Unfalsified adaptive control with weak cost-detectability

In this paper, the unfalsified adaptive control [1] is reestablished with a new term, weak cost-detectability, replacing the cost-detectability. The weak cost-detectability implies that a bounded property of a cost function for the final controller in a switching algorithm is sufficient for stability of an underlying adaptive control system, but the converse may not be true. With the weak cost-detectability instead of the cost-detectability, more choices of cost functions can be employed in the unfalsified adaptive control. Some of the choices introduced in this paper are shown to be greater than the cost functions suggested in [2] but have the same limit values. This property is achieved by seeking a better fictitious reference signal for the purpose of developing greater cost functions while, in [2], a particular choice of fictitious reference signal is used. An example is provided where a weakly cost-detectable cost function leads to faster convergence in the switching algorithm than a cost detectable cost function.