Towards a performance theory of robust adaptive control

Abstract

The main contribution of this thesis is to establish a comparative theory of robust adaptive control designs. We consider dead-zone and projection based robust adaptive controllers for scalar systems, relative degree one, minimum phase linear systems of known high frequency gain, and nonlinear systems in the form of integrator chain. We compare their performance with respect to a worst case non-singular transient cost functional penalising the L^∞ norm on the state, control and control derivative. If a bound on the L^∞  norm of the disturbance is known, it is shown that the dead-zone controller outperforms the projection controller if the a-priori information on the uncertainty level is sufficiently conservative. 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.

A secondary contribution is to present an alternative solution to the problems of robust adaptive control, due to right hand side discontinuity of adaptive law, by developing the so-called hysteresis dead-zone method and showing that the sliding motions are avoided and chattering effects can be mitigated.

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