A performance comparison of robust adaptive controllers: linear systems

Abstract

We consider robust adaptive control designs for relative degree one, minimum phase linear systems of known high frequency gain. The designs are based on the dead-zone and projection modifications, and we compare their performance w.r.t. a worst case transient cost functional with a penalty on the $$\mathcal{L}$$ ∞ norm of the output, control and control derivative. We establish two qualitative results. If a bound on the $$\mathcal{L}$$ ∞ norm of the disturbance is known and the known a priori bound on the uncertainty level is sufficiently conservative, then it is shown that a dead-zone controller outperforms a projection controller. The complementary result shows that the projection controller is superior to the dead-zone controller when the a priori information on the disturbance level is sufficiently conservative.