Excitation signal design for parameter convergence in adaptive control of linearizable systems

In most adaptive control approaches, parameter convergence to their true values can only be ensured if the closed-loop trajectories provide sufficient excitation for the parameter estimation method. In this paper, the design of excitation signal for the adaptive control of linearizable systems is investigated. Based on a sufficient richness condition, two approaches for generating perturbation signals to achieve a desired level of excitation are presented. Moreover, since constant persistently exciting input may deteriorates control performance, we provide a formal design technique for adjusting the excitation magnitude on-line to meet the conflicting objectives of control and identification. The algorithm attenuates the PE signal as parameter convergence is achieved and re-activates it only when required. A simulation example is used to illustrate the developed procedure and ascertain our theoretical results.