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On The Determination Of Parametric Linear Quadratic Regulators for Parametric Systems

Graziano Chesi, Tiantian Shen
This paper addresses the problem of determining parametric linear quadratic regulators (LQRs) for continuous-time linear-time invariant (LTI) systems affected by parameters. In particular, the paper considers the problem of determining a parametric controller that minimizes the worst-case cost over the set of admissible parameters. It is shown that a candidate for such a controller can be obtained by solving a convex optimization problem with linear matrix inequality (LMI) constraints. This candidate is guaranteed to approximate arbitrarily well the sought controller by sufficiently increasing the size of the LMIs. Moreover, a condition for establishing the optimality of the found candidate is provided. Some numerical examples illustrate the proposed methodology.
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