Adaptive optimal robust control in gap metric

Traditional adaptive control algorithms are not robust to dynamic uncertainties. A new self-tuning regulator is designed based on optimal robust control such that all signals in the closed-loop remain bounded for any bounded inputs regardless of the uncertainty in the parameters of the nominal plant and the presence of the non-parametric uncertainty. The graphs of both the plant and the controller are defined by using coprime factorization. A generalized uncertainty called graph uncertainty is proposed equivalent to the coprime factor uncertainty, which can be calculated through orthogonal projection in the gap-metric. The stability and the robustness of the closed-loop system are analyzed, and the condition of robust stability is given. Simulations show that the adaptive optimal robust controller is superior to adaptive H_∞ controller under the bigger graph uncertainty.