LPV) systems LPV control
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