Abstract
AbstractThe certainty equivalent control has achieved asymptotic tracking stability of linearizable systems in the presence of parametric uncertainty. However, two major drawbacks remain to be tackled, namely, the risk of running into singularity for the calculated control input and the poor transient behaviour arising frequently in a general adaptive system. For the first problem, a high gain control is activated in place of the certainty equivalent control until the risk is bypassed. Among others, it requires less control effort by taking advantages of the bounds for the input vector field. Moreover, the switching mechanism is smooth and hence avoids possible chattering behaviour. Next, to solve the second problem, a new type of update algorithm guaranteeing the exponential stability of the overall closed‐loop system, on a weaker persistent excitation (PE) condition, is proposed. In particular, it requires no filtering of the regressor and hence is easier to implement. Simulation results demonstrating the validity of the proposed design are given in the final. Copyright © 2006 John Wiley & Sons, Ltd.
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