An adaptive controller to provide near optimal LQR performance

Here we consider the problem of providing near optimal LQR performance for a large set of admissible models. We consider the single-input single-output (SISO) setting, and prove that given a compact set of controllable and observable plant models of a fixed order, we can construct a single nonlinear periodic controller of low complexity which provides near optimal LQR performance for every admissible plant model. This controller is proven to provide strong linear-like bounds on the state behaviour.

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