A comparison of optimal and suboptimal auxiliary signal design approaches for robust failure detection

Recently a new approach for multi-model identification and failure detection in the presence of model uncertainty and bounded energy noise over finite time intervals was introduced. This approach involved offline computation of an auxiliary signal and online application of the detection and identification test. The theory and algorithms include optimization over a parameter beta. By considering a modification of the original problem it is possible to avoid this parameter and solve a related but different problem which is more of a standard robust control problem. This modification provides a suboptimal solution of the original problem and would appear to greatly speed up the algorithms. This paper provides the first examination of the effect of ignoring the parameter beta. We provide examples showing that the more usual robust control approach cannot solve some problems that the new approach can. We also provide insight into when the simpler algorithm can be used and what is the cost in doing so